Last updated on 2020-09-13 by Christophe Dutang, Patrice Kiener

For most of the classical distributions, base R provides probability distribution functions (p), density functions (d), quantile functions (q), and random number generation (r). Beyond this basic functionality, many CRAN packages provide additional useful distributions. In particular, multivariate distributions as well as copulas are available in contributed packages.

Ultimate bibles on probability distributions are:

• different volumes of N. L. Johnson, S. Kotz and N. Balakrishnan books, e.g. Continuous Univariate Distributions, Vol. 1,
• Thesaurus of univariate discrete probability distributions by G. Wimmer and G. Altmann.
• Statistical Distributions by M. Evans, N. Hastings, B. Peacock.
• Distributional Analysis with L-moment Statistics using the R Environment for Statistical Computing, Asquith (2011).

The maintainer gratefully acknowledges Achim Zeileis, David Luethi, Tobias Verbeke, Robin Hankin, Mathias Kohl, G. Jay Kerns, Kjetil Halvorsen, William Asquith for their useful comments/suggestions. If you think information is not accurate or not complete, please let me know.

## Base functionality:

• Base R provides probability distribution functions `p`foo`()` density functions `d`foo`()`, quantile functions `q`foo`()`, and random number generation `r`foo`()` where foo indicates the type of distribution: beta (foo = `beta`), binomial `binom`, Cauchy `cauchy`, chi-squared `chisq`, exponential `exp`, Fisher F `f`, gamma `gamma`, geometric `geom`, hypergeometric `hyper`, logistic `logis`, lognormal `lnorm`, negative binomial `nbinom`, normal `norm`, Poisson `pois`, Student t `t`, uniform `unif`, Weibull `weibull`. Following the same naming scheme, but somewhat less standard are the following distributions in base R: probabilities of coincidences (also known as "birthday paradox") `birthday` (only p and q), studentized range distribution `tukey` (only p and q), Wilcoxon signed rank distribution `signrank`, Wilcoxon rank sum distribution `wilcox`.
• Probability generating function: Compounding provides pgf for `xxx` distribution, inverse `xxx` distribution, first derivative of the `xxx` distribution, where `xxx` belongs to binomial, binomial-Poisson, geometric, hypergeometric, hyper-Poisson, Katti type H1/H2, logarithmic, logarithmic-binomial, logarithmic-Poisson, negative binomial, Neyman type A/B/C, Pascal-Poisson, Poisson, Poisson-binomial, Poisson-Lindley, Poisson-Pascal, Polya Aeppli, Thomas, Waring, Yule.

## Discrete univariate distributions:

• Beta-binomial distribution: provided in VGAM, extraDistr, rmutil, emdbook. ZI/ZM beta binomial distributions are implemented in gamlss.dist.
• Beta-geometric distribution: provided in VGAM.
• Binomial (including Bernoulli) distribution: provided in stats. Zero-modified, zero-inflated, truncated versions are provided in gamlss.dist, extraDistr, actuar and in VGAM. LaplacesDemon provides dedicated functions for the Bernoulli distribution. rmutil provides the double binomial and the multiplicative binomial distributions.
 Distribution name Packages Functions Distribution suffix binomial stats d, p, q, r `binom` zero-infl. binomial extraDistr d, p, q, r `zib` zero-infl. binomial VGAM d, p, q, r `zibinom` zero-infl. binomial gamlss.dist d, p, q, r `ZIBI` zero mod. binomial VGAM d, p, q, r `zabinom` zero mod. binomial actuar d, p, q, r `zmbinom` zero mod. binomial gamlss.dist d, p, q, r `ZABI` zero trunc. binomial actuar d, p, q, r `ztbinom` trunc. binomial extraDistr d, p, q, r `tbinom`

• Benford distribution: provided in VGAM and BenfordTests.
• Bernoulli distribution: provided in extraDistr.
• Borel-Tanner distribution: provided in VGAM.
• Complex Pearson distribution: cpd provides the complex biparamtric and triparametric Pearson distribution.
• Delaporte distribution: provided in gamlss.dist and Delaporte.
• Dirac distribution: provided in distr.
• Discrete categorical distribution: provided in LaplacesDemon.
• Discrete exponential distribution: provided in poweRlaw.
• Discrete gamma distribution: provided in extraDistr.
• Discrete inverse Weibull distribution: DiscreteInverseWeibull provides d, p, q, r functions for the inverse Weibull as well as hazard rate function and moments.
• Discrete Laplace distribution: The discrete Laplace distribution is provided in extraDistr (d, p, r). The skew discrete Laplace distribution has two parametrization (DSL and ADSL), both provided in DiscreteLaplace and DSL in disclap. LaplacesDemon also provides the DSL parametrization only.
• Discrete lognormal distribution: provided in poweRlaw.
• Discrete normal distribution: provided in extraDistr.
• Discrete power law distribution: provided in poweRlaw.
• Discrete uniform distribution: can be easily obtained with the functions `sum,cumsum,sample` and is provided in extraDistr.
• Discrete Weibull distribution: provided in DiscreteWeibull: d, p, q, r, m for disc. Weib. type 1, d, p, q, r, m, h for disc. Weib. type 3. extraDistr provides d, p, q, r for Type 1.
• Felix distribution: provided in VGAM.
• gamma count distribution: provided in rmutil.
• Geometric distribution: provided in stats. Zero-modified, zero-inflated, truncated versions are provided in gamlss.dist, actuar and in VGAM. The time-varying geometric is provided in tvgeom.
• Geometric (compound) Poisson distribution (also known Polya-Aeppli distribution): provided in polyaAeppli.
• Generalized binomial distribution: provided in GenBinomApps.
• Generalized Hermite distribution: provided in hermite.
• Hypergeometric distribution: provided in stats. Non-central hypergeometric distribution is provided in MCMCpack (d,r). Extended hypergeometric distribution can be found in BiasedUrn package, which provides not only p, d, q, r functions but also mean, variance, mode functions. Generalized hypergeometric distribution is implemented in SuppDists. Negative hypergeometric distribution is provided in tolerance, extraDistr.
• Lagrangian Poisson distribution: RMKdiscrete provides d, p, q, r functions for the univariate and the bivariate Lagrangian Poisson distribution.
• Lindley's power series distribution: provided in LindleyPowerSeries.
• Logarithmic distribution: This can be found in extraDistr, VGAM, actuar, Distributacalcul and gamlss.dist. Zero-modified and zero-truncated versions is provided in actuar. A fast random generator is available for the logarithmic distribution is implemented in Runuran as well as the 'density' function.
• Poisson distribution: provided in stats and in poweRlaw. Zero-modified, zero-inflated, truncated versions are provided in extraDistr, gamlss.dist, actuar and in VGAM. extraDistr provides the truncated Poisson distribution. LaplacesDemon provides the generalized Poisson distribution. rmutil provides the double Poisson, the multiplicative Poisson and the Power variance function Poisson distributions. poibin and PoissonBinomial provide the Poisson binomial distribution. See the mixture section such as the Poisson-lognormal mixture.
• Poisson-Lindley distribution: provided in tolerance.
• Power law distribution: provided in poweRlaw.
• Mana Clash distribution: provided in RMKdiscrete.
• Negative binomial distribution: provided in stats. Zero-modified, zero-inflated, truncated versions are provided in gamlss.dist, extraDistr, emdbook, actuar and in VGAM. New parametrization of the negative binomial distribution is available in RMKdiscrete.
• Sichel distribution: provided in gamlss.dist.
• Skellam distribution: provided in extraDistr, VGAM and skellam.
• Waring distribution: sampling in degreenet.
• Yule-Simon distribution: provided in VGAM and sampling in degreenet.
• Zeta and Haight's Zeta distribution: provided in VGAM, tolerance.
• Zipf distribution and extensions: d, p, q, r functions of the Zipf and the Zipf-Mandelbrot distributions are provided in tolerance, VGAM. Package zipfR provides tools for distribution of word frequency, such as the Zipf distribution. zipfextR provides three extensions of the Zipf distribution: the Marshall-Olkin Extended Zipf, the Zipf-Poisson Extreme and the Zipf-Poisson Stopped Sum distributions.

## Discrete multivariate distributions:

• Bivariate binomial: d, p functions provided in bivariate.
• Bivariate geometric: d, r functions provided in bivgeom. BivGeo provides the Basu-Dhar bivariate geometric distribution.
• Bivariate Poisson: d, p functions provided in bivariate.
• Bivariate Poisson-lognormal: provided in poilog.
• Bivariate uniform: d, p functions provided in bivariate.
• Hyper Dirichlet distribution: provided in hyper2 package.
• Multinomial distribution: stats, mc2d, extraDistr packages provide d, r functions. r is provided in MultiRNG and compositions. p function is provided by pmultinom.
• Multinomial Dirichlet distribution: functions d, r are provided in MCMCpack, mc2d, dirmult, extraDistr and bayesm. r is provided in MultiRNG.
• Negative multinomial distribution: A bivariate distribution with negative-binomial marginals is available in RMKdiscrete. The multiplicative multinomial distribution is implemented in MM.
• Multivariate Poisson distribution: compositions provides a random generator.
• Multivariate hypergeometric distribution: provided in extraDistr.
• Multivariate Polya distribution: functions d, r of the Dirichlet Multinomial (also known as multivariate Polya) distribution are provided in extraDistr, LaplacesDemon and Compositional.
• Multivariate Ewens distribution: not yet implemented?
• Truncated Stick-Breaking distribution: provided in LaplacesDemon.

