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

Extensive functions for L-moments (LMs) and probability-weighted moments (PWMs), parameter estimation for distributions, LM computation for distributions, and L-moment ratio diagrams. Maximum likelihood and maximum product of spacings estimation are also available. LMs for right-tail and left-tail censoring by known or unknown threshold and by indicator variable are available. Asymmetric (asy) trimmed LMs (TL-moments, TLMs) are supported. LMs of residual (resid) and reversed (rev) resid life are implemented along with 13 quantile function operators for reliability and survival analyses. Exact analytical bootstrap estimates of order statistics, LMs, and variances- covariances of LMs are provided. The Harri-Coble Tau34-squared Normality Test is available. Distribution support with "L" (LMs), "TL" (TLMs) and added (+) support for right-tail censoring (RC) encompasses: Asy Exponential (Exp) Power [L], Asy Triangular [L], Cauchy [TL], Eta-Mu [L], Exp. [L], Gamma [L], Generalized (Gen) Exp Poisson [L], Gen Extreme Value [L], Gen Lambda [L,TL], Gen Logistic [L), Gen Normal [L], Gen Pareto [L+RC, TL], Govindarajulu [L], Gumbel [L], Kappa [L], Kappa-Mu [L], Kumaraswamy [L], Laplace [L], Linear Mean Resid. Quantile Function [L], Normal [L], 3-p log-Normal [L], Pearson Type III [L], Rayleigh [L], Rev-Gumbel [L+RC], Rice/Rician [L], Slash [TL], 3-p Student t [L], Truncated Exponential [L], Wakeby [L], and Weibull [L]. Multivariate sample L-comoments (LCMs) are implemented to measure asymmetric associations.

# News

## NEWS for R Package "lmomco"

Version 2.2.9--11/08/2017

1. Added high L-skew example to pargno.Rd as clarification on Issue 4 in 2.2.8.

Version 2.2.8--11/01/2017 (Illumination Album in Probe)

1. Enhancement: lmomkap() and parkap() overhauled into R idioms. Minor errors in old lmomkap() fixed and parkap() breaks entirely from Hosking's Newton- Raphson approach to one based on simultaneous 2-d optimization by optim() using either a mean absolute deviation of Tau3 and Tau4 or square root of total squared divergences (Pythagorean distance). The preference appears to be Pythagorean distance from extensive simulations. The new algorithm performs very similarly to Hosking's but achieves much greater symmetry about Tau3=0 in failures. Hosking's tends to fail in the far upper negative Tau3 and large Tau4 corner of L-moment ratio diagram. Both methods fail as Tau3 and Tau4 approach the theoretical lower bounds of Tau3 and Tau4.
2. Enhancement: Most of the "par***()" functions now have the parameters explicitly initialized as NA. This should mitigate some very subtle user experiences.
3. Enhancement: mle2par() and mps2par() incorrectly stated that initial parameters could be specified as vector. This was incorrect, but now they can be either an lmomco "object" (see vec2par()) or as a vector in which the vec2par() function is called internally. Also the sanity checks on para.int for both mle2par() and mps2par() are written absolutely parallel with each other.
4. Clarification: pargno(), abs(Tau3) > 0.95, now truncates Tau3 to 0.95 instead of failing to return a solution. A warning() is triggered. This still is not an ideal solution and further research into limits of R performance relative to Hosking's original FORTRAN is needed.
5. Added: par2qua2lo(), which is a generalization of par2qua2 for two quantile function mixing when one has two data objects from the x2xlo() function. This has been on the drawing board since version 1.7.3 (January 28, 2013). *** Experimental and subject to overhaul. ***
6. Changes to documentation and code cleaning in par2cdf2.R/Rd, par2qua2.R/Rd, f2flo.Rd, flo2f.Rd, and x2xlo.Rd.
7. Added: xlo=NULL argument to f2flo() and flo2f() as optional means to get the probability level of the threshold into the logic.
8. Added: f2f() to form an idiom for use in conditional probability computations.
9. BUG FIX: "lmrq" is now returned as "Linear Mean Residual Quantile Function" in prettydist(dist.list()). Credit to Berry Boessenkool.

Version 2.2.7--03/07/2017: (Emergency Release)

1. BUG FIX: are.lmom.valid() from version 2.2.6 had a bug that missing Tau5 would short circuit the Tau3-Tau4 consistency check for which that check needed to occur before Tau5 and not after. Author discovered this during algorithmic review of the parkap() function.

Version 2.2.6--03/06/2017: (Daffodil cluster)

1. Documentation revision to lmomco-package.Rd showing quick primer to the package and how to make L-moments, MLE, and MPS estimates for a GEV sample and compare to the same purpose methods from the eva package.
2. Added passing of "..." argument into optim() within mle2par() and mps2par(). Originally, this was not made because of constraints of working with the 3-p Generalized Gamma using the p=3 argument. Now the Examples in the pargam() function show that an init.para argument to mps2par() and by extension mle3par() when the initial parameters are already three para- meters wide then the 3-p version can be triggered without having to get "p=3" passed into mle2par() or mps2par().
3. Presumed Enhancement: Added a trap to convert the Deltas of the U-statistics for mps2par() when NaN to zero. Some further testing indicates that during optimization that parameter space could get accessed for some distributions that cause NaN to be returned from the CDF. The zeros in turn get hit with log(Delta), which the triggers Inf that is fed back to the simplex and a portion of inappropriate parameter space gets flagged during the optimization. This trap is anticipated to enhance the robust- ness of the MPS algorithm.
4. BUG FIX: TLmoms() was trapping for NaN back in NEWS:2.2.2:27. The trap was incorrectly formed and an untrimmed symmetrical data set could cause TAU3 = NA when LAMBDA3 == 0 and LAMBDA2 != 0. Berry Boessenkool provided discovery through an unrelated cascade of errors.
5. Enhancement: are.parln3.valid() could receive non-NA parameters incoming from LN3 estimation for L-skew too large for the underlying pargno() algorithm providing LN3 support. These non-NA leak through to the conditionals on the parameter values. Rearrangement of tests made so that if standard deviation is zero, which is representative of the leak, then immediate return of FALSE is made. Also added a finiteness check on LAM1 and LAM2. Berry Boessenkool provided discovery of a cascade of errors when extremely high L-skew was fed to parln3().
6. Enhancement: removed extra check on L-moment validity in parln3.R by calling pargno(..., checklmom=FALSE).
7. Enhancement: removed most of the code snippets that look something like: opts <- options(warn=-1); Y <- log(X); options(opts) # X might be < 0 as a wrapper on operations that could trigger NaNs. Replaced with code like this: Y <- suppressWarnings(X). Streamlines the overall code base. About 20 functions involved, so about 40 lines of code removed. Berry Boessenkool provided this suggestion.
8. BUG FIX: Infinite L-moments could leak through are.lmom.valid() as testing TRUE. For example, the sample L-moments of logarithms of data having a zero. This should have been fixed years ago for even the author would add elaborate checking in applications. This feature should have long had its own implementation. Thanks to Brian Breaker for pushing the issue.
9. Added a large simulation example within lmomGEV.Rd showing how successive definitions of maxima of n-events per year converge to GEV families no matter what is the parent distribution. Thanks for M.G. Schaefer for demonstrating the idea at a March 2017 meeting.

Version 2.2.5--September 9, 2016: ("PG that Turtle Biscuit" Release)

1. PERFORMANCE FIX: pdfpe3() a certain combination of SIGMA and GAMMA parameters could leak through and cause later div0, for which a passage to Normality should be triggered. This caused intensive study of performance for small variation and near zero skew. Gutted the function and using dgamma() and parallel logic to cdfpe3().
2. BUG FIX: lmompe3() had a misspecified variable accessing the 2nd parameter for the condition of small or zero skewness. Discovered playing with mle2par(), which had yielded the pdfpe3() bug mentioned in Item 1.
3. BUG FIX: mps2par() had a lingering variable name change problem related to the "ties" argument but the old argument "ties.method" receiving the results of match.arg(). The variable ties was still being used in a value check expecting a scalar (the result of match.arg) but ties was remaining the vector as set by the function declaration. Trivially small issue.
4. Added another example to are.lmom.valid() to show a bail-out attempt at L-moment computation via probability-weighted moments computed by plotting-position formula.
5. Added the "null.on.not.converge" argument to mle2par() and mps2par().
6. Added the 3-parameter Generalized Gamma to *gam() functions using the special parameterization of the 3-p GG in the gamlss package. Though a gamlss dependency is not foreseen, cross applications are now possible.
7. Text adjustment to pdfpe3.Rd and addition of two examples related to interaction with the PearsonDS package support for Pearson Type III.
8. Added arguments "alt.other.lab" and "npp.as.aep" to add.lmomco.axis() to support the inversion of axis drawing from nonexceedance probability to exceedance probability.
9. Euler's constant standardization in lmomrevgum(), mps2par(), pargum(), and parrevgum() to the DiGamma: "print(-digamma(1), digits=15)"
10. Added "ptransf" and "pretransf" arguments to mle2par() and mps2par() to support parameter transformation and retransformation if a user needs to impose parameter constraints to assist the optimizer.
11. Added "no.stop" argument to lmoms().
12. Govindarajulu: cdfgov() now returns 0 or 1 if x is outside the support.
13. Added the Cramer--von Mises goodness-of-fit in cvm.test.lmomco() mimicking and using the goftest package.
14. Added the "..." argument to all of the par*() functions [e.g. parwei()], which should have happened a decade ago. A problem was encountered in progressively more complicated functions wrapping these.

