Alternative Continuous and Discrete Distributions

The aim is to develop an R package, which is the 'new.dist' package, for the probability (density) function, the distribution function, the quantile function and the associated random number generation function for discrete and continuous distributions, which have recently been proposed in the literature. This package implements the following distributions: The Power Muth Distribution, a Bimodal Weibull Distribution, the Discrete Lindley Distribution, The Gamma-Lomax Distribution, Weighted Geometric Distribution, a Power Log-Dagum Distribution, Kumaraswamy Distribution, Lindley Distribution, the Unit-Inverse Gaussian Distribution, EP Distribution, Akash Distribution, Ishita Distribution, Maxwell Distribution, the Standard Omega Distribution, Slashed Generalized Rayleigh Distribution, Two-Parameter Rayleigh Distribution, Muth Distribution, Uniform-Geometric Distribution, Discrete Weibull Distribution.

new.dist

The aim is to develop an R package, which is new.dist package, for the probability (density) function, the distribution function, the quantile function and the associated random number generation function for discrete and continuous distributions, which have recently been proposed in the literature. This package implements the following distributions: The Power Muth Distribution, A bimodal Weibull Distribution, The Discrete Lindley Distribution 1, The Discrete Lindley Distribution 2, The Gamma-Lomax Distribution, Weighted Geometric Distribution, A Power Log-Dagum Distribution, Kumaraswamy Distribution, Lindley Distribution, Ram Awadh Distribution, The Unit-Inverse Gaussian Distribution, EP Distribution, Akash Distribution, Ishita Distribution, Maxwell Distribution, The Standard Omega Distribution, Slashed Generalized Rayleigh Distribution, Two-Parameter Rayleigh Distribution, Muth Distribution, Uniform-Geometric Distribution, Discrete Weibull Distribution.

Installation

You can install the development version of new.dist from [GitHub][https://github.com/] with:

# install.packages("devtools")
devtools::install_github("akmn35/new.dist")

Details

new.dist Density, distribution function, quantile function and random generation for parameter estimation of distributions.

Example

dbwd Density function for Bimodal Weibull distribution with shape (alpha) and scale (beta) parameters.

library(new.dist)
dbwd(1,alpha=2,beta=3,sigma=4)
#> [1] 0.01594262

pbwd Distribution function for Bimodal Weibull distribution with shape (alpha) and scale (beta) parameters.

library(new.dist)
pbwd(1,alpha=2,beta=3,sigma=4)
#> [1] 0.003859685

qbwd Quantile function for Bimodal Weibull distribution with shape (alpha) and scale (beta) parameters.

library(new.dist)
qbwd(.7,alpha=2,beta=3,sigma=4)
#> [1] 4.759942

rbwd Random generation for a Bimodal Weibull distribution with shape (alpha) and scale (beta) parameters.

library(new.dist)
rbwd(5,alpha=2,beta=3,sigma=4)
#> [1] 5.787403 3.062926 2.560047 3.406179 2.344262

dsgrd Density function for a Slashed Generalized Rayleigh distribution with shape (alpha), scale (theta) and kurtosis(beta) parameters.

library(new.dist)
dsgrd(2,theta=3,alpha=1,beta=4)
#> [1] 0.08314235

psgrd Distribution function for a Slashed Generalized Rayleigh distribution with shape (alpha), scale (theta) and kurtosis (beta) parameters.

library(new.dist)
psgrd(5,theta=3,alpha=1,beta=4)
#> [1] 0.9989333

qsgrd Quantile function for a Slashed Generalized Rayleigh distribution with shape (alpha), scale (theta) and kurtosis (beta) parameters.

library(new.dist)
qsgrd(.4,theta=3,alpha=1,beta=4)
#> [1] 0.8358487

rsgrd Random generation for a Slashed Generalized Rayleigh distribution with shape (alpha), scale (theta) and kurtosis (beta) parameters.

library(new.dist)
rsgrd(5,theta=3,alpha=1,beta=4)
#> [1] 0.9162424 2.2939520 0.9160551 0.7168782 1.2676308

dsod Density function for a the Standard Omega distribution with alpha and beta parameters.