## Continuous univariate distributions:

• Arcsine distribution: implemented in package distr.
• Beta distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). extraDistr provides the beta distribution parametrized by the mean and the precision. actuar provides moments and limited expected values. sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central beta distribution for computing d, p, q, r functions. extraDistr provides the four-parameter beta with lower and upper bounds. The generalized beta of the first kind (GB1) (exponentiation of beta 1) is provided in gamlss.dist, mbbefd, actuar. betafunctions provides the four-parameter beta (that is with location and scale parameters), the beta parametrized by the mean and the variance as well as the beta compound beta distribution. The beta prime (or beta of the second kind), which is the distribution of X/(1-X) when X follows a beta distribution of the first kind, is provided in VGAM, extraDistr, LaplacesDemon and mc2d. The zero and one inflated beta distribution can be found in gamlss.dist. The generalized beta of the second kind (GB2) is provided in gamlss.dist, GB2. Several special cases of the generalized beta distribution are also implemented in VGAM, mc2d: Lomax, inverse Lomax, Dagum, Singh-Maddala, Pert distributions. actuar provides the Feller-Pareto distribution as special cases Burr, loglogistic, paralogistic, generalized Pareto, Pareto, see also the Pareto subsection. llogistic provides the log-logistic parametrized by the median.
 Distribution name Packages Functions Distribution suffix Beta (1st kind) stats d, p, q, r `beta` Beta actuar m, mgf, lev `beta` Beta betafunctions d, p, q, r `Beta.4P` Doubly non central beta sadists d, p, q, r `nbeta` 4-param beta extraDistr d, p, q, r `nsbeta` 4-param beta extraDistr d, p, q, r `nsbeta` zero-infl beta gamlss.dist d, p, q, r `BEZI` one-infl beta gamlss.dist d, p, q, r `BEOI` one-infl beta mbbefd d, p, q, r, m, ec `oibeta` GB1 gamlss.dist d, p, q, r `GB1` GB1 mbbefd d, p, q, r, m, ec `gbeta` GB1 actuar d, p, q, r, m, lev `genbeta` one-infl GB1 mbbefd d, p, q, r, m, ec `oigbeta`

 Distribution name Packages Functions Distribution suffix Beta (2nd kind) VGAM d, p, q, r `beta` Beta (2nd kind) extraDistr d, p, q, r `invbeta` Beta (2nd kind) LaplacesDemon d, r `betapr` GB2 VGAM d, p, q, r `genbetaII` GB2 gamlss.dist d, p, q, r `GB2` GB2 GB2 d, p, q, r `gb2` Trans beta 2 actuar d, p, q, r, m, lev `trbeta`

• Benini distribution: provided in VGAM.
• Bezier-Montenegro-Torres distribution: provided in BMT.
• Bhattacharjee (normal+uniform) distribution: provided in package extraDistr.
• Birnbaum-Saunders distribution: provided in package VGAM and extraDistr.
• Bridge distribution: provided in bridgedist, as detailed in Wang and Louis (2003). The distribution of random intercept that allows a marginalized random intercept logistic regression to also be logistic regression.
• Box Cox distribution: gamlss.dist provides the Box-Cox normal, the Box-Cox power exponential and the Box-Cox t distributions. rmutil provides the Box-Cox normal.
• Burr distribution: see Pareto.
• Cardioid distribution: provided in VGAM (d,p,q,r) and CircStats, circular (d,r).
• Carthwrite's Power-of-Cosine distribution: provided in circular (d,r).
• Cauchy distribution: Base R provides the d, p, q, r functions for this distribution (see above). Other implementations are available in lmomco and sgt. The skew Cauchy distribution is provided in sn. LaplacesDemon provides d, p, q, r functions for the Half-Cauchy distribution. The wrapped Cauchy distribution is provided in CircStats.
• Chen distribution: provided in reliaR.
• Chi(-squared or not) distribution: Base R provides the d, p, q, r functions for the chi-squared distribution, both central and non-central (see above). Moments, limited expected values and the moment generating function are provided in actuar. extraDistr provides d, p, q, r functions for inverse chi-squared distribution (standard and scaled). Only d,r functions are available for the inverse chi-squared distribution in package geoR and LaplacesDemon. A fast random generator is available for the Chi distribution is implemented in Runuran as well as the density function. The non-central Chi distribution is not yet implemented. The chi-bar-squared distribution is implemented in emdbook. sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for sums of non central chi-squared raised to powers distribution and sums of log of non central chi-squared for computing d, p, q, r functions.

 Distribution name Packages Functions Distribution suffix Chi-squared stats d, p, q, r `chisq` Chi-squared actuar m, mgf, lev `chisq` Chi-squared Runuran d, r `chisq` Chi-bar-squared emdbook d, p, q, r `chibarsq` Chi Runuran d, r `chi` Inverse Chi-squared geoR d, r `invchisq` Inverse Chi-squared extraDistr d, p, q, r `invchisq` Scaled Inverse Chi-squared extraDistr d, p, q, r `invchisq` Sum of power Chi-squared sadists d, p, q, r `sumchisqpow` Sum of log Chi-squared sadists d, p, q, r `sumlogchisq`

• Circular distribution: uniform circular provided in circular (d,r); Generalized von Mises circular provided in circular (d).
• Consul distribution: see rmutil.
• Continuous binomial distribution: cbinom provides the d/p/q/r functions for a continuous analog to the standard discrete binomial with continuous size parameter and continuous support with x in [0, size + 1].
• Dagum distribution: see beta.
• Davies distribution: The Davies distribution is provided in Davies package.
• (non-central) Dunnett's test distribution: provided in nCDunnett.
• Eta-mu distribution: provided in lmomco. sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central eta distribution for computing d, p, q, r functions.
• Exponential distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). actuar provides additional functions such as the moment generating function, moments and limited expected values. It also has the d, p, q, r for the inverse exponential distribution. The shifted (or two-parameter exponential) and the truncated exponential distributions are implemented in lmomco and tolerance packages with d, p, q, r functions. Exponential Power distribution is also known as General Error Distribution: d, p, q, r functions for the power and the skew power exponential type 1-4 distributions are implemented in gamlss.dist and lmomco. The power exponential distribution is also provided in normalp, rmutil, LaplacesDemon and sgt. The skew power exponential is provided sgt. reliaR provides the generalized exponential, the inverse generalized exponential, the logistic exponential, the Marshall-Olkin Extended Exponential and the exponential extension distributions. A fast random generator is available for the power Exponential distribution is implemented in Runuran as well as the density function.

 Distribution name Packages Functions Distribution suffix Exponential stats d, p, q, r `exp` Exponential actuar m, mgf, lev `exp` Exponential gamlss.dist d, p, q, r `EXP` Exponential poweRlaw d, p, q, r `exp` Inverse exponential actuar d, p, q, r, m, lev `invexp` Shifted exponential lmomco d, p, q, r, lm, tlmr `exp` Shifted exponential tolerance d, p, q, r `2exp` Truncated exponential lmomco d, p, q, r, lm, tlmr `texp` Truncated exponential ReIns d, p, q, r `texp` Power exponential normalp d, p, q, r `normp` Power exponential Runuran d, r `exp` Power exponential rmutil d, r `powexp` Skew power exp. lmomco d, p, q, r, lm, tlmr `aep4` Power and skew power exp. gamlss.dist d, p, q, r `PE, SEP` Generalized and inverse gen. exp. reliaR d, p, q, r `gen.exp, inv.genexp` Logistic, Marshall-Olkin Ext. exp. and exp. ext. reliaR d, p, q, r `logis.exp, moee, exp.ext`

• Externally studentized midrange distribution: Package SMR computes the studentized midrange distribution (d, p, q, r).
• Fisher-Snedecor (or F) distribution: Base R provides the d, p, q, r functions for the F distribution, possibly with a non-central parameter. sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central Fisher distribution (and product of multiple doubly non central Fisher distribution) for computing d, p, q, r functions. flexsurv provides d, p, q, r functions as well as hazard (h) and integrated hazard rate (i) functions for the generalized F distribution. fpow returns the noncentrality parameter of the noncentral F distribution if probability of type I and type II error, degrees of freedom of the numerator and the denominator are given.
• Frechet distribution: provided in VGAM, RTDE, ReIns, extraDistr, distributionsrd and evd. A fast random generator is available for the Frechet distribution is implemented in Runuran as well as the density function. The truncated Frechet distribution is provided in ReIns.
• Friedman's Chi distribution: provided in SuppDists.
• Gamma distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). EnvStats provides d, p, q, r functions of the gamma parametrized by the mean and the coefficient of variation. actuar provides d, p, q, r functions of the inverse, the inverse transformed and the log gamma distributions while ghyp provides those functions for the variance gamma distribution. extraDistr and LaplacesDemon provide the inverse gamma distribution. CaDENCE provides the zero-inflated gamma distribution. VarianceGamma provides d, p, q, r functions for the variance gamma distribution as well as moments (skewness, kurtosis, ...). VGAM, ggamma provide d, p, q, r functions of the log gamma and the generalized gamma distribution. The generalized gamma distribution can also be found in gamlss.dist. reliaR provides the log gamma distribution. See Pearson III for a three-parameter gamma distribution with a location parameter. flexsurv provides d, p, q, r functions as well as hazard (h) and integrated hazard rate (i) functions for the generalized gamma distribution. coga provides d, p, r functions for a sum of independent but not identically distributed gamma distributions. MCMCpack provides d, r functions of the Inverse Gamma. rmutil provides the generalized Gamma. distTails provides the full-tail gamma distribution

 Distribution name Packages Functions Distribution suffix Gamma stats d, p, q, r `gamma` Gamma actuar m, mgf, lev `gamma` Gamma EnvStats d, p, q, r `gammaAlt` zero-inflated Gamma CaDENCE d, p, q, r `bgamma` Inverse gamma actuar d, p, q, r, m, lev, mgf `invgamma` Inverse gamma extraDistr d, p, q, r `invgamma` Inverse gamma LaplacesDemon d, r `invgamma` Inverse gamma MCMCpack d, r `invgamma` Log-gamma actuar d, p, q, r, m, lev `lgamma` Log-gamma VGAM d, p, q, r `lgamma` Variance gamma ghyp d, p, q, r `VG` Variance gamma VarianceGamma d, p, q, r, m `vg` Generalized gamma flexsurv d, p, q, r, h, i `gengamma` Generalized gamma gamlss.dist d, p, q, r `GG` Generalized gamma VGAM d, p, q, r `gengamma.stacy` Generalized gamma rmutil d, p, q, r `ggamma` Generalized gamma ggamma d, p, q, r `ggamma` convolution of gamma coga d, p, r `coga` Full-taill gamma distTails d, p, r `dFTG`

• Gaussian (or normal) distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). actuar provides the moment generating function and moments. The truncnorm package provides d, p, q, r functions for the truncated gaussian distribution as well as functions for the first two moments. mvrtn provides random variates for left/right truncated normal distributions. EnvStats provides d, p, q, r functions for the truncated normal distribution and the zero-modified distribution. extraDistr provides the truncated normal. LaplacesDemon provides d, p, q, r functions for the Half-normal distribution. The wrapped normal distribution is provided in CircStats. lmomco implements the generalized normal distribution. The Exponentially modified Gaussian is available in emg, gamlss.dist and retimes. sn implements the skew normal distribution. greybox implements the folded normal distribution. VGAM implements the folded and the skewed normal distribution, and csn provides d, r functions for the closed skew normal distribution. CompQuadForm provides the distribution function of quadratic forms in normal variates. NormalGamma provides the density of the sum of a gaussian and a gamma random variables. NormalLaplace provides d, p, q, r functions for the sum of a normal and a Laplace random variables, while LaplacesDemon provides d, r function of the sum of a normal and a Laplace random variables.
 Distribution name Packages Functions Distribution suffix Normal stats d, p, q, r `norm` Normal actuar m, mgf `norm` Truncated normal truncnorm d, p, q, r, m `truncnorm` Truncated normal mvrtn r, m `tn` Truncated normal EnvStats d, p, q, r `normTrunc` Truncated normal extraDistr d, p, q, r `tnorm` Generalized normal lmomco d, p, q, r `gno` Zero modified Gaussian EnvStats d, p, q, r `zmnorm` Exponentially modified Gaussian emg d, p, q, r `emg` Exponentially modified Gaussian gamlss.dist d, p, q, r `exGAUSS` Exponentially modified Gaussian retimes d, p, q, r `exgauss` Folded and skew normal gamlss.dist d, p, q, r `SN1, SN2` Folded normal greybox d, p, q, r `fnorm` Closed skew normal csn d, p, q, r `csn` Skew normal sn d, p, q, r `sn`