Version 2.2.4--July 8, 2016

1. Added "..." argument to pp(). A higher calling function to pp() could not implement the arguments to pp through the "..." argument of the that higher function with arugments intended to yet a another function.
2. Added "ties" argument to mps2par(), the motivation for Item 1. above.
3. Further refinement of mps2par() during a vacation. Added the "delta", "log10offset", "get.untied", "check.support", and "moran" arguments, where the first three additions are to enhance accommodation of ties. Also extensive expansion of the Note, References, and Examples sections.

Version 2.2.3--May 31, 2016

1. BUG FIX: cdflap() was incorrectly vectorized in R idioms, Berry Boessenkool provided discovery and the fix.
2. BUG FIX: malformed call to supdist() in cdfgld(), Berry Boessenkool provided discovery and the fix.
3. SINISTER R BEHAVIOR(?): Code flow changes in qua2ci.cov() that caused a certain warning() related to the Weibull distribution call. Could not trace the source of the problem, but Weibull, which requires a pass through pargev(), was ending up with Inf for the parameters. However, the cause simply is not known. The problem in qua2ci.cov() was buried inside the quaf construction often for the last simulation but the simulated L-moments convert properly to Weibull if intercepted. WHA thinks the issue was an ifelse() construction at the end of the sapply() for quaf. This code was pretty well vetted. WHA wonders if a change in R version caused the problem, or WHA has misunderstood a subtlety related to the ifelse() construction.
4. Added mps2par() for the maximum product spacing method for parameter estimation. The method is a straightforward parameter optimization method, is not widely available, and simple to implement in this package.

Version 2.2.2--March 20, 2016 (The Density-NA ==> 0 Release [see Item 7])

1. Added example to parglo.Rd concerning relation to log-logistic distribution following an inquiring from user Laura Read.
2. Inserted exp(log()) nests in tau34sq.normtest() to protect against integer overflow as WHA encountered a problem having a sample size in a real-world problem too large for computation of the useHoskingZt4=TRUE circumstance.
3. Added example to lmomtri.Rd showing a positive L-skew, right-triangle distri- bution being compared to the Generalized Pareto with same L-moments.
4. Added "nmom" argument to lmomtri() to avoid calls to expect.max.ostat() if desired. Changes to lmomtri() and partri() to avoid spraying of error messages from partri()-->lmomtri()-->expect.max.ostat()-->integrate() if outside the acceptable parameter range. Also, return vector of NA from partri() if abs(Tau3) is too big. All of this for the distribution is very subtle but issues were identified by Berry Boessenkool. Thanks.
5. BUG FIX: Fixed unity erroneously being returned by pdfgpa(), which was discovered from experiments with Asymmetric Triangular distribution near a positive-skew right triangle density function while thinking about other design thoughts on pdfs raised by Berry Boessenkook. The unity check then yielded next Item.
6. BUG FIX: Fixed unity erroneously returned by pdfgev(), pdfglo(), and pdfgno() as part of trap for log(0). These were discovered by intuition from grep'ing pdf*.R sources for the operation: f[i] <- 1. And this Item in turn yielded Item 7. Source of this was bad cut-paste from CDF algorithms that were written before pdf support was written---dating from circa 2006.
7. Enhanced the entire pdf ensemble using R idioms from original FORTRAN port in functions---mainly this meant replacing a for() loop with sapply(). This should greatly accelerate computation times. The enhancement also uses syntax like this: f[! is.finite(f)] <- NA and (or) additional NA setting for x values outside the domain of the distribution. Thus the reference to this version being the "Density-NA" release. HOWEVER, AFTER ALMOST A YEAR OF INTROSPECTION AND USER OPINION, DENSITIES THAT SHOULD BE NA (say log(negative number) encountered) ARE SET TO ZERO. In other words, the density outside the support of a distribution is set to zero.
8. L-moments dependent on the numerical integration of the PDF might require that PDF values being NA be treated as zero. This trap is in Item 7 but does cascade logically into check.pdf(), dlmomco(), expect.max.ostat(), expect.min.ostat(), and hlmomco().
9. Changed argument "paragld" to "para" in pdfgld(), cdfgld(), and quagld(), and cdfgld() had an example using supdist() added.
10. Added "delexp" argument to supdist().
11. Changed "gldpara" syntax to "para" in GLD distribution functions to mimic style in the functions for other distributions.
12. Updated the Examples section of check.pdf.Rd.
13. Further testing of the Kappa-Mu distribution--still somewhat experimental.
14. Further testing of the Eta-Mu distribution---still somewhat experimental.
15. Changed to R idioms (removed for() loops) in z.par2cdf.R and z.par2qua.R.
16. Added "paracheck" to are.par.valid() for easy of globally switching off parameter checking and then next Item. 17 Added "paracheck" to supdist() so that this function may be called when it is already know that the parameters are valid and added to the returned list the nonexceedance probabilities of the lower and upper supports.
17. Moved a variable into a sum() to that presumably of R will use less memory.
18. R idiom vectorization as may be to all cdfCCC.R lacking it---mainly the replacement of for() loops with either sapply() and in some cases not even sapply() and pure R vectorization is used.
19. R idiom vectorization as may be to all pdfCCC.R lacking it---mainly the replacement of for() loops with either sapply() and in some cases not even sapply() and pure R vectorization is used.
20. R idiom vectorization as may be to all quaCCC.R lacking it---mainly the replacement of for() loops with either sapply() and in some cases not even sapply() and pure R vectorization is used.
21. R idiom vectorization in rmlmomco(), rrmlmomco(), rmvarlmomco(), and rrmvarlmomco()---replacement of for() loops with sapply().
22. Documentation: (1) Corrected a spelling error that called nonexistant function in Examples in rmvarlmomco.Rd; (2) Example expansion quarice.Rd; and (3) Removed "the probability density for" in quatexp.Rd.
23. Added "sig6" to nonexceeds() for +/-6 sigma vector of probability.
24. Documentation: Changed language in z.par2cdf.Rd and z.par2qua.Rd along with syntax changes in z.par2cdf() and z.par2qua() into R idioms for enormous speed increases.
25. Documentation: smoothed language in Examples of dist.list.Rd.
26. Change to TLmoms() and added example to TLmoms.Rd for trapping of NaN coming back from TLmom() and converting to NAs.
27. Title change for "new" CRAN policy by tools::toTitleCase(). WHA does not like "L-Moment" versus "L-moment" but whatever.
28. Added disfitqua() for fitting a distribution by a multi-dimensional optimization to available quantiles. The first hint of this need was circa 2005-2007 from a K. Khorzad whom was needing an LPIII fit (for reasons now forgotten) to quantiles from Asquith and Slade (1997). The reason for implementation now is that WHA has a situation needing LPIII fit to quantiles from Asquith and Roussel (2009).
31. Added the "quafunc" argument to theoTLmoms() for arbirary quantile function.
32. Added lmoms.cov() for distribution-free, variance-covariance computation of the sample L-moments (and probability-weighted moments).
33. Added L-skew and L-kurtosis trajectory for the reversed Govindarajulu, reversed Generalized Pareto, and Weibull distributions to lmrdia().
34. NAME CHANGE: qua2ci() changed to qua2ci.simple() to make NAMESPACE available to qua2ci.cov(). Also genci() changed to genci.simple() because of its close connection. A deprecated name warning is now issued with qua2ci() and genci() and these will be removed at some later date.
35. BUG FIX: Tony Labson was testing with deep close to k=0 in quagev() and required a trapping of effectively close enough to k=0 to not cause oscillation in numerical routines. Because of core relationships, similar modifications made to quaglo() and quagp(). For the GNO, quagno() had a commented out trap like that needed by Tony for the GEV but was using the finiteness of 1/k. Tony's example for GEV would not work for GNO, so quagno() changed too.

Version 2.1.4--April 20, 2015

1. Trival changes to CITATION for CRAN compliance.

Version 2.1.3--February 1, 2015

1. Removed broken URL within man/IRSrefunds.by.state.Rd
2. Removed non-ASCII quotation marks from a comment in cdfaep4.R and pmoms.R.