library(new.dist)
dsod(0.4, alpha=1, beta=2)
#> [1] 0.6986559

psod Distribution function for a the Standard Omega distribution with alpha and beta parameters.

library(new.dist)
psod(0.4, alpha=1, beta=2)
#> [1] 0.1490371

qsod Quantile function for a the Standard Omega distribution with alpha and beta parameters.

library(new.dist)
qsod(.8, alpha=1, beta=2)
#> [1] 0.9607689

rsod Random generation for a the Standard Omega distribution with alpha and beta parameters.

library(new.dist)
rsod(5, alpha=1, beta=2)
#> [1] 0.9626043 0.6029560 0.8908171 0.9719128 0.6324489

dugd Density function for the Uniform-Geometric distribution with theta parameter.

library(new.dist)
dugd(1, theta=0.5)
#> [1] 0.6931472

pugd Distribution function for the Uniform-Geometric distribution with theta parameter.

library(new.dist)
pugd(1,theta=.5)
#> [1] 0.6931472

qugd Quantile function for the Uniform-Geometric distribution with theta parameter.

library(new.dist)
qugd(0.6,theta=.1)
#> [1] 4

rugd Random generation for the Uniform-Geometric distribution with theta parameter.

library(new.dist)
rugd(5,theta=.1)
#> [1]  1 13 13  5  9

dtpmd Density function for the Power Muth distribution with shape (beta) and scale (alpha) parameters.

library(new.dist)
dtpmd(1, beta=2, alpha=3)
#> [1] 0.04952547

ptpmd Distribution function for the Power Muth distribution shape (beta) and scale (alpha) parameters.

library(new.dist)
ptpmd(1,beta=2,alpha=3)
#> [1] 0.008115344

qtpmd Quantile function for the Power Muth distribution with shape (beta) and scale (alpha) parameters.

library(new.dist)
qtpmd(.5,beta=2,alpha=3)
#> [1] 1.990084

rtpmd Random generation for the Power Muth distribution with shape (beta) and scale (alpha) parameters.

library(new.dist)
rtpmd(5,beta=2,alpha=3)
#> [1] 1.806067 1.668991 1.865928 1.775550 1.721437

dtprd Density function for the Two-Parameter Rayleigh distribution with location (mu) and scale (lambda) parameters.

library(new.dist)
dtprd(5, lambda=4, mu=4)
#> [1] 0.1465251

ptprd Distribution function for Two-Parameter Rayleigh distribution with location (mu) and scale (lambda) parameters.

library(new.dist)
ptprd(2,lambda=2,mu=1)
#> [1] 0.8646647

qtprd Quantile function for Two-Parameter Rayleigh distribution with location (mu) and scale (lambda) parameters.

library(new.dist)
qtprd(.5,lambda=2,mu=1)
#> [1] 1.588705

rtprd Random generation for Two-Parameter Rayleigh distribution with location (mu) and scale (lambda) parameters.

library(new.dist)
rtprd(5,lambda=2,mu=1)
#> [1] 2.137743 1.385888 1.788912 1.696368 1.783938

duigd Density function for the Unit Inverse Gaussian distribution with mean (mu) and scale (lambda) parameters.

library(new.dist)
duigd(1, mu=2, lambda=3)
#> [1] 0.4749088

puigd Distribution function for the Unit Inverse Gaussian distribution with mean (mu) and scale (lambda) parameters.

library(new.dist)
puigd(1,mu=2,lambda=3)
#> [1] 0.2873867

quigd Quantile function for the Unit Inverse Gaussian distribution with mean (mu) and scale (lambda) parameters.

library(new.dist)
quigd(.1,mu=2,lambda=3)
#> [1] 0.6104128

ruigd Random generation for the Unit Inverse Gaussian distribution with mean (mu) and scale (lambda) parameters.

library(new.dist)
ruigd(5,mu=2,lambda=3)
#> [1] 1.7037855 2.8067345 0.8597714 0.7931621 1.0315418

dwgd Density function for the Weighted Geometric distribution with alpha and lambda parameters.

