| Maintainer: | Christophe Dutang, Patrice Kiener, Bruce J. Swihart |
| Contact: | dutangc at gmail.com |
| Version: | 2025-12-15 |
| URL: | https://CRAN.R-project.org/view=Distributions |
| Source: | https://github.com/cran-task-views/Distributions/ |
| 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 theContributing guide. |
| Citation: | Christophe Dutang, Patrice Kiener, Bruce J. Swihart (2025). CRAN Task View: Probability Distributions. Version 2025-12-15. URL https://CRAN.R-project.org/view=Distributions. |
| Installation: | The packages from this task view can be installed automatically using thectv package. For example,ctv::install.views("Distributions", coreOnly = TRUE) installs all the core packages orctv::update.views("Distributions") installs all packages that are not yet installed and up-to-date. See theCRAN 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.
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.
pfoo() density functionsdfoo(), quantile functionsqfoo(), and random number generationrfoo() wherefoo indicates the type of distribution: beta (foo =beta), binomialbinom, Cauchycauchy, chi-squaredchisq, exponentialexp, Fisher Ff, gammagamma, geometricgeom, hypergeometrichyper, logisticlogis, lognormallnorm, negative binomialnbinom, normalnorm, Poissonpois, Student tt, uniformunif, Weibullweibull. Following the same naming scheme, but somewhat less standard are the following distributions in base R: probabilities of coincidences (also known as “birthday paradox”)birthday (only p and q), studentized range distributiontukey (only p and q), Wilcoxon signed rank distributionsignrank, Wilcoxon rank sum distributionwilcox.ks.test,shapiro.test,ansari.test,chisq.test,poisson.test.Ecume provides non-parametric two-sample (or k-sample) distribution comparisons in the univariate or multivariate case allowing observation weights and thresholds.Some packages may optionally provide the symbolic derivatives with respect to the parameters for the probability functions. For instance, the first and second derivatives of the log-density can be of some help in estimation and inference tasks, and the derivatives of the quantile function can help when inferring on a given quantile. For that purpose, the following base R functions can be usedstats::D() for derivatives w.r.t. a single parameter, orstats::deriv() for (partial) derivatives w.r.t. multiple parameters. TheDeriv package provides a much more flexible symbolic differentiation interface. One can also use Stan Math library throughStanHeaders package, see e.g.this blog. Thenieve package provides symbolic differentiation for two probability distribution (Generalized Pareto and Generalized Extreme Value) in order to compute the log-likelihood for example.
Beta-binomial distribution: provided inVGAM,extraDistr,rmutil,emdbook. ZI/ZM beta binomial distributions are implemented ingamlss.dist. For a continuous analog with d, p, q, r functions, seecbbinom.
Beta-geometric distribution: provided inVGAM.
Binomial (including Bernoulli) distribution: provided instats. Zero-modified, zero-inflated, truncated versions are provided ingamlss.dist,extraDistr,actuar and inVGAM.LaplacesDemon provides dedicated functions for the Bernoulli distribution.rmutil provides the double binomial and the multiplicative binomial distributions.
| Distribution name | Packages | Functions | Distribution suffix |
| binomial | stats | d,p,q,r | binom |
| zero-infl. binomial | extraDistr | d,p,q,r | zib |
| zero-infl. binomial | VGAM | d,p,q,r | zibinom |
| zero-infl. binomial | gamlss.dist | d,p,q,r | ZIBI |
| zero mod. binomial | VGAM | d,p,q,r | zabinom |
| zero mod. binomial | actuar | d,p,q,r | zmbinom |
| zero mod. binomial | gamlss.dist | d,p,q,r | ZABI |
| zero trunc. binomial | actuar | d,p,q,r | ztbinom |
| trunc. binomial | extraDistr | d,p,q,r | tbinom |
Bell Touchard distribution: standard and zero-inflated provided incountDM.
Benford distribution: provided inVGAM andBenfordTests.
Bernoulli distribution: provided inextraDistr.
Borel-Tanner distribution: provided inVGAM.
Delaporte distribution: provided ingamlss.dist andDelaporte.
Dirac distribution: provided indistr.
Discrete Burr-Hatke distribution:DiscreteDists provides d, p, q, r functions.
Discrete categorical distribution: provided inLaplacesDemon.