Version 2.1.2--January 31, 2015 (never pushed to CRAN for trival but new checks)

1. Fixed a typo in the DESCRIPTION, indexing typo in pdfgep.Rd, and a typo in a default axis label within add.lmomco.axis.R.
2. Fixed parlab.Rd that incorrectly identified the Generalized Logistic distribution and not the Laplace distribution in first sentence as reported by Berry Boessenkool.
3. Added supdist() as a single interface to determine a distribution's support. Hints of the author's original ideals maybe found in the list returned by parkap() but never fully matured as a design idea. An inquiry about probability density functions in lmomco by Berry Boessenkool spawned the development of supdist().
4. BUG FIX: are.parkur.valid() was not checking the beta parameter as reported by Amaranthe R. Biessen.
5. The are.parkur.valid() bug and subsequent audit added some additional error trapping in the are.parCCC.valid() suite of functions. Primarily, if any of the parameters are NA then invalidity is returned. The truncated- exponential (texp) distribution is a special case in which only NA in the 3rd index can be used for such testing.
6. The subsequent audit of are.parCCC.valid.R resulted in better description on a parameter-by-parameter basis if that value of the parameter is not consistent with the requirements of the distribution.
7. Added dat2bernquaf() to invert dat2bernqua() for a scalar value. A. Pascal Martinus needed a tool to estimate the nonexceedance probability of a single value not otherwise in a sample using the Bernstein smoothing on the empirical quantile function. Minor changes to dat2bernqua.Rd made.
9. Converted choose()'s in Lcomoment.Wk to exp(lchoose()'s).
10. Converted a for() loop to sapply() in Lcomoment.Lk12().
11. Minor changes in documentation throughout following full re-reading.
12. Minor changes to DESCRIPTION following CRAN email dated 12/03/2014.
13. Spelling correction pass through the NEWS file.
14. Minor changes to CITATION following CRAN email dated 01/09/2014.
15. Added the Asymmetrical Triangular distribution for which it seems(?) that the L-moments have not been previously described.
16. Added the "showterms" argument to theoLmoms.max.ostat() so the multipliers on the expectations of the order statistic maxima and minima can be rapidly seen for pedagogic reasons.
17. Added internal numerical support estimation for pdfwak() following inquiry by Berry Boessenkool (see Item 3).
18. Added systemic vector pre-allocation throughout the package following inquiry by Berry Boessenkool. This is particularly important for the cdfCCC(), pdfCCC(), and quaCCC() functions for speed in large simulations. Many functions dated from a time when WHA knew less about optimizing R. WHA should have done the pre-allocation from the beginning.

Version 2.1.1--May 31, 2014 (The Concordance Release and Residual Life Release)

1. Enormous effort in indexing consistency and new keywords for most of the Rd files (see no. 4). George R. Herrmann provided a correction to lmom.ub.Rd.
2. Added another reference to the Govindarajulu distribution documentation: Nair et al. (2012).
3. Enhanced expect.max.ostat() and theoLmom.max.ostat() to use a quantile func.
4. COMPREHENSIVE AUDIT of Rd files and adjustments in many fewer R files as needed for sweeping consistency changes in a rigorous effort to make documentation in concordance with Asquith (2011), approximately 200 hours of effort from hand edits on the then 428p+ hardcopy of the manual. One effect is that the named format for an L-moment object is finally deprecated in favor of the list format (lmoms()).
5. BUG FIX: parln3() had an incorrect subtraction when attempting to fit with a known lower bounds. WHA has never used this feature and no users have commented on it---the audit bore fruit. Documentation of LN3 completed.
6. Added to lmrdia() and plotlmrdia() the Slash dist. and other adjustments.
7. Added the Linear Mean Residual Quantile distribution: "lmrq". This is a special distribution that exhibits a mean residual quantile function in the the form of Y = mX + b.
8. Added reslife.lmoms() and rreslife.lmoms(), which respectively are the L-moments of residual life and reversed residual life for a quantile func.
9. Added cmlmomco(), rmlmomco(), rrmlmomco(), rmvarlmomco(), rrmvarlmomco(), ralmomco(), rralmomco(), tttlmomco(), stttlmomco(), brflmomco(), lrzlmomco(), lkhlmomco(), and riglmomco(), which are a suite of quantile function operators on a distribution using the quantile functions outlined by Nair et al. (2013). These functions are all tabulated, referenced, and other details given in rmlmomco.Rd. These functions and the functions reslife.lmoms() are substantial extensions of the package in the field of reliability analysis.
10. Added the Generalized Exponential Poisson distribution (gep). The L-moments but more importantly, the parameter computations are difficult using derivations in the literature. Consider this dist. as semi-experimental.
11. Added the Barnes Extended Hypergeometric function with exploration of the numerical limits in the context of GEP implementation.
12. BUG FIX: quakap(), for f=1 and "next" command was missing in an if().
13. Removed lmomsf01() never could quite get the intended features to work, and it seems no longer appropriate to leave this experiment in place. It is archived in inst/legacy.
14. Reduced the DESCRIPTION by 24 percent yet added more details.
16. Added slmomco() to provide a survival function now that reliability/lifetime features are present.
17. Added to pwm.ub.Rd additional proof of sample PWM computation reliability after an inquiry by J.M. Miller found inconsistencies in other literature. I.E. DOI = 10.1002/joc.3887 (Beguer'{i}a1 et. al, ... SPEI ..., eq. 3) and an error on the SPEI website (May 2014). Well done J.M. Miller!
18. Added plotradarlmr() to make radar plots of L-moment ratios. Occasionally in past 5 years some users have asked for a way to "see" higher into L-moment dimension that provided by plotlmrdia(). However, new request for a radar plot in of itself has been made.
19. Added Gumbel reduced variates (prob2grv(), grv2prob()) and logistic reduced variates (prob2lrv(), lrv2prob()).
20. Added sentiv.curve() for construction of sensitivity curves.

Version 2.0.1--March 14, 2014

1. BUG FIX: quakap() hit an incorrect stop() because of the absence of a "next" associated with the conditional: H <= 0 & G >= 0 when nonexceedance probability was F=0.
2. Added the "force.exact" (default TRUE) and "nsim" arguments to lmoms.bootbarvar(). It seems that numerical problems are firmly occurring in matrices at about a sample size of 50. So a hardwired threshold hold between the exact analytical and simulation-only estimates of the variances is set at 40. This can be superseded by force.exact---when simulation is used only the observed L-moments and the variances via simulation are reported. The much lengthier output results when the exact method is used are set to NA.
3. According to Daniel Wollschlaeger, the Marcum Q function can be computed by marcumQ <- function(a, b, nu=1) { pchisq(b^2, df=2*nu, ncp=a^2, lower.tail=FALSE) } where the nu=1 makes it the MarcumQ1 function associated with the Rice and the Kappa-Mu distributions. Use of this function would simplify some code and might have numerical advantages---or might not, testing is needed.
4. BUX FIX (mostly enhancement): x2xlo() needed some conditioning to handle the logical situation of a lower threshold for which there are not data below that threshold and also the opposite condition of no data above the threshold. Added an echoing of the threshold to the returned listed as in application, this is useful.
5. Added the Student t (3-parameter) distribution ("st3") by request from Amaranthe R. Biessen. This distribution made an appearance in my book but had not actually been implemented. Amaranthe is credited for providing the polynomial approximation of Tau4 as a function of Nu and Tau6 as a func. of Tau4. A suggested research topic would be the comparison of the ST3 to the AEP4 as these both handle symmetry and Tau4 > Kappa dist.
6. Extended documentation and utility functions to support the st3 distribution. These are: are.par.valid.R, check.pdf.R, dist.list.R, par2cdf.R, par2lmom.R, par2pdf.R, par2qua.R, prettydist.R, vec2par.R, are.par.valid.Rd, dist.list.Rd, par2lmom.Rd, vec2par.Rd.
7. Slight adjustments to lmoms.bootbarvar.Rd to eliminate margin protrusion.
8. Added the ghosting variable to x2xlo(). The feature became evident when WHA was experimenting with trying to track a third variable, such as the year of data collection, as the sample is split between those "in" and those "out." This is for convenience only but enormously useful to have.
9. Minor revision to parcau.Rd.
10. Added the Slash distribution, which uses trim=1 TL-moments.
11. Added the Govindarajulu distribution and included a polynomial to approxi- mate the relation between tau4 and tau3 (see examples in lmomgov.Rd).
12. Added the Govindarajulu to plotlmrdia() and lmrdia() and updated references in both of those functions.
13. Documentation tweak in lmomgld.Rd.
14. Updated references in all of the AEP4 Rd files.
15. Cleaned up spurious (inapplicable) \details{} in parcau.Rd.
16. Removed the use of factorial() in theoTLmoms() and replaced with a combin- ation of exp(lgamma()) with the proper +1 to the argument.
17. Cleaned up Rd cross links for GLO distribution---a TODO is to do similar and audit the cross links for all of the distributions in the very early release(s). Some consistency is missing.

Version 1.8.1--January 27, 2014

1. Added extensions to dat2bernqua() to use alternative support of the distribution based on the extreme order statistics and two references added. Numerical exploration of this new feature is needed. Expanded the function to handle the Kantorovich and Bernstein polynomial methods. Extended the documentation.
2. Added lmoms.bernstein() and started a paper involving it.
4. Added pfactor.bernstein() for a smoothed but not regressed estimate of the optimal p-factor with various controls by the function arguments. This is a complementary function to the Berstein-like smoothing. An example shows how to potentially use pfactor.bernstein() using uniroot() for direct estimation of the p-factor by optimization.
5. Major topical indexing initiated by request of Amaranthe R. Biessen. All Rd files modified slightly, sorry, but the results are nice.
6. Slight shortening of DESCRIPTION.
7. Fixed a misspelling of a list attribution in lmoms.bootbarvar.Rd.