• General error distribution (also known as exponential power distribution): see exponential item.
• Generalized extreme value distribution: d, p, q provided in lmomco; d, p, q, r, provided in VGAM, evd, evir, FAdist, extraDistr, EnvStats, TLMoments, rmutil, QRM, ROOPSD and fExtremes. evdbayes, revdbayes provide d,p,q,r functions of the GEV distribution in a Bayesian setting.
• Gompertz distribution: provided in reliaR, flexsurv, extraDistr. flexsurv also provides hazard (h) and integrated hazard rate (i) functions. The shifted Gompertz distribution is implemented in extraDistr.
• Govindarajulu distribution: provided in lmomco.
• Gumbel distribution: provided in packages lmomco, VGAM, gamlss.dist, FAdist, extraDistr, reliaR, QRM, TLMoments, dgumbel, EnvStats and evd. actuar provides the raw moments and the moment generating function (mgf) in addition to the d, p, q, r functions. A fast random generator is available for the Gumbel distribution is implemented in Runuran as well as the density function. The reverse Gumbel distribution is implemented in lmomco and gamlss.dist.
• Hjorth distribution: provided in rmutil.
• Huber distribution: Huber's least favourable distribution provided in package smoothmest (d, r), and in VGAM, marg, extraDistr (d, p, q, r).
• (generalized) G-and-K, G-and-H distributions: gk provides d, p, q, r functions for the g-and-k and generalized g-and-h distributions which are nonlinear transforms of the Gaussian variables.
• (generalized) Hyperbolic distribution: fBasics, ghyp, GeneralizedHyperbolic and HyperbolicDist packages provide d, p, q, r functions for the generalized hyperbolic distribution. QRM provides d, r functions for the generalized hyperbolic distribution. SkewHyperbolic provides the skewed Hyperbolic Student t-Distribution. fBasics also implements the standardized generalized Hyperbolic distribution. A fast random generator is available for the hyperbolic distribution is implemented in Runuran as well as the density function.
• Hyperbolic sine distribution and extension: gamlss.dist provides the sinh and the asinh distributions. Generalized Power Hyperbolic sine distributions are provided in FatTailsR.
• Inverse Gaussian (also known Wald) distribution: d, p, q, and r functions of the inverse Gaussian are provided in statmod, extraDistr, SuppDists, rmutil and STAR. LaplacesDemon provides d, r functions for the inverse Gaussian distribution. actuar provides d, p, q, r, m, lev, mgf functions for the Inverse Gaussian distribution. SuppDists also provides a function that returns moments, skewness, kurtosis. fBasics the normal inverse Gaussian and standardized normal inverse Gaussian distributions. The generalized inverse gaussian distribution can be found in gamlss.dist, QRM, rmutil, and HyperbolicDist. A random generator is available for the (generalized) Inverse Gaussian distribution is implemented in Runuran as well as the density function. GIGrvg generates random variables from the generalized inverse Gaussian distribution. frmqa computes p function of the generalized inverse Gaussian distribution.
• Johnson distribution: provided in SuppDists. ForestFit provides d, p of Johnson SB distribution.
• Jones and Pewsey distribution: provided in circular (d).
• K-prime distribution: sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for K-prime distribution for computing d, p, q, r functions.
• Kappa distribution: A 4-parameter Kappa distribution is provided in lmomco and FAdist.
• Kappa-mu distribution: provided in lmomco.
• Kato-Jones distribution: provided in circular (d, r).
• Kendall's tau distribution: provided in SuppDists.
• Kiener distribution: a family of distributions generalizing hyperbolic sine distributions (see hyperbolic sine section), d, p, q, r, m provided in FatTailsR.
• Kolmogorov distribution: p function provided in kolmim.
• Kruskal Wallis distribution: provided in SuppDists.
• Kumaraswamy distribution: provided in packages VGAM, extraDistr and lmomco. elfDistr provides the Kumaraswamy Complementary Weibull Geometric Probability Distribution.
• (Tukey) Lambda distribution and its extensions: The generalized Lambda distribution (GLD) is well known for its wide range of shapes. The original Tukey Lambda distribution can be obtained as a special case of the generalized Lambda distribution. There exists different parametrization of GLD in the literature: RS (Ramberg-Schmeiser or tail-index param), FMKL (Freimer-Mudholkar-Kollia-Lin), FM5 (Five-parameter version of FKML by Gilchrist), GPD (gen. Pareto dist.) and AS (Asymmetry-steepness). The following packages implement such distributions (with d, p, q, r functions): gld (RS, FKML, FM5, GPD), Davies (RS), gb (RS), lmomco (FMKL), extraDistr (original Tukey). ecd provides the elliptic lambda distribution and its use for financial pricing.
• Tukey's H distribution: provided as a special case of Lambert W x F distribution.
• Lambda-prime distribution: sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for K-prime distribution for computing d, p, q, r functions.
• Lambert W x F distribution: LambertW package provides d, p, q, r functions as well as the first 4 central moments and a qqplot.
• Laplace (also called double exponential distribution) and asymmetric Laplace distribution: provided in distr, lmomco, LaplacesDemon, VGAM, sgt, extraDistr, greybox, rmutil and HyperbolicDist packages. LaplacesDemon provides the Laplace distribution parametrized by the precision parameter as well as the skew Laplace distribution. Asymetric Laplace distribution is implemented in ald, greybox. A fast random generator is available for the Laplace distribution is implemented in Runuran as well as the density function. smoothmest implements the density and the random generator. The skew Laplace distribution is available in sgt. LaplacesDemon provides the log-Laplace distribution.
• LASSO distribution: provided in LaplacesDemon.
• Lévy distribution: provided in rmutil.
• Lindley distribution: provided in VGAM and gambin.
• Linear failure rate distribution: provided in reliaR.
• Loglog distribution: provided in reliaR
• Lomax distribution: see beta.
• Logistic distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). actuar and VGAM provide d, p, q, r functions for the log logistic (also called Fisk), the paralogistic and the inverse paralogistic distributions. FAdist the log-logistic distribution with two and three parameters. The generalized logistic distribution (Type I, also known as skew-logistic distribution) is provided in lmomco, sld, rmutil, SCI and glogis.
 Distribution name Packages Functions Distribution suffix Logistic stats d, p, q, r `logis` Logistic actuar m, mgf `logis` Log logistic actuar d, p, q, r, m, lev `llogis` Log logistic VGAM d, p, q, r `fisk` Log logistic FAdist d, p, q, r `llog, llog3` Paralogistic actuar d, p, q, r, m, lev `paralogis` Paralogistic VGAM d, p, q, r `paralogistic` Inv. paralogistic actuar d, p, q, r, m, lev `invparalogis` Inv. paralogistic VGAM d, p, q, r `inv.paralogistic` Generalized logistic glogis d, p, q, r `glogis` Generalized logistic SCI d, p, q `genlog` Generalized logistic lmomco d, p, q, r `glo` Generalized logistic sld d, p, q, r `sl` Generalized logistic rmutil d, p, q, r `glogis`

• Logit-normal distribution: provided in logitnorm.
• Log-normal distribution and its extensions: The log normal distribution is implemented in Base R (see above) and poweRlaw. The log normal distribution parametrized by its mean and its coefficient of variation is also provided in EnvStats. LaplacesDemon provides the lognormal parametrized by the precision parameter. The truncated lognormal distribution is provided in EnvStats with two possible parametrizations as well as in ReIns. The 3-parameter lognormal distribution is available in lmomco, greybox, TLMoments, EnvStats and FAdist. The package loglognorm implements d, p, q, r functions for the double lognormal distribution, as well as the raw moment, the expected value and the variance functions. EnvStats provides d, p, q, r functions for the zero-modified lognormal distribution with two possible parametrizations. distributionsrd provides the double Pareto-lognormal distribution, the left Pareto-lognormal distribution, the truncated lognormal distribution.
• Makeham distribution: provided in VGAM and
• Maxwell distribution: provided in VGAM.
• Minimax distribution: provided in minimax.
• Mittag-Leffler distribution: d, p, q, r functions provided in MittagLeffleR.
• Nakagami distribution: provided in VGAM.
• Pareto distribution: d, p, q, r functions are implemented in VGAM for the Pareto distribution type IV (which includes Burr's distribution, Pareto type III, Pareto type II (also called the lomax distribution) and Pareto type I) and the (upper/lower) truncated Pareto distribution. In an actuarial context, actuar provides d, p, q, r functions as well as moments and limited expected values for the Pareto I and II, the inverse Pareto, the 'generalized pareto' distributions, the Burr and the inverse Burr distributions, all special cases of the transformed beta II distribution. A fast random generator for the Burr and the Pareto II distribution is implemented in Runuran as well as the density. EnvStats and LaplacesDemon provides d, p, q, r functions for Pareto I distribution. extremefit provides the Burr, the Pareto II, mixture of Pareto I distributions and a composite distribution of two Pareto I distributions. lmomco, evd, fExtremes, extraDistr, QRM, Renext, revdbayes, FAdist, LaplacesDemon, TLMoments qrmtools and evir packages implement the Generalized Pareto Distribution (from Extreme Value Theory), which is depending the shape parameter's value a Pareto II distribution, a shifted exponential distribution or a generalized beta I distribution. ParetoPosStable implements the Pareto positive stable distribution. The extended Pareto distribution is implemented in RTDE and the shifted truncated (to unit interval) Pareto is implemented in mbbefd. ReIns provides Burr, extended Pareto, generalized Pareto, Pareto 1 distributions and their truncated version. CaDENCE provides the Pareto 2 and the zero-inflated Pareto 2 distribution.
 Distribution name Packages Functions Distribution suffix Pareto I VGAM d, p, q, r `paretoI` Pareto I actuar d, p, q, r, m, lev `pareto1` Pareto I EnvStats d, p, q, r `pareto` Pareto I extraDistr d, p, q, r `pareto` Pareto I ReIns d, p, q, r `pareto` Pareto I LaplacesDemon d, p, q, r `pareto` Pareto I distributionsrd d, p, q, r `pareto` Trunc. Pareto I ReIns d, p, q, r `tpareto` Pareto II VGAM d, p, q, r `paretoII` Pareto II actuar d, p, q, r, m, lev `pareto, pareto2` Pareto II Runuran d, r `pareto` Pareto II extraDistr d, p, q, h `lomax` Pareto II extremefit d, p, q, h `pareto` Pareto II Renext d, p, q, r `lomax` Pareto II rmutil d, p, q, r `pareto` Pareto II CaDENCE d, p, q, r `pareto2` zero-inflated Pareto II CaDENCE d, p, q, r `bpareto2` Pareto III VGAM d, p, q, r `paretoIII` Pareto III actuar d, p, q, r `pareto3` Pareto IV VGAM d, p, q, r `paretoIV` Pareto IV actuar d, p, q, r `pareto4` Inverse Pareto actuar d, p, q, r, m, lev `invpareto` Inverse Pareto distributionsrd d, p, q, r, m, lev `invpareto` Extended Pareto RTDE d, p, q, r `EPD` Extended Pareto ReIns d, p, q, r `epd` Shift. trunc. Pareto mbbefd d, p, q, r, m, ec `stpareto` Gen. Pareto (actuarial) actuar d, p, q, r, m, lev `genpareto` Gen. Pareto (EVT) lmomco d, p, q, r `gpa` Gen. Pareto (EVT) evd d, p, q, r `gpd` Gen. Pareto (EVT) fExtremes d, p, q, r `gpd` Gen. Pareto (EVT) evir d, p, q, r `gpd` Gen. Pareto (EVT) extraDistr d, p, q, r `gpd` Gen. Pareto (EVT) QRM d, p, q, r `GPD` Gen. Pareto (EVT) ReIns d, p, q, r `gpd` Gen. Pareto (EVT) LaplacesDemon d, r `gpd` Gen. Pareto (EVT) TLMoments d, p, q, r `gpd` Trunc. Gen. Pareto (EVT) ReIns d, p, q, r `tgpd` Gen. Pareto (EVT) revdbayes d, p, q, r `gp` Gen. Pareto (EVT) Renext d, p, q, r `GPD` Gen. Pareto (EVT) qrmtools d, p, q, r `GPD` Gen. Pareto (EVT) ROOPSD d, p, q, r `gpd` Feller-Pareto actuar d, p, q, r, m, lev `fpareto` Burr actuar d, p, q, r, m, lev `burr` Burr extremefit d, p, q, r `burr` Burr ReIns d, p, q, r `burr` Burr rmutil d, p, q, r `burr` Trunc. Burr ReIns d, p, q, r `tburr` Inverse Burr actuar d, p, q, r, m, lev `invburr`

