CRAN Task View: Probability Distributions

Maintainer:Christophe Dutang, Patrice Kiener
Contact:Christophe.Dutang at
Contributions:Suggestions and improvements for this task view are very welcome and can be made through issues or pull requests on GitHub or via e-mail to the maintainer address. For further details see the Contributing guide.
Citation:Christophe Dutang, Patrice Kiener (2022). CRAN Task View: Probability Distributions. Version 2022-03-07. URL
Installation:The packages from this task view can be installed automatically using the ctv package. For example, ctv::install.views("Distributions", coreOnly = TRUE) installs all the core packages or ctv::update.views("Distributions") installs all packages that are not yet installed and up-to-date. See the CRAN Task View Initiative for more details.

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:

The maintainers gratefully acknowledge 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 send an e-mail to the maintainer or submit an issue or pull request in the GitHub repository linked above.

Table of contents

Base functionality:

Discrete distributions:

Discrete univariate distributions:

Discrete multivariate distributions:

Continuous distributions:

Continuous univariate distributions:

Continuous multivariate distributions:

Other distributions:

Mixed-type distributions:

Mixture of probability laws:

Random matrices:


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

Moments, skewness, kurtosis and etc:

Random number generators (RNG):


CRAN packages

Core:actuar, copula, distr, fCopulae, gamlss.dist, lmomco, mnormt, mvtnorm, PearsonDS, VGAM.
Regular:AdMit, agricolae, ald, bayesm, BenfordTests, betafunctions, bgumbel, BiasedUrn, Bivariate.Pareto, BivarP, BivGeo, bivgeom, bmixture, BMT, bridgedist, CaDENCE, cbinom, chyper, CircStats, circular, cmvnorm, coga, CompLognormal, Compositional, compositions, Compounding, CompQuadForm, condMVNorm, copBasic, cort, crch, csn, Davies, degreenet, Delaporte, dgumbel, dirmult, disclap, DiscreteInverseWeibull, DiscreteLaplace, DiscreteWeibull, distcrete, distr6, distrDoc, distrEllipse, distrEx, distributional, distributions3, distributionsrd, DistributionUtils, distrMod, distrSim, distrTeach, distrTEst, distTails, dng, DPQ, dqrng, e1071, ecd, Ecume, elfDistr, emdbook, emg, empichar, EnvStats, evd, evir, evmix, extraDistr, extremefit, FAdist, FatTailsR, fBasics, fExtremes, fgac, fitdistrplus, fitteR, flexsurv, FMStable, ForestFit, fpow, frmqa, fromo, gambin, gaussDiff, gb, GB2, GenBinomApps, gendist, GeneralizedHyperbolic, GenOrd, ggamma, ghyp, GIGrvg, gk, gld, GLDEX, glogis, greybox, GSM, gumbel, GWI, HAC, hermite, HI, HistogramTools, hyper2, HyperbolicDist, igcop, kdist, kernelboot, KScorrect, LambertW, LaplacesDemon, lcopula, LearnBayes, lhs, LindleyPowerSeries, llogistic, lmom, Lmoments, logitnorm, loglognorm, marg, MASS, matrixNormal, matrixsampling, mbbefd, mc2d, mclust, MCMCpack, mded, MEPDF, minimax, MittagLeffleR, MixedTS, mixSPE, mixtools, MM, MNB, mniw, modeest, moments, MomTrunc, movMF, MPS, msm, MultiRNG, mvrtn, nCDunnett, nCopula, Newdistns, NonNorMvtDist, nor1mix, NormalGamma, NormalLaplace, normalp, OneStep, ORDER2PARENT, OrdNor, OwenQ, parameters, ParetoPosStable, pbv, PDFEstimator, PDQutils, pmultinom, poibin, poilog, PoissonBinomial, poistweedie, polyaAeppli, poweRlaw, qmap, QRM, qrmtools, qrng, random, randtoolbox, RDieHarder, ReIns, relliptical, Renext, revdbayes, rlecuyer, RMKdiscrete, RMTstat, rmutil, ROOPSD, rstream, RTDE, rtdists, Runuran, rust, s20x, sadists, SCI, scModels, setRNG, sfsmisc, sglg, sgt, SimJoint, skellam, SkewHyperbolic, skewt, sld, smoothmest, SMR, sn, spacefillr, spam, sparseMVN, spd, stabledist, STAR, statmod, SuppDists, symmoments, SymTS, Tinflex, TLMoments, tmvmixnorm, tmvtnorm, tolerance, trapezoid, trawl, triangle, TruncatedNormal, truncdist, truncnorm, tsallisqexp, TTmoment, tukeyGH, tvgeom, tweedie, ugomquantreg, UnivRNG, VarianceGamma, vasicek, VineCopula, vines, vistributions, visualize, WienR, zipfextR, zipfR.
Archived:benchden, cpd, evdbayes, geoR, MBSP, mgpd, mvprpb, QBAsyDist, reliaR, rngwell19937.

Related links

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