Version 1.7.9--December 3, 2013

1. BUG FIX: Problems with L-skew <= 0 for parln3(). The 3-parameter log- normal distribution is not valid. A warning is now triggered and suggestion to reverse the data, Y <- -X, so as to get L-skew > 0. Then re-reversing would be needed: e.g., -qualn3(1-nonexceeds(), LN3) for parameters parln3(lmoms(Y)) instead of parln3(lmoms(X)) [failure]. Special thanks to Daniel Eilertz for discovering the problem.
2. New Data Added: The TX38lgtrmFlow.RData was added to the package. These L-moments and estimated variances of annual mean streamflow for 35 long-term streamgages in Texas discussion in a cited USGS SIR.
3. Added pp.f() and pp.median(), which support median rankit estimation of the probability distribution of an order statistic. These are included to round out plotting position operations, although the median is arguably already available using the pp(..., a=0.3175).
4. BUG FIX: Another return() was needed for paraep4() in order to properly fall back to pure Kappa distribution if below the lower bounds of the AEP4. Thanks to Amaranthe R. Biessen for the discovery. In turn, this prompted me to make changes in 5 and 6 described below.
5. Updated the citation to my CSDA paper on AEP4 in all the aep4.Rd files.
6. Added quaaep4kapmix(): A continuous mixture between the AEP4 and the Kappa distributions. The AEP4 is exclusive if Tau4 above GLO line (upper bounds of the Kappa), and the Kappa is exclusive if Tau4 below the lower bounds of the AEP4. A prorated mixture based on Tau4 in the over- lapping parameter space of the two distributions is used. This idea was in the cover letter on my CSDA paper submission but was outside the scope of it (Asquith, W.H., 2014, Parameter Estimation for the 4-Parameter Asymmetric Exponential Power Distribution by the Method of L-moments using R, Computational Statistics and Data Analysis, v. 41, pp. 955--970, http://dx.doi.org/10.1016/j.csda.2012.12.013).

Version 1.7.8--July 5, 2013

1. BUG FIX: Problems with kappa == 0 condition for quagpa() and pdfgpa() resolved. Special thanks to Jona Lilienthal for discovering the bug in pdfgpa().

Version 1.7.7--May 13, 2013

1. Added dat2bernqua(): The empirical quantiles through Bernstein polynomial.
2. Stripped tildes for nonbreaking spaces in LaTeX, which are not used in the Rd format: IRSrefunds.by.state.Rd Lcomoment.Lk12.Rd Lcomoment.Wk.Rd Lcomoment.coefficients.Rd Lcomoment.correlation.Rd Lcomoment.matrix.Rd cdf2lmom.Rd gini.mean.diff.Rd lcomoms2.Rd sen.mean.Rd.

Version 1.7.6--May 13, 2013

1. Spelling corrections to DESCRIPTION that were not passing CRAN checks.

Version 1.7.5--May 10, 2013 (never released, see version 1.7.6)

1. BUG FIX: Revision to unbiased correction on product moment kurtosis. An incorrect formula exists in a source originally used to build the function. This has been corrected and numerous comments in the source code point to several sources and shows consistent results now. Much thanks to Sergio Gomez for discovering the bug and assisting in reference track down. Also, added the "excess" kurtosis outputs as apparently Sergio Gomez and other practitioners in his discipline have interest in kurtosis as it differs from the Normal distribution. The two references in the pmoms.Rd are correct and match each other computationally.
2. Further reductions in R CMD check --timings in the following Rd files: cdfgld.Rd is.gld.Rd lmomTLgld.Rd lmomsf01.Rd quagam.Rd quagld.Rd tlmrcau.Rd tlmrexp.Rd tlmrgev.Rd tlmrglo.Rd tlmrgno.Rd tlmrgpa.Rd tlmrgum.Rd tlmrnor.Rd tlmrpe3.Rd tlmrray.Rd theoLmoms.max.ostat.Rd dist.list.Rd.
3. Clarified some messaging associated with an error trap for Tau4 plot- ting above AEP4-max(Tau4) and Kappa distribution NOT fit instead.
4. Documentation tweaks to keep right margin incursion of the PDF manual. gen.freq.curves.Rd pdfwei.Rd pwmLC.Rd pwmRC.Rd vec2lmom.Rd z.par2qua
5. Prof. Ripley remarked that the DESCRIPTION of copBasic was too long. So following that critique, DESCRIPTION of lmomco has been contracted.

Version 1.7.5---March 30, 2013

1. Revisions to truncated exponential distribution both to methods of computation as well as documentation. Actually, a major rebuilding was needed as the limiting conditions of L-CV = 1/3 and L-CV = 1/2 were not properly achieved.
2. BUG FIX: vec2lmom() operated incorrectly when trying to build L-moment objects having only one or two moments, which should have been caught years ago: e.g. vec2lmom(c(1)) or vec2lmom(c(1,3)).
3. lmoms.bootbarvar() now has an argument to early-exit if inversion of the variance-covariance matrices is not desired.
4. Added lmomcoNews() and lmomcoBook() to view the NEWS file and the ERRATA for my book ISBN 978-1463508418.
5. Moved the ChangeLog to NEWS to support the function in number 4.

Version 1.7.4---February 15, 2013

1. Added .Rbuildignore in the top-level directory so that the directory containing legacy .R and .Rd files for deprecated functions is ignored. Prof. Brian Ripley sent a request to do this so that the legacy *.Rd file are not "seen" by the R building process. So WHA responded accordingly.

Version 1.7.3---January 28, 2013

1. BUG FIX: Improper use of print() instead of warning() in check.fs.R.
2. Added f2flo(), flo2f(), and x2xlo() to support conditional probability conversions when a fraction of the left end of the distribution is removed as in the treatment of zero values when analyzing the distribution of the logarithms of a random variable.
3. Added f2fpds() and fpds2f() to support partial duration series analysis.
4. Added the Tau34-squared test for Normality by Harri and Coble (2011). Email communication during the last week of January 2013 with Dr. Adrian Harri reinforces the preference of Harri and Coble (2013) recommended that the "T34-squared" test be preferred for general application. WHA agrees. The general example code for tau34sq.normtest() is capable of reproducing, within expected rounding tolerances, Harri and Coble (2011, table 1). As a result, it appears as though general validation of tau34sq.normtest() has been made. Let us name the test the "Harri-Coble Tau34-squared Test for Normality."

Version 1.7.2---November 16, 2012

1. Documentations to speed-up overall examples for the CRAN: are.pargld.valid.Rd, cdfgld.Rd, man/lmomgld.Rd, man/pargld.Rd, man/pdfgld.Rd, man/pdfkmu.Rd, man/pdfwak.Rd, and man/quagld.Rd. And DESCRIPTION reworked modestly.

Version 1.7.1---October 30, 2012

1. Added lmoms.bootbarvar() for computation of the exact bootstrap mean and variances of L-moments (uncensored or trimmed).
2. Added the "Kappa-Mu" distribution with the abbreviation "kmu".
3. Added the "Eta-Mu" distribution with the abbreviation "emu". Yacoub, M.D., 2007, The kappa-mu distribution and the eta-mu distribution: IEEE Antennas and Propagation Magazine, v. 49, no. 1, pp. 68--81.
4. Added aliases to expect.min.ostat() and theoLmoms.min.ostat() respectively in expect.max.ostat.Rd and theoLmoms.max.ostat.Rd to support inclusion for functional dispatchers for expectations of minimum order statistics and theoretical L-moment computation using such expectations. Support for these computations using maximums of order statistics were already present and generalized enough for easy extension to left-hand side of distribution-based computations. These changes were necessary to support L-moment computation for the bounded-below-by-zero, 2-parameter distributions of the Kappa-Mu and Eta-Mu (see 2 and 3 above).
5. Minor refinements to error trapping to NA values for L-moments in theoLmoms.max.ostat.R following extensive testing of computations using minimum order statistic expectations compared to maximum order statistic expectations using the Kappa-Mu distribution.
6. Added the cdf2lmom() and cdf2lmoms() functions for computation of L-moments from numerical integration of the cumulative distribution function. cdf2lmoms() has a special enhancement (flexibility) that permits the user to specify the r-th order L-moment starting point. Mainly this has been added so that integration of the quantile function for the mean can be bypassed. The cumulative distribution function is used for r > 1. It is often the case the quantile function results from integration of cumulative distribution function and there can be some difficulties with numerical limits. Frequently, experts in particular distributions publish closed-form or semi-closed-form equations for estimation of the mean. The users are then free to use these instead and save computational time.
7. BUG FIX: pargev.R has an error for L-skew < -0.97, the Newton-Raphson method was being short circuited by an if-statement. Bug discovered by Ross Woods when comparing lmomco sources to Hosking FORTRAN. Correction verified by Hosking's FORTRAN as well as sources of lmom package and numerical tests.
8. Added KMU_lmompara_bykappa and EMU_lmompara_byeta dataframes to the .lmomcohash to facilitate operations with the Kappa-Mu and Eta-Mu distributions. These tables were double checked through some careful reanalysis following further improvements to CDFs of each distribution.
9. Added an example to derive a polynomial approximation for the L-skew and L-kurtosis relation of the Rice distribution within the Examples section of lmomrice.Rd.
10. Added pwm.beta2alpha() and pwm.alpha2beta() functions to facilitate potential alpha-pwm derivations involving the Marcum Q-function or Yacoub integral for the Kappa-Mu and Eta-Mu distributions.