• Pearson's distribution: Pearson type III available in lmomco and FAdist. A log-Pearson type III distribution is also available in FAdist. PearsonDS provides the d, p, q, r functions as well as the first four moments for the Pearson distributions: types I, II, III, IV, V, VI, VII.
• Pearson's Rho distribution: provided in SuppDists.
• Perks distribution: provided in VGAM.
• Planck's distribution: a random generator is available in Runuran.
• Phase-type distribution: provided in actuar
• Poisson subordinated distributions: provided in LIHNPSD (d, p, q, r, m functions).
• Power distribution: reliaR and poweRlaw implement the exponential power distribution. Two-sided power distribution provided in rmutil.
• Proportion distribution: this is the distribution for the difference between two independent beta distributions. d, p, q, r functions in tolerance.
• Rayleigh distribution: provided in packages VGAM, extraDistr and lmomco. Generalized and logistic Rayleigh distributions are available in reliaR.
• Response time distribution: rtdists provides d, p, q, r functions for the (Ratcliff) diffusion distribution and for the linear ballistic accumulator (LBA) with different underlying drift-distributions (Normal, Gamma, Frechet, and log-normal).
• Rice distribution: provided in VGAM and lmomco.
• Simplex distribution: provided in rmutil.
• Slash distribution: provided in lmomco, extraDistr and VGAM.
• Spearman's Rho distribution: provided in SuppDists.
• Stable distribution: d, p, q, r functions are available in fBasics and stabledist, the functions use the approach of J.P. Nolan for general stable distributions. MixedTS provides mixed tempered stable distribution (d, p, q, r). FMStable provides (d, p, q) the extremal or maximally skew stable and the finite moment log stable distributions.
• Student distribution and its extensions: Base R provides the d, p, q, r functions for Student and non central Student distribution (see above). extraDistr and LaplacesDemon provides the Student distribution with location and scale parameters. LaplacesDemon provides d, p, q, r functions for the Half-Student distribution. sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central Student distribution for computing d, p, q, r functions. The skewed Student distribution is provided in skewt, sn and gamlss.dist packages. The generalized skew distribution is provided in sgt. d, p, q, r functions for the generalized t-distribution can be found in gamlss.dist. fBasics provides d, p, q, r functions for the skew and the generalized hyperbolic t-distribution. The L-moments of the Student t (3-parameter) are provided in lmomco.
 Distribution name Packages Functions Distribution suffix Student stats d, p, q, r `t` Student with loc. and scal. extraDistr d, p, q, r `lst` Student with loc. and scal. LaplacesDemon d, p, q, r `st` Doubly non central St. sadists d, p, q, r `dnt` Skew Student skewt d, p, q, r `skt` Skew Student sn d, p, q, r `st` Skew St. Type 1-5 gamlss.dist d, p, q, r `ST1, ST2, ST3, ST4, ST5` Gen. Student gamlss.dist d, p, q, r `GT` Gen. Hyp. Student fBasics d, p, q, r `ght` Skew Gen. Student sgt d, p, q, r `sgt`

• Triangle/trapezoidal distribution: packages triangle, extraDistr, mc2d, EnvStats and VGAM provide d, p, q, r functions for the triangle or triangular distribution, while the package trapezoid provides d, p, q, r functions for the Generalized Trapezoidal Distribution. CircStats, circular provide d, r functions for triangular distribution. A fast random generator is available for the triangle distribution is implemented in Runuran as well as the density function.
• Tsallis or q-Exponential distribution: tsallisqexp provides d, p, q, r functions for two parametrizations of the Tsallis distribution and also implements a left-censored version.
• Tweedie distribution: the Tweedie distribution is implemented in package tweedie. Let us note that the Tweedie distribution is not necessarily continuous, a special case of it is the Poisson distribution.
• Uniform distribution: d, p, q, r functions are of course provided in R. See section RNG for random number generation topics. HI generates uniformly random points on a bounded convex set, in particular the unit ball. KScorrect provides d, p, q, r functions for the log-uniform distribution.
• Upsilon distribution: sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for Upsilon distribution for computing d, p, q, r functions.
• von Mises distribution: The CircStats package provides d, p, r functions; the circular package provides d, p, q, r functions.
• Wakeby distribution: A 5-parameter Wakeby is provided in lmomco.
• Weibull distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). The inverse Weibull is provided in actuar package and also the moments and the limited expected value for both the raw and the inverse Weibull distribution. FAdist implements the three-parameter Weibull distribution, while reliaR implements the exponential Weibull, the flexible Weibull, the generalized power weibull, the Marshall-Olkin Extended Weibull and the Weibull extension distributions. Furthermore, lmomco implements the Weibull distribution while evd implements the reverse Weibull distribution. The reverse generalized extreme value distribution are provided in gamlss.dist (d, p, q, r) and the shifted left truncated Weibull distribution is provided in Renext. The right truncated Weibull is provided in ReIns. The generalized Weibull is provided in rmutil. The tail Weibull is provided in distTails. CaDENCE provides the zero-inflated Weibull distribution.

## Continuous multivariate distributions:

• Bivariate normal: d, p functions provided in bivariate.
• Bivariate Pareto: Bivariate.Pareto provides a random generator for the bivariate Pareto distribution.
• Bivariate uniform: d, p functions provided in bivariate.
• Multivariate beta distribution: NonNorMvtDist provides d, p, q, r, s functions for inverted beta distribution.
• Multivariate Burr distribution: NonNorMvtDist provides d, p, q, r, s functions.
• Multivariate Cauchy distribution: sn provide d, p, r functions for the multivariate skew Cauchy distribution, while LaplacesDemon provides d, r functions for the multivariate Cauchy distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega.
• Cook-Johnson’s Multivariate Uniform Distribution: NonNorMvtDist provides d, p, q, r, s functions.
• Multivariate Dirichlet distribution: Compositional, LaplacesDemon, MCMCpack packages provide d, r functions as well as a fitting function for Compositional. compositions, bayesm provide r function. bivariate provides d function for the trivariate Dirichlet.
• Multivariate exponential distribution: while LaplacesDemon provides d, r functions for the multivariate power exponential distribution parametrized either by sigma, or by the Cholesky decomposition of sigma.
• Multivariate F distribution: NonNorMvtDist provides d, p, q, r, s functions.
• Multivariate Gaussian (or normal) distribution: The multivariate Gaussian distribution is provided in the packages mvtnorm (d, p, r), mnormt (d, p, r), mniw (d, r), Compositional (r), compositions (r). pbv provides d, p functions for bivariate normal distributions. mvprpb computes the orthant probability of the multivariate Gaussian distribution. symmoments computes central and non-central moments of the multivariate Gaussian distribution. LaplacesDemon provides d, r functions for the multivariate normal distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega. Futhermore, the multivariate truncated normal is implemented in TruncatedNormal for d, p, r functions; tmvtnorm for p, q, r, m(oments) functions; tmvmixnorm for a fast RNG. sparseMVN implements very fast algorithms to compute the density and generate random variates of a multivariate normal distribution for which the covariance matrix or precision matrix is sparse. cmvnorm implements the complex multivariate normal distribution (d, r). Finally, condMVNorm implements d, p, r functions for the conditional multivariate normal distribution. Furthermore, sn besides providing facilities for their distribution functions, sn allows the creation of S4 objects which encapsulate these distributions and provide facilities for plotting, summary, marginalization, conditioning, affine transformations of these S4 objects. mnormpow computes the expected product of the components of a multivariate Gaussian vector. Compositional provides random generator for the multivariate normal distribution on the simplex and multivariate skew normal distribution on the simplex. A random generator of the multivariate normal is provided in MultiRNG.
• Multivariate generalized hyperbolic distribution: QRM provides d, r functions of the standard and the symmetric multivariate generalized hyperbolic distribution. ghyp provides d, p, r functions of the standard multivariate generalized hyperbolic distribution.
• Multivariate generalized extreme value distribution: Both bivariate and multivariate Extreme Value distributions as well as order/maxima/minima distributions are implemented in evd (d, p, r).
• Multivariate Laplace distribution: LaplacesDemon provides d, r functions for the multivariate Laplace distribution parametrized either by sigma, or by the Cholesky decomposition of sigma. r is provided in MultiRNG.
• Multivariate logistic distribution: VGAM package implements the bivariate logistic distribution, while NonNorMvtDist implements the multivariate logistic distribution.
• Multivariate lognormal distribution: compositions provides r function.
• Multivariate Pareto distribution: mgpd provides the density for the multivariate generalized Pareto distribution of type II, while evd provides the density for type I. NonNorMvtDist provides d, p, q, r, s functions for multivariate Lomax (type II) distributions and its generalized version. NonNorMvtDist provides d, p, q, r, s functions for Mardia's Multivariate Pareto Type I Distribution
• Multivariate Stable distribution: not yet implemented?
• Multivariate Student distribution: The multivariate Student distribution is provided in the packages mvtnorm (d, r), mnormt (d, p, r), Compositional (r), tmvmixnorm (r), QRM (d, r), bayesm (r). The multivariate truncated student is implemented in TTmoment for r (sampling) and moments (m); TruncatedNormal for d, p, r functions; tmvtnorm for d, p, q, r functions. sn provides d, p, r functions for the multivariate skew t distribution. LaplacesDemon provides d, r functions for the multivariate Student distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega. Random generator r is provided in MultiRNG. A special case of a bivariate noncentral t-distribution called Owen distribution is provided in OwenQ.
• Multivariate Uniform distribution: r is provided in MultiRNG. compositions provides a random generator on the simplex.