Discrete Cauchy (Cauchy-Cacoullos) distribution: provided inCCd.
Discrete exponential distribution: provided inpoweRlaw. A generalized version of the second type is inDiscreteDists.
Discrete gamma distribution: provided inextraDistr.
Discrete inverted Kumaraswamy distribution:DiscreteDists provides d, p, q, r functions.
Discrete inverse Weibull distribution:DiscreteInverseWeibull provides d, p, q, r functions for the inverse Weibull as well as hazard rate function and moments.
Discrete Laplace distribution: The discrete Laplace distribution is provided inextraDistr (d, p, r). The skew discrete Laplace distribution has two parametrization (DSL and ADSL), both provided inDiscreteLaplace and DSL indisclap.LaplacesDemon also provides the DSL parametrization only.
Discrete Lindley distribution:DiscreteDists provides d, p, q, r functions.
Discrete lognormal distribution: provided inpoweRlaw.
Discrete Marshall–Olkin Length Biased Exponential distribution:DiscreteDists provides d, p, q, r functions.
Discrete normal distribution: provided inextraDistr.
Discrete power law distribution: provided inpoweRlaw.
Discrete uniform distribution: can be easily obtained with the functionssum,cumsum,sample and is provided inextraDistr.
Discrete Weibull distribution: provided inDiscreteWeibull: d, p, q, r, m for disc. Weib. type 1, d, p, q, r, m, h for disc. Weib. type 3.extraDistr provides d, p, q, r for Type 1.
Felix distribution: provided inVGAM.
gamma count distribution: provided inrmutil.
Geometric distribution: provided instats . Zero-modified, zero-inflated, truncated versions are provided ingamlss.dist,actuar and inVGAM. The time-varying geometric is provided intvgeom.
Geometric (compound) Poisson distribution (also known Polya-Aeppli distribution): provided inpolyaAeppli. Uniform-geometric distribution provided innew.dist.
Generalized/fractional binomial distribution:GenBinomApps provides the generalized binomial distribution.frbinom provides the fractional binomial distribution where trials are from a generlized Bernoulli process.
Generalized Geometric distribution: provided inDiscreteDists.
Generalized Hermite distribution: provided inhermite.
Good distribution: no longer provided: package of the same name is archived.
Hyper-Poisson distribution: provided inDiscreteDists.
Hypergeometric distribution: provided instats . Non-central hypergeometric distribution is provided inMCMCpack (d,r). Extended hypergeometric distribution can be found inBiasedUrn package, which provides not only p, d, q, r functions but also mean, variance, mode functions. Generalized hypergeometric distribution is implemented inSuppDists. Negative hypergeometric distribution is provided intolerance,extraDistr.
Lagrangian Poisson distribution:RMKdiscrete provides d, p, q, r functions for the univariate and the bivariate Lagrangian Poisson distribution.
Lindley’s power series distribution: provided inLindleyPowerSeries and innew.dist.
Logarithmic distribution: This can be found inextraDistr,VGAM,actuar, andgamlss.dist. Zero-modified and zero-truncated versions is provided inactuar. A fast random generator is available for the logarithmic distribution is implemented inRunuran as well as the ‘density’ function.
Poisson distribution: provided instats and inpoweRlaw. Zero-modified, zero-inflated, truncated versions are provided inextraDistr,gamlss.dist,actuar and inVGAM.extraDistr provides the truncated Poisson distribution.LaplacesDemon provides the generalized Poisson distribution.rmutil provides the double Poisson, the multiplicative Poisson and the Power variance function Poisson distributions.poibin andPoissonBinomial provide the Poisson binomial distribution. See the mixture section such as the Poisson-lognormal mixture.
Poisson-Lindley distribution: provided intolerance.
Power law distribution: provided inpoweRlaw.
Mana Clash distribution: provided inRMKdiscrete.
Negative binomial distribution: provided instats . Zero-modified, zero-inflated, truncated versions are provided ingamlss.dist,extraDistr,emdbook,actuar and inVGAM. New parametrization of the negative binomial distribution is available inRMKdiscrete.nbconv provides p, q, r functions for convolutions of negative binomial distributions.
Sichel distribution: provided ingamlss.dist.
Skellam distribution: provided inextraDistr,VGAM andskellam.
Waring distribution:degreenet provides a random generator,cpd provides d, p, q, r functions for extended biparametric Waring.