Version 1.6.2---July 16, 2012

1. Included strategic dontrun{} directives in the examples of lmomgld.Rd, paraep4.Rd, parTLgld.Rd, pargld.Rd, and qua.ostat.Rd, which resulted in a 60-percent reduction in elapsed time of R CMD check --timings on one of my platforms. (Trying to help out the CRAN check timings facility.)
2. Revisions to cdfgum.Rd, cdfrevgum.Rd, pdfgum.Rd, and pdfrevgum.Rd to make equations more consistent with code as well as my book. The book had some errors (see inst/ERRATA*.txt of this package).
3. Code cleaning in pdfgum.R and pdfrevgum.R for more consistency with documentation---note a bug fix.
4. Added return of the product moments for the distribution of the quantile for qua2ci() so that a simple squaring of the returned standard deviation could return the variation of the prediction.
5. Added passage of . . . (three dots) argument to plot() within gen.freq.curves().
6. Added better handling of the estimated parameters for the error distribution in genci(), which now places them as individual lists within an environment that is returned.
7. Code cleaning on genci.R and documentation clarification in genci.Rd.
8. Enhancement to gen.freq.curves() so that, if one has a priori estimates of the confidence limits, one can computed discrete counts of simulated frequency curves (at a given nonexceedance probability) inside and outside the estimated limits. This feature could be used in the evaluation of the choose error distribution (edist) in the function genci().

Version 1.6.1---May 10, 2012

1. Enhanced error trapping on integration failures in theoTLmoms(). The function now abandons operation should any of the integrations for the rth L-moment fail for reasons such as divergent integral or round off problems. The function returns NAs for all L-moments.
2. Added the tabulated lookup of initial guesses for K and H of AEP distribution in the .lmomcohash in sysdata.rda.
3. BUGFIX: lmom2par() did not route the AEP correctly.
4. Renamed AEP to AEP4 throughout code to make syntactic room for a 5-parameter AEP should it ever be implemented.
5. Enhancement: paraep() now returns NA for the parameters should the sample L-kurtosis violate the lower bounds of the L-skew and L-kurtosis relation as defined by a polynomial approximation. This polynomial has not previously been published.
6. File renaming. All aep files renamed to aep4 to make eventual room for 5-parameter Asymmetric Exponential Power distribution.
7. Overhaul of vec2lmom() and vec2TLmom() to support arbitrary lengths of input L-moments or L-moment ratios (or TL versions) in the input vector. In fact, vec2TLmom() now dispatches to vec2lmom(), which has become more generalized. lmorph() required some adjustments as well.
8. Overhauls in step 7 required removal of a stop() in vec2TLmom(), which likely should note have been in there anyway.
9. Added the PDF of the Weibull in pdfwei.Rd.
10. Documentation tweaks to pdfgld.Rd and pdfrevgum.Rd including addition or changes to the dontrun{} directives.
11. Enhanced genci.R/Rd to return more details about the fitted error model as well as returning NA for the lower and upper limits if failure in fitting of the error distribution occurs. Documentation tweaks to primarily enhance the example including the GNO and now the new AEP4 distributions and wrapping all in dontrun{} directive.
12. Enhanced qua2ci() to return NA for failure on the upper and lower limits and trapped a return of NA for the parameters from the fitted error distribution.

Version 1.5.1---April 15, 2012

1. Documentation tweaks
2. Added the Asymmetric Exponential Power distribution ("aep") with direct use of pgamma() and qgamma() functions of R for CDF and QDF implementation. The parameter estimation routines look ok, but should be considered experimental. The author needs to work on a table of K,H ---> T3,T4 mappings to add the optimizers in the return direction.
3. Added the "minF" and "maxF" arguments to theoLmoms() and theoTLlmoms() so that one can try to get past divergent integrals should they occur using the defaults. These were added as the far-far tails of the AEP4 distribution do not behave well. Testing against the AEP4 with minF=0.00001 and maxF=0.99999 seems to nearly hit the true L-moments from lmomaep4().
4. Added the "#" sign in front of Package lmomco (1.5.1) loaded when the library is loaded. This is done so that users running a standard out redirection are able to embedded "#" as comment lines in the output and thus ease the burden in post processing by skipping all lines beginning with the prompt or the "#" sign.
5. Correction to clearforkporosity.Rd.

Version 1.4.5---April 30, 2012

1. inst/doc/Introduction.Rd permanently removed from package and from versioning control system. The *.Rd was interfering with latest R versions in the R CMD check, which I could not identify with my installed R versions.

2. Major revision to inst/doc/references.txt. This file is now a dump of references used in my book. I figure that these might be useful to someone. The book is available royalty free:

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: First edition, CreateSpace, ISBN 978-1463508418, 344 p. http://www.amazon.com/ Distributional-Statistics-Environment-Statistical-Computing/dp/ 1463508417

Version 1.4.4---April 30, 2012

1. Added the Laplace distribution ("lap").
2. BUG FIX: tlmrgpa.R did not declare T5 and T6 vectors.
3. DOC FIX: theoTLmoms.Rd, tlmrgpa.Rd, USGSstaXXXXXXXXYYYY.Rd, amarilloprecip.Rd, canyonprecip.Rd, claudeprecip.Rd, herefordprecip.Rd, tuliaXXprecip.Rd, vegaprecip.Rd DrillBitLifetime.Rd, pmoms.Rd, plotlmrdia.Rd, pdfgld.Rd, pdfgno.Rd, cdfnor.Rd

Version 1.4.3---August 30, 2011

1. BUG FIX: Added the "checklmom" argument to parTLgld() and pargld() as part of an check on how the functions of lmomco interact.
2. BUG FIX: pwm.pp() did not fully accommodate user supplied probabilities. Removed the feature for now. Further, some a major bug was introduced in version 1.4.2. This function now appears through testing as shown in the examples for lmomsf01() to now work properly again.
3. BUG FIX: quagno() did not function properly for k values near zero for which the standard normal distribution needed to be triggered.
4. Added lmomsf01(), which computes L-moments given an irregular spacing of nonexceedance probabilities. The bounds for the probabilities are taken as [0,1] for the integration. Linear interpolation on the empirical quantile function is used and extrapolation to [0,1] bounds is made. Testing with GNO simulation shows that this function can help interface with Kaplan-Meier survival curves from the Survival package. Consider the lmomsf01() function experimental.
5. Change the minimum R version in DESCRIPTION so that the deeper compress of the RData files can be supported. The recompressed RData files are: data/IRSrefunds.by.state.RData, data/USGSsta01515000peaks.RData data/USGSsta02366500peaks.RData, data/USGSsta05405000peaks.RData data/USGSsta06766000dvs.RData, data/USGSsta08151500peaks.RData data/USGSsta08167000peaks.RData, data/USGSsta08190000peaks.RData data/USGSsta09442000peaks.RData, data/USGSsta14321000peaks.RData data/amarilloprecip.RData, data/canyonprecip.RData data/claudeprecip.RData, data/herefordprecip.RData data/tulia6Eprecip.RData, data/tuliaprecip.RData data/vegaprecip.RData

Version 1.4.2---July 21, 2011

1. BUG FIX: The function pwm.pp() did not function quite right through the various conditionals. In the process the function was extended to handle user supplied nonexceedance probabilities. The function was also optimized a bit.
2. Extended the tlmrXXX() functions to compute tau5 and tau6.

Version 1.4.1--July 7, 2011

1. Added "paracheck=TRUE" argument to the quaXXX() functions and vec2par(). This was added to bypass the validity checks in terms of L-moments so that the quantile functions remain accessible when TL-moment computations are desired. This argument had long existed for the GLD distribution because the parameter range changes depending on the TL-moment trimming level. These paracheck changes are made now in preparation for TL-moment computation of trimmed distributions.
2. Added tlmrcau(), tlmrexp(), tlmrgev(), tlmrglo(), tlmrgno(), tlmrgpa(), tlmrgum(), tlmrln3(), tlmrnor(), tlmrpe3(), and tlmrray(). *** TL-moment ratios (tau2, tau3, and tau4) are experimental *** The TL-moment ratios are implemented through use of the theoTLmoms() function that in turn uses numerical integration of the quantile function. The issue in application, which is directly related to paracheck=TRUE, is that the recognized parameter range (validity) of distributions for L-moment computation are expanded during trimming. The tlmrXXX() functions do not currently perform any parameter checking and integration errors might occur, which will require the user to manually control the parameter range through function arguments. Thanks to O.A. Hussien in early July for a TL-moment ratio diagram inquiry. Many of these functions have such diagram construction in their examples.

Version 1.3.6---June 24, 2011

1. Slight changes in DESCRIPTION.
2. Slight changes in Changelog
3. Changes to zzz.Z after the inclusion of NAMESPACE a few months back.

Version 1.3.5---May 14, 2011

1. Added tau34=FALSE to lmomTLgld() for certain research applications of the generalized lambda distribution.
2. BUG FIX: in LaguerreHalf() and pdfrice(). Both of these functions called besselI() [built-in to R] using an argument 'n' for 'nu' (a partial argument match). Unreleased versions of R 2.14 on some platforms were showing a warning about partial match. The LaguerreHalf() and pdfrice() are now updated internally (no Rd changes needed).
3. BUG FIX: in TLmoms(). This function was using a partial argument match on a call to TLmom(). The argument was 'sort' but 'sortdata' was needed by TLmom(). Again, this was an unreleased R 2.14 on some platforms reporting the warning.