## Mixed-type distributions:

• Maxwell-Boltzmann-Bose-Einstein-Fermi-Dirac (MBBEFD) distribution : provided in mbbefd.
• Mixed ordinal and normal distribution: provided in OrdNor.
• One-inflated distributions: a generic distribution as well as special cases (OI-beta, OI-uniform, OI-GB1, OI-Pareto) are provided in mbbefd. The zero and one inflated beta distribution can be found in gamlss.dist.
• Zero-modified distributions: EnvStats provides the zero-modified normal distribution and the zero-modified lognormal distribution.

## Mixture of probability laws:

• Bernoulli-dist mixture: d, p, q, r functions for Bernoulli-exponential, Bernoulli-Gamma, Bernoulli-lognormal, Bernoulli-Weibull distributions are provided in qmap.
• Cauchy-polynomial quantile mixture: d, p, q, r functions are provided in Lmoments.
• Chi-square mixture: d, p, q, r functions are provided in emdbook.
• Gaussian mixture: Functions d, r are provided in mixtools, bmixture package when dealing with finite mixture models. nor1mix, extraDistr, mclust, LaplacesDemon, KScorrect provides d, p, r functions for Gaussian mixture. EnvStats provides d, p, q, r functions for mixture of two normal distributions. bayesm provides d function for the mixture of multivariate normals.
• Gamma Poisson: provided in extraDistr.
• Gamma mixture: Ga GSM package provides d, p, r, bmixture provides d, r, evmix provides d, p, q, r.
• Generic mixtures: there is an implementation via S4-class UnivarMixingDistribution in package distr. gendist provides d, p, q, r functions for two-distribution mixture models working with any distribution defined by its d, p, q, r functions.
• Horseshoe distribution: provided in LaplacesDemon.
• Laplace mixture distribution: provided in LaplacesDemon.
• Log normal mixture: d, p, q, r functions are provided in EnvStats with two possible parametrizations.
• Normal-polynomial quantile mixture: d, p, q, r functions are provided in Lmoments.
• Pareto distribution: extremefit implements the mixture of two Pareto I distributions.
• Poisson beta distribution: provided in scModels.
• Poisson Binomial distribution: poibin implements the Poisson Binomial distribution.
• Poisson lognormal distribution: poilog implements the Poisson lognormal distribution.
• Poisson mixture: provided in extraDistr.
• Poisson-Tweedie exponential family models: provided in poistweedie.
• Student mixture: The AdMit package provides d, r functions for Student mixtures in the context of Adaptive Mixture of Student-t distributions. MitISEM, bmixture package also provide d, r functions for mixture of Student-t distributions.
• von Mises Fisher (or Langevin) mixture: The movMF and CircStats packages provide d, r functions for finite von Mises Fisher mixtures.

## Compound, composite, discretized, exponentiated and transformation of distributions:

• Absolute value or half distribution: Half-Cauchy, half normal and half-student are implemented both in extraDistr and in LaplacesDemon.
• Composite distribution also known as spliced distribution: Composite lognormal distributions provided in CompLognormal. Split-normal (also known as the two-piece normal distribution) not yet implemented. Split-student provided in package dng. evmix provides d, p, q, r of the following composite distributions: gamma-GPD, lognormal GPD, normal-GPD, Weibull-GPD as well as bulk models such as GPD-normal-GPD distribution. gendist provides d, p, q, r functions for composite models working with any distribution defined by its d, p, q, r functions.
• Compound distribution: d, p, q, r, m functions are implemented by Compounding where the parent distribution is any continuous distribution and the compound distribution is any distribution among the list: binomial, binomial-Poisson, geometric, hypergeometric, hyper-Poisson, Katti type H1/H2, logarithmic, logarithmic-binomial, logarithmic-Poisson, negative binomial, Neyman type A/B/C, Pascal-Poisson, Poisson, Poisson-binomial, Poisson-Lindley, Poisson-Pascal, Polya Aeppli, Thomas, Waring, Yule. kdist provides d, p, q, r functions of the K distribution.
• Discretized distribution: distcrete allows discretised versions of continuous distribution by mapping continuous values to an underlying discrete grid, based on a (uniform) frequency of discretisation, a valid discretisation point, and an integration range.
• Quantile-based asymmetric (QBA) family of distributions: QBAsyDist provides d, p, q, r functions for QBA version of exponential power, Laplace, logistic, normal, Student, generalized exponential distributions.
• Transformed distribution: Newdistns provides G-transformed distributions for a selected number of distributions which includes Marshall Olkin G distribution, exponentiated G distribution, beta G distribution, gamma G distribution, Kumaraswamy G distribution, generalized beta G distribution, beta extended G distribution, gamma G distribution, gamma uniform G distribution, beta exponential G distribution, Weibull G distribution, log gamma G1/G2 distribution, exponentiated generalized G distribution, exponentiated Kumaraswamy G distributions, geometric exponential Poisson G distribution, truncated-exponential skew-symmetric G distribution, modified beta G distribution, and exponentiated exponential Poisson G distribution. MPS provides also G-transformed distributions, such as beta exponential G distribution, beta G distribution, exponentiated exponential Poisson G distribution, exponentiated G distribution, exponentiated generalized G distribution, exponentiated Kumaraswamy G distribution, gamma uniform G distribution, gamma uniform type I/II G distribution, generalized beta G distribution, geometric exponential Poisson G distribution, gamma-X family of modified beta exponential G distribution, exponentiated exponential Poisson G distribution, gamma-X generated of log-logistic-X familiy of G distribution, Kumaraswamy G distribution, log gamma G type I/II distribution, modified beta G distribution, Marshall-Olkin Kumaraswamy G distribution, odd log-logistic G distribution, truncated-exponential skew-symmetric G distribution, T-X{log-logistic}G distribution, Weibull G distribution. gendist provides d, p, q, r functions for composite models, folded models, skewed symmetric models and arctan models working with any distribution defined by its d, p, q, r functions.
• Truncated distribution: A generic code snippet is available in the JSS. This code is now available in two packages: truncdist is a dedicated package providing d, p, q, r, m(oments) functions for a univariate truncated distribution given a user-supplied distribution; LaplacesDemon provides a generic function in a Bayesian environment.
• Wrapped G distribution: Wrapped provides d, p, q, r functions for a large family of distributions.

## Moments, skewness, kurtosis and etc:

• Empirical mean, standard deviation and variance: base R provides `mean()`, `sd()`, `var()` functions to compute the mean, standard deviation and variance, respectively.
• Empirical skewness: available in agricolae, e1071, GLDEX, HyperbolicDist, modeest, moments, s20x, fromo, DistributionUtils, EnvStats, parameters packages.
• Empirical kurtosis: available in agricolae, DistributionUtils, e1071, EnvStats, GLDEX, HyperbolicDist, fromo, moments, parameters packages. The raw or centered moments are provided in e1071, moments.
• Empirical L-moments: L-moments are available in lmom, lmomco, Lmoments, GLDEX, EnvStats, trimmed L-moments are available in lmomco, TLMoments and Lmoments, right-censored L-moments are available in lmomco, and cumulants in GLDEX. TLMoments provides a function to convert them to some distribution parameters.
• Empirical probability weighted moments: Probability weighted moments are available in EnvStats and fromo.
• Empirical cumulants: fromo provides centered and standardized cumulants.
• Mode estimation: Package modeest provides mode estimation for various distributions.
• Order statistics: Distribution function of the jth order statistic can be obtained with base R functions. ORDER2PARENT transforms distribution function of order statistics to its parent distribution function.
• Empirical characteristic function: empichar evaluates the empirical characteristic function of univariate and multivariate samples.
• Theoretical moments:
• common distributions: The actuar package implements raw moments, limited expected values and moment generating function for base R distributions. lmomco provides L-moments (L), trimmed L-moments (TL), and right-censored [RC] for the following distributions: Asymmetric Exponential Power (L), Cauchy (TL), Eta-Mu (L), Exponential (L), Gamma (L), Generalized Extreme Value (L), Generalized Lambda (L and TL), Generalized Logistic (L), Generalized Normal (L), Generalized Pareto (L[RC] and TL), Govindarajulu (L), Gumbel (L), Kappa (L), Kappa-Mu (L), Kumaraswamy (L), Laplace (L), Normal (L), 3-parameter log-Normal (L), Pearson Type III (L), Rayleigh (L), Reverse Gumbel (L[RC]), Rice/Rician (L), Slash (TL), 3-parameter Student T (L), Truncated Exponential (L), Wakeby (L), and Weibull (L). Multivariate L-moments (L-comoments).
• hyperbolic distributions: HyperbolicDist provides the mean, variance, skewness, kurtosis, mode, raw and centered moments for the hyperbolic, the generalized hyperbolic and the generalized inverse Gaussian distributions.
• Lambda distribution: GLDEX also provides the mean, variance, skewness, kurtosis of generalized Lambda distribution.
• Normal distribution: mvrtn provides mean, variance for left/right truncated normal distributions.
• multivariate distributions: MomTrunc provides mean vector, covariance matrices and raw moments for truncated or folded of the following multivariate distributions: normal, skew normal, extended skew normal and student.