library(new.dist)
dwgd(1,alpha=.2,lambda=3)
#> [1] 0.79872

pwgd Distribution function for the Weighted Geometric distribution with alpha and lambda parameters.

library(new.dist)
dwgd(1,alpha=.2,lambda=3)
#> [1] 0.79872

qwgd Quantile function for the Weighted Geometric distribution with alpha and lambda parameters.

library(new.dist)
qwgd(.98,alpha=.2,lambda=3)
#> [1] 3

rwgd Random generation for the Weighted Geometric distribution with alpha and lambda parameters.

library(new.dist)
rwgd(5,alpha=.2,lambda=3)
#> [1] 1 1 3 1 2

ddLd1 Density function for the Discrete Lindley distribution 1 with theta parameter.

library(new.dist)
ddLd1(1,theta=2)
#> [1] 0.1828223

pdLd1 Distribution function for the Discrete Lindley distribution 1 with theta parameter.

library(new.dist)
ddLd1(1,theta=2)
#> [1] 0.1828223

qdLd1 Quantile function for the Discrete Lindley distribution 1 with theta parameter.

library(new.dist)
qdLd1(.993,theta=2)
#> [1] 3

rdLd1 Random generation for the Discrete Lindley distribution 1 with theta parameter.

library(new.dist)
rdLd1(5,theta=1)
#> [1] 0 2 0 2 0

dmd Density function for Maxwell distribution with scale (theta) parameter.

library(new.dist)
dmd(1,theta=2)
#> [1] 0.4839414

pmd Distribution function for a Maxwell distribution with scale (theta) parameter.

library(new.dist)
pmd(1,theta=2)
#> [1] 0.198748

qmd Quantile function for a Maxwell distribution with scale (theta) parameter.

library(new.dist)
qmd(.4,theta=5)
#> [1] 2.161694

rmd Random generation for a Maxwell distribution with scale (theta) parameter.

library(new.dist)
rmd(5,theta=1)
#> [1] 0.9270855 2.2550202 1.2018527 0.9012689 1.6375431

dkd Density function for Kumaraswamy distribution with shape (alpha, lambda) parameters.

library(new.dist)
dkd(0.1,lambda=2,alpha=3)
#> [1] 0.58806

pkd Distribution function for Kumaraswamy distribution with shape (alpha, lambda) parameters.

library(new.dist)
dkd(0.1,lambda=2,alpha=3)
#> [1] 0.58806

qkd Quantile function for Kumaraswamy distribution with shape (alpha, lambda) parameters.

library(new.dist)
pkd(0.5,lambda=2,alpha=3)
#> [1] 0.578125

rkd Random generation for Kumaraswamy distribution with shape (alpha, lambda) parameters.

library(new.dist)
rkd(5,lambda=2,alpha=3)
#> [1] 0.6415521 0.5272059 0.2329670 0.4351743 0.5657495

dgld Density function for the Gamma-Lomax distribution with shape (a, alpha) and scale (beta) parameters.

library(new.dist)
dgld(1,a=2,alpha=3,beta=4)
#> [1] 0.2056491

pgld Distribution function for the Gamma-Lomax distribution with shape (a, alpha) and scale (beta) parameters.

library(new.dist)
dgld(1,a=2,alpha=3,beta=4)
#> [1] 0.2056491

qgld Quantile function for the Gamma-Lomax distribution with shape (a, alpha) and scale (beta) parameters.

library(new.dist)
qgld(.8,a=2,alpha=3,beta=4)
#> [1] 6.852518

rgld Random generation for the Gamma-Lomax distribution with shape (a, alpha) and scale (beta) parameters.

library(new.dist)
rgld(5,a=2,alpha=3,beta=4)
#> [1] 2.8217781 5.5886484 8.4958716 0.9864014 2.1699043

ddLd2 Density function for a Discrete Lindley distribution 2 with theta parameter.

library(new.dist)
ddLd2(2,theta=2)
#> [1] 0.03530023

pdLd2 Distribution function for a Discrete Lindley distribution 2 with theta parameter.