Version 1.3.3---April 3, 2011

1. BUG FIX: in a "<= test" in cdfln3().
2. BUG FIX: in plotlmrdia() pertaining to the Cauchy distribution.
3. Added lmrdiscord() for computation of the discordance of triplets of the first three L-moment ratios.

Version 1.3.4---April 15, 2011

1. Added lmomco/NAMESPACE and export of all *.R functions in the R directory. For example, with out the library(lmomco) operation, an lmomco function can be accessed by examparametersWOlibrary <- lmomco:::vec2par(c(0,1), type="nor") for a standard Normal distribution parameter set.
2. Added "lmrdigits" argument to lmrdiscord().
3. Title change of the entire package to a more logical ordering of terms.

Version 1.3.2---March 15, 2011

1. Added the passage of the ... argument in lmom2par() to all the parXXX() functions. In particular, this was needed to permit zeta=?? to be passed into the parln3() function. It should be quite harmless to now pass ... to the other parXXX().
2. Added the inst/CITATION and inst/WARRANTY files

Version 1.3.1---March 6, 2011

2. Tweaks to genci.Rd, parTLgld.Rd, pdfwak.Rd, plotlmrdia.Rd, pwm.Rd, and pwm.ub.Rd.
3. Tweaks to USGS*peaks.Rd and USGSsta06766000dvs.Rd as escaping of underscores in items is evidently no longer needed.

Version 1.2.4---February 13, 2011

1. Added limiting condition of Cauchy to plotlmrdia() and lmrdia().
2. Added "as.list" argument to vec2pwm() so that it can return both PWM data structures support in the package. This was done in preparation of example computations for comparison of pwmLC() (by flipping) to pwmRC() to support left-tail censored PWMs.
3. BUG FIX: for pwmRC(), which previous did not support nmom number of A-type PWMs as the documentation states and need requires.
4. Added pwmLC() for support of left-tail censored PWMs. Presently, there are no distributions supporting left-tail directly. It is suggested for now to rely on variable flipping and use the right-tail censoring features.