## Random matrices:

• Huang-Wan distribution: provided in LaplacesDemon.
• Inverse matrix gamma distribution: provided in LaplacesDemon.
• Inverse Wishart distribution: LaplacesDemon provides inverse Wishart distribution parametrized either by Sigma or by its Cholesky decomposition. LaplacesDemon provides the scaled inverse Wishart distribution. MCMCpack and mniw provides the inverse Wishart distribution.
• Marcenko-Pastur distribution: provided in RMTstat, MCMCpack and bayesm.
• Matrix gamma distribution: provided in LaplacesDemon.
• Matrix normal distribution: MBSP (r) provides a random generator using a Cholesky decomposition; matrixsampling (r) provides a random generator using a spectral decomposition; LaplacesDemon and mniw (d, r); matrixNormal (d, p, r) collects these forms in one place and allows users to be flexible in simulating random variates (Cholesky, spectral, SVD).
• Matrix student distribution: provided in mniw.
• Normal Inverse Wishart distribution: provided in LaplacesDemon, mniw.
• Normal Wishart distribution: provided in LaplacesDemon.
• Tracy-Widom distribution: provided in RMTstat, MCMCpack and bayesm: supported beta values are 1 (Gaussian Orthogonal Ensemble), 2 (Gaussian Unitary Ensemble), and 4 (Gaussian Symplectic Ensemble).
• Sparse matrix: spam provides functionalities to draw random numbers from a user-supplied RNG (e.g. `rexp`) or from a multivariate normal distribution for large sparse matrices: typically for sparse covariance matrices.
• Spiked Wishart Maximum Eigenvalue Distribution: provided in RMTstat, MCMCpack and bayesm.
• Wishart distributions: Base R provides the r function for the Wishart distribution. MCMCpack, RMTstat, bayesm, mniw provides d, r functions, bayesm provides r function. LaplacesDemon provides Wishart distribution parametrized either by Sigma or by its Cholesky decomposition.
• White Wishart Maximum Eigenvalue Distribution: provided in RMTstat, MCMCpack and bayesm.
• Yang-Berger distribution: provided in LaplacesDemon.
• Zellner distribution: provided in LaplacesDemon.

## Copulas:

• Unified approaches: The packages fCopulae, copula, and copBasic provide a lot of general functionality for copulas. Although lacking support for many existing copulas themselves, copBasic is primarily oriented around utility functions for the general mathematics of copulas as described in the well known introduction to copulas by Nelsen.
• Archimedean copulas: gumbel is a standalone package for the Gumbel copula fCopulae implements the 22 Archimedean copulas of Nelsen (1998, Introduction to Copulas, Springer-Verlag) including Gumbel, Frank, Clayton, and Ali-Mikhail-Haq. VGAM provides Ali-Mikhail-Haq, Clayton, Frank, Frechet copulas. copula provides Ali-Mikhail-Haq, Clayton, Frank, Gumbel and Joe copulas. The Frank bivariate distribution is available in RTDE. CDVine and VineCopula provide Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8 copulas. Nested Archimedean copulas are available in the HAC package. Generalized Archimedean copulas are implemented in the fgac package. BivarP provides cdf, pdf and survival function for Clayton, Gumbel and Frank copula. copBasic provides functions for Ali-Mikhail-Haq, Clayton, Frechet copulas. QRM provides pdf and random generator for Clayton, Gumbel, Frank, BB9 copula. Bivariate.Pareto provides a random generator for the Frank copula with Pareto margins. nCopula, HAC provide hierarchical archimedean copulas. lcopula provides the Liouville copula. Distributacalcul provides Ali-Mikhail-Haq, Clayton, EFGM, Frank, Gumbel, Marshall-Olkin copulas.
• Blomqvist copula: provided in copBasic.
• Composition of copula: copBasic provides functions for composition of a single symmetric copula and composition of two copulas.
• Cubic copula: Not yet implemented?
• Dirichlet copula: Not yet implemented?
• Empirical copula: provided in copBasic, HAC and cort. GenOrd provides sampling function for multivariate discrete random vectors with a specified correlation matrix.
• Elliptical copulas: Gaussian, Student and Cauchy copulas are implemented in fCopulae for the bivariate cases. copula, CDVine, VGAM, VineCopula provide the Gaussian and the Student copulas. QRM provides pdf and random generator for Gaussian, Student copulas.
• Extreme value copulas: fCopulae provides the following copulas Gumbel, Galambos, Husler-Reiss, Tawn, or BB5. copula implements Gumbel, Galambos and Husler-Reiss.
• Eyraud-Farlie-Gumbel-Morgenstern copula: provided in VGAM, RTDE, and copula.
• Mardia copula: Not yet implemented?
• Nested copulas: arbitrary nested versions of copulas can be implemented in copula.
• Plackett: provided in VGAM, copBasic and copula.
• Vine copulas: Packages CDVine, vines provide functions for C- and D-vine copulas and VineCopula for general R-vine copulas.

## Random number generators (RNG):

• Basic functionality: R provides several random number generators (RNGs). The random seed can be provided via `set.seed` and the kind of RNG can be specified using `RNGkind`. The default RNG is the Mersenne-Twister algorithm. Other generators include Wichmann-Hill, Marsaglia-Multicarry, Super-Duper, Knuth-TAOCP, Knuth-TAOCP-2002, as well as user-supplied RNGs. For normal random numbers, the following algorithms are available: Kinderman-Ramage, Ahrens-Dieter, Box-Muller, Inversion (default). In addition to the tools above, setRNG provides an easy way to set, retain information about the setting, and reset the RNG.
• Pseudo-randomness: RDieHarder offers several dozen new RNGs from the GNU GSL. randtoolbox provides more recent RNGs such as SF Mersenne-Twister and WELL, which are generators of Mersenne Twister type, but with improved quality parameters. rngwell19937 provides one of the WELL generators with 53 bit resolution of the output and allows seeding by a vector of integers of arbitrary length. randaes provides the deterministic part of the Fortuna cryptographic pseudorandom number generator (AES). SuppDists implements two RNGs of G. Marsaglia. dqrng provides PCG family by O'Neill (2014) as well as Xoroshiro128+ and Xoshiro256+ by Blackman and Vigna (2018).
• Support for several independent streams: rstream focuses on multiple independent streams of random numbers from different sources (in an object oriented approach). dqrng provides RNG for parallel computation either in R or in C++.
• For non-uniform generation, the Runuran package interfaces to the UNU.RAN library for universal non-uniform generation as well as customised distributions based on polynomial interpolation of the inverse cumulative distribution function. rust performs non-uniform random variate generation from unimodal (low-dimensional) multivariate continuous distributions, using the generalized ratio-of-uniforms method. UnivRNG provides 17 non-uniform generators either using an acceptance/rejection algorithm or the inverse CDF method. MultiRNG provides 11 multivariate generators, see each distribution.
• kernelboot provides functions for random generation from univariate and multivariate kernel densities (in particular multivariate Gaussian kernels).
• Quasi-randomness: The randtoolbox provides the following quasi random sequences: the Sobol sequence, the Halton (hence Van Der Corput) sequence and the Torus sequence (also known as Kronecker sequence). lhs and mc2d packages implement the latin hypercube sampling, an hybrid quasi/pseudo random method. sfsmisc also provides the Halton sequence. qrng provides Korobov, generalize Halton and Sobol quasi-random sequences.
• True randomness: The random package provides several functions that access the true random number service at random.org.
• RNG tests: RDieHarder offers numerous tests of RNGs based on a reimplementation and extension of Marsaglia's DieHarder battery. randtoolbox provides basic RNG tests.
• Parallel computing: Random-number generators for parallel computing are available via the rlecuyer package. See the HighPerformanceComputing task view for more details.

## Miscellaneous:

• Computation:
• Approximation of d, p, q, r functions: PDQutils provides tools for computing the density, cumulative distribution, and quantile functions of a distribution when the cumulants or moments are given, using the classical Gram Charlier, Edgeworth and Cornish-Fisher approximations. sadists is a showcase for PDQutils, providing density, cumulative distribution, quantile, and random generation for the doubly non-central t, doubly non-central F, K-prime, Lambda-prime, Upsilon, and sum of (non-central) chi-squares to powers distributions. Various approximations and alternative computations for d, p, q functions of probability distributions in R are given DPQ.
• For non-uniform generation, see the Runuran above.
• Benchmark: A set of 28 densities suitable for comparing nonparametric density estimators in simulation studies can be found in the benchden package. The densities vary greatly in degree of smoothness, number of modes and other properties. The package provides d,p,q and r functions.
• Non parametric models:
• Binned Empirical distributions: The HistogramTools package provides a number of methods for manipulating empirical data that has been binned into histogram form, including: (1) the empirical cumulative distribution function, (2) the empirical quantile, and (3) information loss metrics associated with binning.
• Empirical distribution: Base R provides functions for univariate analysis: (1) the empirical density (see density()), (2) the empirical cumulative distribution function (see ecdf()), (3) the empirical quantile (see quantile()) and (4) random sampling (see sample()). distributionsrd provides d, p, q, r user-friendly functions for the empirical distributions as well as moments. mded provides a function for measuring the difference between two independent or non-independent empirical distributions and returning a significance level of the difference. MEPDF provides functions to compute and visualize empirical density functions for multivariate data. probhat computes nonparametric probability distributions (d, p, q) using kernel smoothing. probhat supports univariate, multivariate and conditional distributions, and weighted data.
• Non Parametric distributions : spd provides the Semi Parametric Piecewise Distribution, while fBasics implements spline smoothed distributions.
• Hierarchical models: Distributions whose some parameters are no longer constant but random according to a particular distribution. VGAM provides a lot of hierarchical models: beta/binomial, beta/geometric and beta/normal distributions. bayesm implements: binary logit, linear, multivariate logit and negative binomial models. Furthermore LearnBayes and MCMCpack provides poisson/gamma, beta/binomial, normal/normal and multinomial/Dirichlet models.
• Unified interface to handle distributions:
• S3 Object-orientation: distributions3 provides tools to create and to manipulate probability distributions using S3, that is distributions3, generics `random()`, `pdf()`, `cdf()` and `quantile()` provide replacements for base R's `r/d/p/q` style functions. distributional also provides tools to create and to manipulate probability distributions using S3, with `cdf()`, `density()`, `hdr()`, `mean()`, `median()`, `quantile()`,...
• S4 Object-orientation: General discrete and continuous distributions are implemented in package distr respectively via S4-class DiscreteDistribution and AbscontDistribution providing the classic d, p, q and r functions. distrEx extends available distributions to multivariate and conditional distributions as well as methods to compute useful statistics (expectation, variance,...) and distances between distributions (Hellinger, Kolmogorov,... distance). Finally package distrMod provides functions for the computation of minimum criterion estimators (maximum likelihood and minimum distance estimators). See other packages of the distr-family (distrSim, distrTEst, distrTeach, distrDoc, distrEllipse).
• R6 Object-orientation: distr6 provides a complete R6 Probability Distributions Interface for 42 probability distributions and 11 kernels including functionality for multiple scientific types. Additionally, distr6 gives some functionalities for composite distributions and numerical imputation. ROOPSD provides a R6 class interface to classic statistical distribution.
• Transformation: Lebesgue decomposition are implemented in distr, as well as Convolution, Truncation and Huberization of distributions. Furthermore, distr provides distribution of the maximum or minimum of two distributions. See Object-orientation above.
• Transversal functions:
• Histogram, tail plots, distance estimation: DistributionUtils provides log-histogram, tail plots, functions for testing distributions using inversion tests and the Massart inequality. visualize provides functions to plot the pdf or pmf with highlights on area or when probability is present in user defined locations, as well as the graph is the mean and variance of the distribution. visualize provides lower tail, bounded, upper tail, and two tail calculations. visualize contains convenience functions for constructing and plotting bivariate probability distributions (probability mass functions, probability density functions and cumulative distribution functions). vistributions provides visualization tools for a selected number of distributions.
• Parameter estimation: lmomco and Lmoments focus on univariate/multivariate (L-)moments estimation. VGAM provides a lot of parameter estimation for usual and "exotic" distributions. gaussDiff provides a collection difference measures for multivariate Gaussian probability density functions Package MASS implements the flexible `fitdistr` function for parameter estimations. fitdistrplus greatly enlarges and enhances the tools to fit any probability distribution. EnvStats and fitteR also provides tools to fit most common distributions. flexsurv and msm provides a quantile function for a generic distribution based on numerical computation based on a dichotomic search.