library(new.dist)
pdLd2(1,theta=2)
#> [1] 0.9572635

qdLd2 Quantile function for a Discrete Lindley distribution 2 with theta parameter.

library(new.dist)
qdLd2(.5,theta=2)
#> [1] 0

rdLd2 Random generation for a Discrete Lindley distribution 2 with theta parameter.

library(new.dist)
rdLd2(5,theta=1)
#> [1] 3 0 1 0 0

dEPd Density function for the EP distribution with lambda and beta parameters.

library(new.dist)
dEPd(1, lambda=2, beta=3)
#> [1] 0.05165063

pEPd Distribution function for the EP distribution with lambda and beta parameters.

library(new.dist)
pEPd(1, lambda=2, beta=3)
#> [1] 0.9836125

qEPd Quantile function for the EP distribution with lambda and beta parameters.

library(new.dist)
qEPd(.8,lambda=2,beta=3)
#> [1] 0.295895

rEPd Random generation for the EP distribution with lambda and beta parameters.

library(new.dist)
rEPd(5,lambda=2,beta=3)
#> [1] 0.08754699 0.01152708 0.27621565 0.12618652 0.18547342

dRA Density function for a Ram Awadh distribution with scale (theta) parameter.

library(new.dist)
dRA(1,theta=2)
#> [1] 0.1412194

pRA Distribution function for a Ram Awadh distribution with scale (theta) parameter.

library(new.dist)
pRA(1,theta=2)
#> [1] 0.3115553

qRA Quantile function for a Ram Awadh distribution with scale (theta) parameter.

library(new.dist)
dRA(.8,theta=2)
#> [1] 0.163461

rRA Random generation for a Ram Awadh distribution with scale (theta) parameter.

library(new.dist)
rRA(5,theta=2)
#> [1] 0.9774141 2.8355960 1.9192415 4.0137512 2.5296763

domd Density function for the Muth distribution with alpha parameter.

library(new.dist)
domd(1,alpha=.2)
#> [1] 0.4123689

pomd Distribution function for the Muth distribution with alpha parameter.

library(new.dist)
pomd(1,alpha=.2)
#> [1] 0.596272

qomd Quantile function for the Muth distribution with alpha parameter.

library(new.dist)
qomd(.8,alpha=.2)
#> [1] 1.637047

romd Random generation for the Muth distribution with alpha parameter.

library(new.dist)
romd(5,alpha=.2)
#> [1] 2.291542 1.144422 1.345481 2.172140 1.377844

dpldd Density function for a Power Log Dagum distribution with alpha, beta and theta parameters.

library(new.dist)
dpldd(1, alpha=2, beta=3, theta=4)
#> [1] 0.1766842

ppldd Distribution function for a Power Log Dagum distribution with alpha, beta and theta parameters.

library(new.dist)
ppldd(1, alpha=2, beta=3, theta=4)
#> [1] 0.9742603

qpldd Quantile function for a Power Log Dagum distribution with alpha, beta and theta parameters.

library(new.dist)
qpldd(.8, alpha=2, beta=3, theta=4)
#> [1] 0.6109249

rpldd Random generation for a Power Log Dagum distribution with alpha, beta and theta parameters.

library(new.dist)
rpldd(5, alpha=2, beta=3, theta=4)
#> [1]  0.05775973 -0.28725832  0.53623427  0.64797737  0.01620600

dLd Density function for Lindley distribution with theta parameter.

library(new.dist)
dLd(1,theta=2)
#> [1] 0.3608941

pLd Distribution function for Lindley distribution with theta parameter.

library(new.dist)
pLd(1,theta=2)
#> [1] 0.7744412

qLd Quantile function for Lindley distribution with theta parameter.

library(new.dist)
qLd(.5,theta=2)
#> [1] 0.4872058

rLd Random generation for Lindley distribution with theta parameter.

library(new.dist)
rLd(5,theta=1)
#> [1] 0.3935864 1.7494001 0.2860219 1.1050805 1.8812775

Corresponding Author

Department of Statistics, Faculty of Science, Selcuk University, 42250, Konya, Turkey
Email:[email protected]

References

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