Version 1.2.3---February 1, 2011

1. Added the return of the support of a fitted Kappa to parkap.R/Rd. This facilitates mimicry of parts of Dupuis and Winchester (2001) in J. Statis Comput. Sim., v.71] easier. (WHA is considering returning the support for other distributions in the parXXX() functions.)
2. Re-engineered the pargld() and parTLgld() functions to return the best solution based on a good enough minimization of RMSE between Tau3 and Tau4 and then sorting based on difference in Tau5. Other possible solutions are returned in a new entry "$rest". 3. Added Kumaraswamy, log-Normal3, and Rice to pretty.dist.R. 4. Added Tau6 to lmomgld() and lmomTLgld() in preparation to adapt pargld() and parTLgld() to returning smallest DeltaTau5 or DeltaTau6. 5. Major overhaul of lmomTLgld() and lmomgld() to support the generalized equation for arbitrary level of L-moment and TL-moments with arbitrary left and right trimming. Version 1.2.2---November 29, 2010 1. Revisions to lmomrice() to kick over to return of Normal distribution L-moments for high and very high SNR. Also, kick over to return of Rayleigh distribution L-moments for very low SNR. 2. Fixed parrice() from stop()ing and switched to warning() if LCV is out of range. Version 1.2.1---November 20, 2010 1. Revisions to the DESCRIPTION file. 2. Revisions to SysDataBuilder.R to better canvas LCV, SNR, and G pairings to the Rice L-moment to parameter lookup table. 3. Added the LaguerreHalf.R/Rd to support variance estimation of a set of Rician parameters so that hand off to Normal distribution functions for high SNR can be made. 4. Revisions in parameterization of the Rice distribution over the confusion caused by having several different definitions of the signal-to-noise ratio SNR in the literature. Also, if nu=0 for the Rice, then behind-the-scenes generation of Rayleigh parameters with xi=0 is made and the Rayleigh distribution functions are used. If SNR > 24 for the Rice, then behind-the- scenes generation of Normal parameters is made and the Normal distribution functions used. This SNR threshold was determined by careful evaluation of the LCV, Tau3, Tau4, SNR, and G used in RiceTable generation in the file inst/doc/SysDataBuilder.R. The evaluation looks and numerical problems such as Tau3 and Tau4 breakdown as Normal distribution is approached and filtering for sub Rayleigh solutions. Finally, if SNR > 52 for the Rice, then the use of the Laguerre polynomial for variance estimation to feed to the Normal is bypassed and the SNR used in place of sqrt(pi/2) * LaguerreHalf(-SNR^2/2) because: sqrt(pi/2)*LaguerreHalf(-53^2/2) \approx 52 == 52.00962 sqrt(pi/2)*LaguerreHalf(-53^2/2) \approx 53 == 53.00943 sqrt(pi/2)*LaguerreHalf(-54^2/2) \approx 54 --> Inf (Bessel breaks down) Version 1.2.0---November 14, 2010 1. Trapping NULL values for xleg and yleg in plotlmrdia.R, which was discovered in giving a presentation concerning the diagrams. 2. BUG FIX: for incorrect "gum" references in are.parray.valid.Rd, pdfray.Rd, quaray.Rd, and lmomray.Rd. 3. BUG FIX: for incorrect "kur" dispatch in par2lmom.R and in par2qua.R. 4. Added the Rice distribution ("rice") functions and the SysDataBuilder.R and of course the now present R/sysdata.rda because Rice distribution uses tabular lookup and interpolation for parameter estimation. The theoLmoms.max.ostat() function is used to compute the L-moments of the Rice distribution. The sysdata.rda contains the .lmomcohash hash that at least contains "RiceTable" (LCV, SNR, G) and "RiceT3T4" for construction of L-moment ratio diagram using the TAU3 and TAU4 values for various distributions (see parrice.Rd). ** CONSIDER RICE DISTRIBUTION EXPERIMENTAL ** For the author's part, much original reading, coding, and testing has been accomplished concerning the Rice. 5. Added expect.max.ostat.R/Rd for the computation of the expected value of a maximum order statistic (although the function is generalized for other order statistics). The function is added to provided for the theoLmoms.max.ostat() function. 6. Added theoLmoms.max.ostat.R/Rd for the computation of theoretical L-moments of a distribution using a system of maximum order statistic expectations. This function is used in L-moment computation for the Rice distribution. Version 1.1.0---October 31, 2010 1. Deprecated lmom.test*.R/Rd and lmom.diff.R/Rd and moved them to inst/legacy. These were simply no longered needed and were originally created for development purposes anyway. Also lmom.references.Rd is now in inst/legacy. 2. Added the Kumaraswamy distribution ("kur") functions and other required functions. This distribution is bounded on (0,1) and is a semi-beta replacement with very convenient distribution functions that are not dependent on the Beta function family. Additions to the supporting functions provided the discovery of missing ln3 as described below. 3. Added the 3-parameter log-Normal distribution ("ln3") to dist.list.R/Rd. 4. Added the 3-parameter log-Normal distribution ("ln3") to lmom2par.R/Rd. 5. Fixed text running over the right margin of the user manual for cdfrevgum.Rd, genci.Rd, lmomsRCmark.Rd, parrevgum.Rd, pdfrevgum.Rd, plotlmrdia.Rd, pwm.Rd, pwmRC.Rd, quarevgum.Rd, and sen.mean.Rd. Version 1.0.01---August 10, 2010 (version "1" because of censoring support) 1. Added lmomsRCmark() and fliplmoms() for right-tail censoring and left-tail censoring support, respectively (somewhat). Additional examples added to document how to do right-tail censoring (see lmomsRCmark()) and left-tail censoring (see fliplmoms()). 2. Additional example in Lcomoment.Wk() to show how this function can be use to compute weight factors representing the relative contribution of each sample order statistics in the computation of a given order of L-moment. The example shows how to double check output of lmoms(). Thanks to the anonymous poster. 3. Very minor tweaks to documentation as R version change identified some formatting problems. Version 0.97.2---October 27, 2009 1. Tweaks to lmomgld.Rd, prob2T.Rd, z.par2cdf.Rd, z.par2qua.Rd in preparation for new release of R. Version 0.97.1---July 18, 2009 1. Tweak in documentation in is.ray(). 2. BUG FIX: in parray() and lmomray(). 3. Added the 3-parameter log-Normal distribution ("ln3") by referencing the algorithms in the lmom package by J.R.M. Hosking. Remember that the 3-parameter is an alternative parameterization of the Generalized Normal distribution ("gno"). Version 0.96.3---February 20, 2009 1. Added the par2vec() function (added to aid feeding of parameters into functions of the lmom package by J.R.M. Hosking). 2. Added the hlmomco() function to compute the hazard function or hazard rate of distributions. 3. Added the zzz.R file that holds operations to perform when the lmomco package is loaded. I have a message printed to terminal on loading of the package. This feature needed the packageDescription() function from the utils package. So the Depends: section of DESCRIPTION is now populated accordingly. 4. Tweaks to perhaps two dozen Rd files in preparation for the R-based parsing in the R +2.8.x series in which previous LaTeX loop holes have been shut. Version 0.96.2---November 17, 2008 1. Tweak to quawak() for condition of F=1. 2. Added the "sort=TRUE" argument to pp() so that sorted (default and historical) and unsorted plotting positions could be returned. An appropriate example was added. Also strengthened the condition of the plotting-position coefficient range---have restricted the coefficient between Weibull (a=0) and Hazen (a=0.50) so "a \in [0,0.5]." The pp() function uses the rank() function, which has specific settings to handle tied data. For the pp() function, the ties.method="first" method is used for rank(). 3. Fixed Lcomoment.matrix() to return NA in the off diagonal elements if the moment order is 1. Version 0.96---September 15, 2008 1. Added support for known xi in parameter estimation in pargpa() and pargpaRC(). 2. BUG FIX: cdfgam() was not properly vectorized. 3. Added the Rayleigh distribution as abbreviation "ray". 4. Added the attributes() function to strip parameters names from the parameter vector within ALL the lmomXXX() functions. Unsightly, L-moments were otherwise being returned. 5. The example in is.revgum() did not actually call the function--does now. 6. Added the "quiet" argument to genci(). 7. Added lcomoms2() to make it much easier to access bundles of sample L-comoments values. Output of---that is, return of---the matrices or diagonals can be specified. Version 0.95---August 23, 2008 1. Warning message tweak (capitalization) in sen.mean(). 2. Added names() to the parameters in the$para field of the parameter list returned by the parXXX() functions. These names parallel the Greek letters used in the formal mathematical definitions of the distributions in the package documentation and any additional write ups that your humble author might make. The idea was derived from the evir package that provides maximum likelihood estimation for the GEV distribution. Your author admits that these names should have been added long ago.
3. Added names() to the parameters in the $para field of the parameter list returned by the vec2par() function. 4. quakap() and quawak() now return Inf (or -Inf) for appropriate limits as dictated by the values of the arguments. 5. Typo fixed in z.par2qua.Rd. 6. Formally added the data subdirectory and a suite of data files suitable for various exercises with lmomco. Version 0.94---June 6, 2008 0. Documentation tweaks to remove or populated empty sections of check.pdf.Rd, are.parrevgum.valid.Rd, and lmomrevgum.Rd. 1. Added gini.mean.diff(). 2. Added sen.mean(). 3. Harmonic.mean() now strips is.na() values in similar fashion as gini.mean.diff() and sen.mean(). In time such operations are expected in other functions. Several users have commented on original lack of x <- x[! is.na(x)] filtering in other functions. Version 0.93.4---April 28, 2008 1. parrevgum() and lmomrevgum() had a str() on the L-moments and produced output---left over from original development. 2. BUG FIX: par2qua, par2cdf, and par2pdf did not properly dispatch for the reverse Gumbel distribution. Fixed. 3. Added the pwm2vec() function because there was an lmom2vec() already. 4. BUG FIX: Small near zero gamma parameter for pdfpe3() was triggering an Inf error on the gamma() function. This is now trapped and the Normal distribution being used as required. 5. Added prettydist() to produce full distribution names from the abbrev- iations, such as returned by dist.list(). 6. Added clearforkporosity.R data set. 7. BUG FIX: For the UMVE of standard deviation by pmoms() the ratio of two gamma() functions blows up for large sample sizes. Therefore, computations are now performed in log-space. Version 0.93.3---February 2, 2008 1. Added dlmomco() to complete the quartet of R-like named distribution accessing functions: dlmomco(), plmomco(), qlmomco(), rlmomco(). 2. BUG FIX: are.pargpa.valid() mistakenly did not trip failure for K == -1. Version 0.93.2---December 19, 2007 1. BUG FIX: lmom2pwm() did not properly trap conditions that should result in the return of NULL. Thanks to Roberto Ugoccioni for discovery and for providing a patch. Version 0.93---December 12, 2007 1. BUG FIX: prob2T() and T2prob() error traps were not sufficiently vectorized. 2. Documentation error fixed on equation for pdfcau(). Version 0.92---November 20, 2007 1. Documentation tweaks. 2. Added pdfkap() and pdfwak() following written communication with J.R.M Hosking. 3. Added qua.ostat() for computation of the quantile distribution of an arbitrary order statistic given a sample size and parameters of a fitted distribution. 4. Added digits=4 and signif() functions for reduction in returned numbers from the lmom.test.CCC() and lmom.diff() functions in response to comments from an anonymous reviewer. 5. Added lmom2vec() for conversion of L-moment object to a simple vector. This function spawned from discussions with an L-moment user who did not use the parameter list model of lmomco functions. Version 0.91---October 24, 2007 1. Refined plotlmrdia(). 2. Added pdfrevgum() and pdfwei(). 3. Documentation fix for cdfrevgum(). 4. Added check.pdf(), which will be an important convenience function for testing the properties of the pdfCCC() functions and the cdfCCC() functions. 5. BUG FIX: on parwei(). Function was unnecessarily querying fifth L-moment when the fifth L-moment is not needed. So one did not have five or more L-moments then parwei() would not work. This was unnecessarily restrictive. 6. Added z.par2cdf() and z.par2qua() to accommodate zero values or other in the building of "blipped distributions" to quote Gilchrist (2000, p. 148). 7. Added umvu.sd to pmoms()---uniformly-minimum variance unbiased estimator. 8. BUG FIX: on quacau(). Function did not return a vector if one of the F values happened to be equal to exactly 0.5. 9. BUG FIX: on are.pargam.valid(). Test did not permit Beta > 0, but mistakenly tested for Beta > 1. 10. BUG FIX: on are.parcau.valid(). Test did not check that Alpha > 0. Version 0.90---October 2, 2007 1. Added the "autolegend", "xleg", and "yleg" arguments to plotlmrdia(). 2. Error in lmrdia.Rd regarding gamma distribution fixed. 3. Error in equation in pwm.ub.Rd fixed. 4. BUG FIX: on pwm.pp(). Why has getting the plotting-position estimator working correctly been a nightmare? I think it is finally correct. Part of the problem is in inconsistencies in nomenclature in the literature as well as your humble author. 5. Correction to math in TLmoms.Rd. 6. Correction to math in parTLgpa.Rd. 7. BUG FIX: on cdfpe3() and a correction made to the documentation. The function did not work for negative skew. Whew! Problem was discovered during development of pdfpe3(). 8. Added probability density functions for cau, exp, gam, gev, gld, glo, gno, gpa, gum, nor, pe3. More to come---in another release. 9. Added par2pdf(). Version 0.88---September 1, 2007 1. Added the prob2T() and T2prob() functions for annual nonexceedance probability and T-year return period conversions. 2. Added the harmonic.mean() function for support of a zero-value corrected computation of this particular statistics. Whereas, this statistic is not L-moment related, it is important in the field of surface-water hydrology and the lmomco package is a convenient place to store the function for the specific needs of your author. Version 0.87---August 1, 2007 1. Added the "xlab" and "ylab" arguments to plotlmrdia(), which provide user flexibility of the naming of each axis. 2. Added the "checklmom=TRUE" argument to parexp(), pargam(), pargev(), parglo(), pargno(), pargpa(), pargpaRC(), pargum(), parkap(), parnor(), parpe3(), parrevgum(), parwak(), and parwei() to bypass the internal call to are.lmom.valid(). This feature was added after discussion with Hosking about a simulation study of the Pearson Type III distribution. One can simulate values and compute L-moments that fail the tau4/tau3 inequality and parameters can not be estimated. However, because that distribution has only three parameters, we do not care whether the tau4 is actually viable. Invalid L-moments can manifest with the Pearson Type III when the sample size is small and the standard deviation and skew magnitude are large. Version 0.86---July 23, 2007 1. Added the pmoms() function, justified in part by revisions Pearson Type III. 2. Cleaned up the documentation for the Pearson Type III to better reflect the meaning of the parameters. Re-implemented cdfpe3() in more native R from Hosking's FORTRAN. This function is now broken from the FORTRAN code base. The original cdfpe3() of this package is now renamed to cdfpe3.original() and is not loaded with the package, but resides elsewhere in the directory structure. This reworking was spawned by an inquiry from R.R.P. van Nooyen in July 2007. 3. BUG FIX: on parpe3(). Condition of negative L-skew was not implemented correctly---fixed and rigorously tested using the pmoms() function. Version 0.85---July 14, 2007 1. Textual fixes to documentation of qua2ci() and warning message change in qua2ci(). 2. BUG FIX: on pwm.ub() by fixing pwm.pp(). I had misinterpreted Hosking's argument call in his samlmr FORTRAN function. The unbiased PWMs were certainly not being correctly computed. I gutted the code entirely and now rely on R's choose() to get binomial coefficients. The much cleaner code no longer shares structure with Hosking's function. The changes in pwm.ub() and pwm.pp() caused a cascade of adjustments to pwm.gev(). Each of these functions now returns a more logical list structure containing the betas in a similar fashion as lmoms(). Some of the last vestiges of the original lmomco package (preCRAN) are now updated. The new list structure supports an arbitrary number of moments now. This activity was spawned by the addition of pwm(), which in turn was spawned by the addition of pwmRC() described in the next Item. In fact pwm.ub() now dispatches to pwm(). Also if A=0 and B=0 in pwm.pp(), then a dispatch is made to pwm(); this mimics Hosking's ideas of implementation. 3. Added the pwm() function. The function provides a nice neat and clean code structure which provides a simple implementation example of PWM computation. I used the logic structure of pwm() to test and in turn implement the more complex logic of the pwmRC() function. Further the pwm() name shares a style with the lmoms() name, but I can not decide whether pwm() should really be pwms(); note the plural "s." I think I will stay with the shorter version and leave lmoms() alone for legacy reasons. 4. Added the pwmRC() function. The RC stands for right censored; that is values larger than some value are not observed. The function computes the A-type and B-type Probability-Weighted Moments and the censoring fraction given a sample data set and an upper threshold. This new function can be used to compute B-type PWMs and hence B-type L-moments for the Reversed Gumbel and Generalized Pareto Distributions. 5. Added the lmomgpaRC() and pargpaRC() functions. These compute the B-type L-moments from the parameters of a right-censored Generalized Pareto Distribution, and compute the parameters of a right-censored Generalized Pareto Distribution. The distributions continues to be type "gpa" and implemented in the usual fashion via quagpa() and cdfqpa(). Only the L-moments and parameter estimation functions are separately implemented. 6. Added the cdfrevgum(), lmomrevgum(), parrevgum(), and quarevgum() functions to implement the Reverse Gumbel distribution. 7. Modified the vec2par() function to accept an extra parameter (the last in the vector), which will become the zetas of the Reverse Gumbel ("revgum") and right-censored Generalized Pareto Distributions. 8. Modified the lmom2par() function to accept the "revgum" (Reverse Gumbel) and right-censored Generalized Pareto Distributions through the passage of "..." to the pargpa() and parrevgum() functions. The "..." would be the zeta or right-censoring fraction for each. 9. Adjustments to pwm2lmom() and in a few other locations to return NA for the first L-moment ratio as it does not exist. 10. Adjustments made to par2lmom() to accept "revgum" (Reversed Gumbel). 11. Added the Apwm2Bpwm() and Bpwm2Apwm() functions. 12. Modified lmom.diff() to accommodate both the named L-moment object style and the vector style through a dispatch to the lmorph() function. Version 0.84---May 2, 2007 1. BUG FIX: on genci() related to overwriting the sample size by the length of the nonexceedance probability vector. Fixed and tested. The function was extended to handle the ifail value from qua2ci(). 2. Additional warning message added to qua2ci() when the L-moments of the simulated sample are not valid---likely a cause of a small sample size and a complex (high parameter number distribution), which produces one or more giant magnitude numbers for a simulated quantile. Added the ifail and ifailtext return elements from the qua2ci() function for better processing by the genci() or other calling functions. Also, added the maxlogdiff argument to control whether a simulated quantile is actually retained before the completion sequence of the function is begun. This argument is used to control whether hideously "out-of-whack," which would likely occur for heavy-tailed infinite limit upper tails. Version 0.83---April 10, 2007 0. Further tweaks to documentation. 1. Added callplot and showsample options to gen.freq.curves(). 2. Added plmomco() and qlmomco() as adjuncts to rlmomco() and to better parallel built-in distribution functions of R itself. 3. BUG FIX: on examples in genci() that manifested as the April 2007 release of R approached. Version 0.82---July 13, 2006 0. Further tweaks to the documentation. 1. Word of caution about lack of checking by the function of monotonic increase of par2cdf2() an par2qua2(). 2. Added the qua2ci() function for estimation of confidence limits of quantiles of a distribution using Monte Carlo simulation. 3. It was possible to call are.lmom.valid() with an object from lmoms() without an actual check on the L-moments because length(lmom$L1) == 0 was not checked. The function lmorph() is now used to convert prior to validation.
4. Added the gen.freq.curves() function for plotting randomly generated frequency curves by specifying: sample size, the parent distribution, and the number of simulations.
5. Added the genci() function for generation of lists or data.frames of confidence intervals for a vector of nonexceedance probabilities, a given sample size, and a specified parent using Monte Carlo simulation.
6. Recognition that the quaCCC() functions had been extended into the features provided by freq.curve.CCC() functions. Thus, all freq.curve.CCC() functions were removed from the package.
7. BUG FIX: on F=0||1 probabilities into quape3(). Bug occurred in extension of function to handle a vector of probabilities during development of version 0.7 of this package.
8. lmompe3() did not compute and hence return L-CV---incomplete port from Hosking library. L-CV is returned now.
9. pargam() would return invalid parameters as the specific range of L-moments for a valid gamma was not being checked. This was because of an incomplete port of Hosking FORTRAN library.