## Packages

### actuar — 3.0-0

Actuarial Functions and Heavy Tailed Distributions

### agricolae — 1.3-3

Statistical Procedures for Agricultural Research

### ald — 1.2

The Asymmetric Laplace Distribution

### bayesm — 3.1-4

Bayesian Inference for Marketing/Micro-Econometrics

### benchden — 1.0.5

28 benchmark densities from Berlinet/Devroye (1994)

### BenfordTests — 1.2.0

Statistical Tests for Evaluating Conformity to Benford's Law

### betafunctions — 1.2.2

Functions for Working with Two- And Four-Parameter Beta Probability Distributions

### BiasedUrn — 1.07

Biased Urn Model Distributions

### bivariate — 0.6.0

Bivariate Probability Distributions

### Bivariate.Pareto — 1.0.3

Bivariate Pareto Models

### BivarP — 1.0

Estimating the Parameters of Some Bivariate Distributions

### bivgeom — 1.0

Roy's Bivariate Geometric Distribution

### BivGeo — 2.0.1

Basu-Dhar Bivariate Geometric Distribution

### bmixture — 1.6

Bayesian Estimation for Finite Mixture of Distributions

### BMT — 0.1.0.3

The BMT Distribution

### bridgedist — 0.1.0

An Implementation of the Bridge Distribution with Logit-Link as in Wang and Louis (2003)

Conditional Density Estimation Network Construction and Evaluation

### cbinom — 1.3

Continuous Analog of a Binomial Distribution

### CDVine — 1.4

Statistical Inference of C- And D-Vine Copulas

### CircStats — 0.2-6

Circular Statistics, from "Topics in Circular Statistics" (2001)

### circular — 0.4-93

Circular Statistics

### cmvnorm — 1.0-6

The Complex Multivariate Gaussian Distribution

### coga — 1.1.0

Convolution of Gamma Distributions

### CompLognormal — 3.0

Functions for actuarial scientists

### Compounding — 1.0.2

Computing Continuous Distributions

### Compositional — 4.1

Compositional Data Analysis

### compositions — 2.0-0

Compositional Data Analysis

Distribution Function of Quadratic Forms in Normal Variables

### condMVNorm — 2020.1

Conditional Multivariate Normal Distribution

### copBasic — 2.1.5

General Bivariate Copula Theory and Many Utility Functions

### copula — 1.0-0

Multivariate Dependence with Copulas

### cort — 0.3.1

Some Empiric and Nonparametric Copula Models

### cpd — 0.1.0

Complex Pearson Distributions

### csn — 1.1.3

Closed Skew-Normal Distribution

### Davies — 1.1-9

The Davies Quantile Function

### degreenet — 1.3-3

Models for Skewed Count Distributions Relevant to Networks

### Delaporte — 7.0.3

Statistical Functions for the Delaporte Distribution

### dgumbel — 1.0.1

The Gumbel Distribution Functions and Gradients

### dirmult — 0.1.3-4

Estimation in Dirichlet-Multinomial distribution.

### disclap — 1.5

Discrete Laplace Exponential Family

### DiscreteInverseWeibull — 1.0.2

Discrete Inverse Weibull Distribution

### DiscreteLaplace — 1.1.1

Discrete Laplace Distributions

### DiscreteWeibull — 1.1

Discrete Weibull Distributions (Type 1 and 3)

### distcrete — 1.0.3

Discrete Distribution Approximations

### distr — 2.8.0

Object Oriented Implementation of Distributions

### distr6 — 1.4.3

The Complete R6 Probability Distributions Interface

### distrDoc — 2.8.0

Documentation for 'distr' Family of R Packages

### distrEllipse — 2.8.0

S4 Classes for Elliptically Contoured Distributions

### distrEx — 2.8.0

Extensions of Package 'distr'

### DistributionUtils — 0.6-0

Distribution Utilities

### distributionsrd — 0.0.6

Distribution Fitting and Evaluation

### distrMod — 2.8.4

Object Oriented Implementation of Probability Models

### distrSim — 2.8.0

Simulation Classes Based on Package 'distr'

### distTails — 0.1.2

A Collection of Full Defined Distribution Tails

### distributional — 0.2.0

Vectorised Probability Distributions

### distributions3 — 0.1.1

Probability Distributions as S3 Objects

### Distributacalcul — 0.3.0

Probability Distribution Functions

### distrTeach — 2.8.0

Extensions of Package 'distr' for Teaching Stochastics/Statistics in Secondary School

### distrTEst — 2.8.0

Estimation and Testing Classes Based on Package 'distr'

### DPQ — 0.4-1

Density, Probability, Quantile ('DPQ') Computations

### dqrng — 0.2.1

Fast Pseudo Random Number Generators

### e1071 — 1.7-3

Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien

### ecd — 0.9.1

Elliptic Lambda Distribution and Option Pricing Model

### elfDistr — 1.0.0

Kumaraswamy Complementary Weibull Geometric (Kw-CWG) Probability Distribution

### emdbook — 1.3.12

Support Functions and Data for "Ecological Models and Data"

### emg — 1.0.9

Exponentially Modified Gaussian (EMG) Distribution

### empichar — 1.0.0

Evaluates the Empirical Characteristic Function for Multivariate Samples

### EnvStats — 2.3.1

Package for Environmental Statistics, Including US EPA Guidance

### evd — 2.3-3

Functions for Extreme Value Distributions

### evdbayes — 1.1-1

Bayesian Analysis in Extreme Value Theory

### evir — 1.7-4

Extreme Values in R

### evmix — 2.12

Extreme Value Mixture Modelling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

### extremefit — 1.0.2

Estimation of Extreme Conditional Quantiles and Probabilities

Distributions that are Sometimes Used in Hydrology

### FatTailsR — 1.7-5

Kiener Distributions and Fat Tails in Finance

### fBasics — 3042.89.1

Rmetrics - Markets and Basic Statistics

### fCopulae — 3042.82.1

Rmetrics - Bivariate Dependence Structures with Copulae

### fExtremes — 3042.82

Rmetrics - Modelling Extreme Events in Finance

### fgac — 0.6-1

Generalized Archimedean Copula

### fitdistrplus — 1.1-1

Help to Fit of a Parametric Distribution to Non-Censored or Censored Data

### fitteR — 0.1.0

Fit Hundreds of Theoretical Distributions to Empirical Data

### flexsurv — 1.1.1

Flexible Parametric Survival and Multi-State Models

### FMStable — 0.1-2

Finite Moment Stable Distributions

### ForestFit — 0.6.1

Statistical Modelling for Plant Size Distributions

### fpow — 0.0-2

Computing the noncentrality parameter of the noncentral F distribution

### frmqa — 0.1-5

The Generalized Hyperbolic Distribution, Related Distributions and Their Applications in Finance

### fromo — 0.2.1

Fast Robust Moments

### gambin — 2.4.4

Fit the Gambin Model to Species Abundance Distributions

### gamlss.dist — 5.1-7

Distributions for Generalized Additive Models for Location Scale and Shape

### gaussDiff — 1.1

Difference measures for multivariate Gaussian probability density functions

### gb — 2.3.3

Generalize Lambda Distribution and Generalized Bootstrapping

### GB2 — 2.1

Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

### gendist — 2.0

Generated Probability Distribution Models

### geoR — 1.8-1

Analysis of Geostatistical Data

### GenBinomApps — 1.1

Clopper-Pearson Confidence Interval and Generalized Binomial Distribution

### GenOrd — 1.4.0

Simulation of Discrete Random Variables with Given Correlation Matrix and Marginal Distributions

### GeneralizedHyperbolic — 0.8-4

The Generalized Hyperbolic Distribution

### ggamma — 1.0.1

Generalized Gamma Probability Distribution

### GIGrvg — 0.5

Random Variate Generator for the GIG Distribution

### gk — 0.5.1

g-and-k and g-and-h Distribution Functions

### gld — 2.6.2

Estimation and Use of the Generalised (Tukey) Lambda Distribution

### GLDEX — 2.0.0.7

Fitting Single and Mixture of Generalised Lambda Distributions (RS and FMKL) using Various Methods

### glogis — 1.0-1

Fitting and Testing Generalized Logistic Distributions

### ghyp — 1.6.1

Generalized Hyperbolic Distribution and Its Special Cases

### greybox — 0.6.2

Toolbox for Model Building and Forecasting

### GSM — 1.3.2

Gamma Shape Mixture

### gumbel — 1.10-2

The Gumbel-Hougaard Copula

### HAC — 1.0-8

Estimation, Simulation and Visualization of Hierarchical Archimedean Copulae (HAC)

### hermite — 1.1.2

Generalized Hermite Distribution

### HI — 0.4

Simulation from distributions supported by nested hyperplanes

### HistogramTools — 0.3.2

Utility Functions for R Histograms

### HyperbolicDist — 0.6-2

The hyperbolic distribution

### hyper2 — 1.0-7

The Hyperdirichlet Distribution, Mark 2

### kdist — 0.2

K-Distribution and Weibull Paper

### kernelboot — 0.1.7

Smoothed Bootstrap and Random Generation from Kernel Densities

### kolmim — 1.0

An Improved Evaluation of Kolmogorov's Distribution

### KScorrect — 1.4.0

Lilliefors-Corrected Kolmogorov-Smirnov Goodness-of-Fit Tests

### LambertW — 0.6.5

Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

### LaplacesDemon — 16.1.4

Complete Environment for Bayesian Inference

### lcopula — 1.0.4

Liouville Copulas

### LearnBayes — 2.15.1

Functions for Learning Bayesian Inference

### lhs — 1.0.2

Latin Hypercube Samples

### LIHNPSD — 0.2.1

Poisson Subordinated Distribution

### LindleyPowerSeries — 0.1.0

Lindley Power Series Distribution

### llogistic — 1.0.3

The L-Logistic Distribution

### logitnorm — 0.8.37

Functions for the Logitnormal Distribution

### loglognorm — 1.0.1

Double log normal distribution functions

L-Moments

### lmomco — 2.3.6

L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

### Lmoments — 1.3-1

L-Moments and Quantile Mixtures

### MASS — 7.3-53

Support Functions and Datasets for Venables and Ripley's MASS

### marg — 1.2-2.1

Approximate Marginal Inference for Regression-Scale Models

### matrixNormal — 0.0.4

The Matrix Normal Distribution

### matrixsampling — 2.0.0

Simulations of Matrix Variate Distributions

### mbbefd — 0.8.8.5

Maxwell Boltzmann Bose Einstein Fermi Dirac Distribution and Destruction Rate Modelling

### MBSP — 1.0

Multivariate Bayesian Model with Shrinkage Priors

### mc2d — 0.1-18

Tools for Two-Dimensional Monte-Carlo Simulations

### mclust — 5.4.6

Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

### MCMCpack — 1.4-9

Markov Chain Monte Carlo (MCMC) Package

### mded — 0.1-2

Measuring the Difference Between Two Empirical Distributions

### MEPDF — 3.0

Creation of Empirical Density Functions Based on Multivariate Data

### mgpd — 1.99

mgpd: Functions for multivariate generalized Pareto distribution (MGPD of Type II)

### minimax — 1.0

Minimax distribution family

### MitISEM — 1.2

Mixture of Student t Distributions using Importance Sampling and Expectation Maximization

### MittagLeffleR — 0.3.0

Mittag-Leffler Family of Distributions

### MixedTS — 1.0.4

Mixed Tempered Stable Distribution

### mixtools — 1.2.0

Tools for Analyzing Finite Mixture Models

### MM — 1.6-5

The Multiplicative Multinomial Distribution

### mniw — 1.0

The Matrix-Normal Inverse-Wishart Distribution

### mnormpow — 0.1.1

Multivariate Normal Distributions with Power Integrand

### mnormt — 2.0.2

The Multivariate Normal and t Distributions, and Their Truncated Versions

Mode Estimation

### moments — 0.14

Moments, cumulants, skewness, kurtosis and related tests

### MomTrunc — 5.89

Moments of Folded and Doubly Truncated Multivariate Distributions

### movMF — 0.2-4

Mixtures of von Mises-Fisher Distributions

### MPS — 2.3.1

Estimating Through the Maximum Product Spacing Approach

### msm — 1.6.8

Multi-State Markov and Hidden Markov Models in Continuous Time

### MultiRNG — 1.2.3

Multivariate Pseudo-Random Number Generation

### mvprpb — 1.0.4

Orthant Probability of the Multivariate Normal Distribution

### mvrtn — 1.0

Mean and Variance of Truncated Normal Distribution

### mvtnorm — 1.1-1

Multivariate Normal and t Distributions

### nCopula — 0.1.1

Hierarchical Archimedean Copulas Constructed with Multivariate Compound Distributions

### nCDunnett — 1.1.0

Noncentral Dunnett's Test Distribution

### Newdistns — 2.1

Computes Pdf, Cdf, Quantile and Random Numbers, Measures of Inference for 19 General Families of Distributions

### NonNorMvtDist — 1.0.2

Multivariate Lomax (Pareto Type II) and Its Related Distributions

### nor1mix — 1.3-0

Normal aka Gaussian (1-d) Mixture Models (S3 Classes and Methods)

### NormalGamma — 1.1

Normal-gamma convolution model

### NormalLaplace — 0.3-0

The Normal Laplace Distribution

### normalp — 0.7.2

Routines for Exponential Power Distribution

### ORDER2PARENT — 1.0

Estimate parent distributions with data of several order statistics

### OrdNor — 2.2.2

Concurrent Generation of Ordinal and Normal Data with Given Correlation Matrix and Marginal Distributions

Owen Q-Function

### parameters — 0.8.6

Processing of Model Parameters

### ParetoPosStable — 1.1

Computing, Fitting and Validating the PPS Distribution

### pbv — 0.4-22

Probabilities for Bivariate Normal Distribution

### PearsonDS — 1.1

Pearson Distribution System

### pmultinom — 1.0.0

One-Sided Multinomial Probabilities

### poibin — 1.5

The Poisson Binomial Distribution

### PoissonBinomial — 1.1.3

Efficient Computation of Ordinary and Generalized Poisson Binomial Distributions

### poilog — 0.4

Poisson lognormal and bivariate Poisson lognormal distribution

### poistweedie — 1.0

Poisson-Tweedie exponential family models

### polyaAeppli — 2.0

Implementation of the Polya-Aeppli distribution

### probhat — 0.3.1

Multivariate Generalized Kernel Smoothing and Related Statistical Methods

### PDQutils — 0.1.6

PDQ Functions via Gram Charlier, Edgeworth, and Cornish Fisher Approximations

### poweRlaw — 0.70.6

Analysis of Heavy Tailed Distributions

### QBAsyDist — 0.1.2

Asymmetric Distributions and Quantile Estimation

### qmap — 1.0-4

Statistical Transformations for Post-Processing Climate Model Output

### QRM — 0.4-31

Provides R-Language Code to Examine Quantitative Risk Management Concepts

### qrmtools — 0.0-13

Tools for Quantitative Risk Management

### qrng — 0.0-7

(Randomized) Quasi-Random Number Generators

### randaes — 0.3

Random number generator based on AES cipher

### random — 0.2.6

True Random Numbers using RANDOM.ORG

### randtoolbox — 1.30.1

Toolbox for Pseudo and Quasi Random Number Generation and Random Generator Tests

### RDieHarder — 0.2.1

R Interface to the 'DieHarder' RNG Test Suite

### ReIns — 1.0.10

Functions from "Reinsurance: Actuarial and Statistical Aspects"

### reliaR — 0.01

Package for some probability distributions.

### Renext — 3.1-0

Renewal Method for Extreme Values Extrapolation

### retimes — 0.1-2

Reaction Time Analysis

### revdbayes — 1.3.9

Ratio-of-Uniforms Sampling for Bayesian Extreme Value Analysis

### rlecuyer — 0.3-5

R Interface to RNG with Multiple Streams

### RMKdiscrete — 0.1

Sundry Discrete Probability Distributions

### RMTstat — 0.3

Distributions, Statistics and Tests derived from Random Matrix Theory

### rmutil — 1.1.5

Utilities for Nonlinear Regression and Repeated Measurements Models

### rngwell19937 — 0.6-0

Random number generator WELL19937a with 53 or 32 bit output

### ROOPSD — 0.2.5

R Object Oriented Programming for Statistical Distribution

### rstream — 1.3.6

Streams of Random Numbers

### RTDE — 0.2-1

Robust Tail Dependence Estimation

### rtdists — 0.11-2

Response Time Distributions

### Runuran — 0.30

R Interface to the 'UNU.RAN' Random Variate Generators

### rust — 1.3.10

Ratio-of-Uniforms Simulation with Transformation

### s20x — 3.1-29

Functions for University of Auckland Course STATS 201/208 Data Analysis

### SCI — 1.0-2

Standardized Climate Indices Such as SPI, SRI or SPEI

### scModels — 1.0.1

Fitting Discrete Distribution Models to Count Data

### setRNG — 2013.9-1

Set (Normal) Random Number Generator and Seed

### sfsmisc — 1.1-7

Utilities from 'Seminar fuer Statistik' ETH Zurich

### sgt — 2.0

Skewed Generalized T Distribution Tree

### skellam — 0.2.0

Densities and Sampling for the Skellam Distribution

### skewt — 0.1

The Skewed Student-t Distribution

### SkewHyperbolic — 0.4-0

The Skew Hyperbolic Student t-Distribution

### sld — 0.3.3

Estimation and Use of the Quantile-Based Skew Logistic Distribution

### smoothmest — 0.1-2

Smoothed M-estimators for 1-dimensional location

### SMR — 2.0.1

Externally Studentized Midrange Distribution

### sn — 1.6-2

The Skew-Normal and Related Distributions Such as the Skew-t

SPArse Matrix

### sparseMVN — 0.2.1.1

Multivariate Normal Functions for Sparse Covariance and Precision Matrices

### spd — 2.0-1

Semi Parametric Distribution

### stabledist — 0.7-1

Stable Distribution Functions

### statmod — 1.4.34

Statistical Modeling

### STAR — 0.3-7

Spike Train Analysis with R

### SuppDists — 1.1-9.5

Supplementary Distributions

### symmoments — 1.2.1

Symbolic Central and Noncentral Moments of the Multivariate Normal Distribution

### TLMoments — 0.7.5

Calculate TL-Moments and Convert Them to Distribution Parameters

### tmvmixnorm — 1.1.1

Sampling from Truncated Multivariate Normal and t Distributions

### tmvtnorm — 1.4-10

Truncated Multivariate Normal and Student t Distribution

### tolerance — 2.0.0

Statistical Tolerance Intervals and Regions

### trapezoid — 2.0-0

The Trapezoidal Distribution

### triangle — 0.12

Provides the Standard Distribution Functions for the Triangle Distribution

### truncdist — 1.0-2

Truncated Random Variables

### truncnorm — 1.0-8

Truncated Normal Distribution

### TruncatedNormal — 2.2

Truncated Multivariate Normal and Student Distributions

### tsallisqexp — 0.9-3

Tsallis q-Exp Distribution

### TTmoment — 1.0

Sampling and Calculating the First and Second Moments for the Doubly Truncated Multivariate t Distribution

### tvgeom — 1.0.1

The Time-Varying (Right-Truncated) Geometric Distribution

### tweedie — 2.3.2

Evaluation of Tweedie Exponential Family Models

### UnivRNG — 1.2.2

Univariate Pseudo-Random Number Generation

### VarianceGamma — 0.4-0

The Variance Gamma Distribution

### VGAM — 1.1-3

Vector Generalized Linear and Additive Models

### VineCopula — 2.3.0

Statistical Inference of Vine Copulas

### vines — 1.1.5

Multivariate Dependence Modeling with Vines

### vistributions — 0.1.1

Visualize Probability Distributions

### visualize — 4.4.0

Graph Probability Distributions with User Supplied Parameters and Statistics

### Wrapped — 2.0

Computes Pdf, Cdf, Quantile, Random Numbers and Provides Estimation for any Univariate Wrapped Distributions

### zipfextR — 1.0.2

Zipf Extended Distributions

### zipfR — 0.6-66

Statistical Models for Word Frequency Distributions