Version 0.80---June 20, 2006 0. Further tweaks to the documentation.

1. Warning message added when TAU5 missing on call to pargld() and parTLgld().
2. Added support for user supplied initial guess for pargld() and parTLgld().
3. BUG FIX: on pargev(). The function was broken for TAU3 < -0.80. Bug caused during port from Hosking FORTRAN library. Bug was discovered during tests of parwei().

Version 0.77---May 15, 2006 0. Pertaining to number 1, enhancement to documentation of the L-comoment functions has been made.

1. BUG FIX: on a single conditional in Lcomoment.coefficients(). Function was handling a first-order first argument, but crashing on order evaluation of the second argument.

Version 0.76---May 11, 2006 0a. Further progress on documentation following R-help feedback and my own proofreads. 0b. Adding more examples to the documentation.

1. Added par2cdf2() and par2qua2() for combining two quantile functions into one through minor abilities to control weight factors.
2. BUG FIX: on vec2lmom()---function did not retain NULL for undefined L-moment (because of sample size) prior to calling are.lmom.valid().
3. Plotting-position formula changed in pp.R and substantial documentation added to parallel that in Handbook of Hydrology.
4. Adjusted all parCCC() functions (not including parameter estimation using TL-moments) to support either the lmom.ub() or lmoms() L-moment objects. The new function lmorph() is used for the object conversion.
5. Added the dist.list() function for convenience.

Version 0.75---April 30, 2006

1. Added lmoms(), which in reality dispatches to TLmoms(), but provides a lower case name space and eventually could take the place of lmom.ub().
3. Added the Weibull distribution (wei).
4. Added the random deviate generator rlmomco() given sample size and parameter object.
5. Added the plotting-position formula by pp().

Version 0.7---April 13, 2006

1. Added full vectorization of the quaCCC() and cdfCCC() functions. Previously each function did not handle a vector of nonexceedance probability and quantile values in each respective function.
2. Added "extract" argument to the pargld() and parTLgld() functions.
3. Incorporated endpoint or range checking on cdfgld().

Version 0.6---March 25, 2006 0. Tweaks and corrections to documentation---learning more about LaTeX too.

1. are.par.valid() could not dispatch to Wakeby distribution---fixed.
2. Extension of TL-moments to asymmetry: trimming in either tails is available.
3. Addition of theoLmoms() to compute theoretical L-moments: uses theoTLmoms().
4. Addition of theoTLmoms() to compute theoretical TL-moments using numerical integration of the quantile function. A valuable check on par2lmom() or the lmomCCC() functions.
5. par2cdf() did not dispatch to Generalized Lambda distribution---fixed.
6. Addition of nowarn toggle to vec2par() {implemented therein}, through are.par.valid() via the "..." argument, and each of the are.parCCC.valid() {implemented therein}. This was done so that parameter optimization algorithms could be built on top of the parameter validation checks and cascading warning messages that the user would not care about can be suppressed.

Version 0.5---March 12, 2006

1. Total redesign of pargld() and parTLgld().
2. Adjustments to interface of lmomTLgpa() and parTLgpa() for consistency with the GLD distribution.
3. Major additions to freq.curve.all() (addition of plotting options and more verbose messaging).
4. Speed up of freq.curve.gld() by addition of paracheck=FALSE to quagld().
5. Internal functions to lmomkap() are now defined internal to the function.
7. Improvement to output of lmom.test.CCC() functions.

Version 0.4---February 28, 2006 0. Numerous enhancements to the documentation.

1. BUG FIX: on fourth L-moment of Cauchy distribution in lmomcau().
2. BUG FIX: on absolute value of TAU5 in are.lmom.valid().
3. BUG FIXES on are.pargld.valid().
4. Addition of cdfgld() [stable], lmomgld() [stable], pargld() [experimental].
5. Addition of lmomTLgld() [stable] and parTLgld() [experimental].
6. Addition of lmomTLgpa() [stable] and parTLgpa() [stable].

Version 0.3---January 31, 2006 Initial Release Note that "CCC" in these notes generically reflects the abbreviation of supported distributions such as "gam" for the Gamma distribution.

# Reference manual

install.packages("lmomco")

2.2.9 by William Asquith, 3 months ago

http://www.amazon.com/dp/1463508417/

Browse source code at https://github.com/cran/lmomco

Authors: William Asquith

Documentation:   PDF Manual

Task views: Probability Distributions, Extreme Value Analysis

Imports goftest, Lmoments, MASS

Depends on utils

Suggests copBasic

Imported by copBasic, extremeStat.

Depended on by SCI, SPEI.

Suggested by TLMoments.

See at CRAN