Yule-Simon distribution: provided inVGAM and sampling indegreenet.
Zeta and Haight’s Zeta distribution: provided inVGAM,tolerance.
Zipf distribution and extensions: d, p, q, r functions of the Zipf and the Zipf-Mandelbrot distributions are provided intolerance,VGAM. PackagezipfR provides tools for distribution of word frequency, such as the Zipf distribution.zipfextR provides three extensions of the Zipf distribution: the Marshall-Olkin Extended Zipf, the Zipf-Poisson Extreme and the Zipf-Poisson Stopped Sum distributions.
Arcsine distribution: implemented in packagesdistr andskewunit.
Argus distribution: implemented in packageargus.
Beta distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above).extraDistr provides the beta distribution parametrized by the mean and the precision.actuar provides moments and limited expected values.sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central beta distribution for computing d, p, q, r functions.extraDistr provides the four-parameter beta with lower and upper bounds. The generalized beta of the first kind (GB1) (exponentiation of beta 1, also known as McDonald distribution) is provided ingamlss.dist,mbbefd,actuar,gkwdist.betafunctions provides the four-parameter beta (that is with location and scale parameters), the beta parametrized by the mean and the variance as well as the beta compound beta distribution. The beta prime (or beta of the second kind), which is the distribution of X/(1-X) when X follows a beta distribution of the first kind, is provided inVGAM,extraDistr,LaplacesDemon andmc2d. The zero and one inflated beta distribution can be found ingamlss.dist. The generalized beta of the second kind (GB2) is provided ingamlss.dist,GB2. Several special cases of the generalized beta distribution are also implemented inVGAM,mc2d: Lomax, inverse Lomax, Dagum, Singh-Maddala, Pert distributions.actuar provides the Feller-Pareto distribution with special cases Burr, log-logistic, paralogistic, generalized Pareto, Pareto, see also the Pareto subsection.skewunit provides d, p, r for a symmetric beta.
| Distribution name | Packages | Functions | Distribution suffix |
| Beta (1st kind) | stats | d, p, q, r | beta |
| Beta | actuar | m, mgf, lev | beta |
| Beta | betafunctions | d, p, q, r | Beta.4P |
| Doubly non central beta | sadists | d, p, q, r | nbeta |
| 4-param beta | extraDistr | d, p, q, r | nsbeta |
| zero-infl beta | gamlss.dist | d, p, q, r | BEZI |
| one-infl beta | gamlss.dist | d, p, q, r | BEOI |
| one-infl beta | mbbefd | d, p, q, r, m, ec | oibeta |
| GB1 | gamlss.dist | d, p, q, r | GB1 |
| GB1 | mbbefd | d, p, q, r, m, ec | gbeta |
| GB1 | actuar | d, p, q, r, m, lev | genbeta |
| GB1 | gkwdist | d, p, q, r | mc |
| one-infl GB1 | mbbefd | d, p, q, r, m, ec | oigbeta |
| Distribution name | Packages | Functions | Distribution suffix |
| Beta (2nd kind) | VGAM | d, p, q, r | beta |
| Beta (2nd kind) | extraDistr | d, p, q, r | invbeta |
| Beta (2nd kind) | LaplacesDemon | d, r | betapr |
| GB2 | VGAM | d, p, q, r | genbetaII |
| GB2 | gamlss.dist | d, p, q, r | GB2 |
| GB2 | GB2 | d, p, q, r | gb2 |
| Trans beta 2 | actuar | d, p, q, r, m, lev | trbeta |
Bell-G distribution:BGFD provides d, p, q, r functions for Bell exponential, Bell extended exponential, Bell Weibull, Bell extended Weibull, Bell-Fisk, Bell-Lomax, Bell Burr-XII, Bell Burr-X, complementary Bell exponential, complementary Bell extended exponential, complementary Bell Weibull, complementary Bell extended Weibull, complementary Bell-Fisk, complementary Bell-Lomax, complementary Bell Burr-XII and complementary Bell Burr-X distribution.
The package also provides hazard function and an estimation procedure.
Benini distribution: provided inVGAM.
Bezier-Montenegro-Torres distribution: provided inBMT.
Bhattacharjee (normal+uniform) distribution: provided in packageextraDistr.
Birnbaum-Saunders distribution: provided inbsgof,extraDistr,VGAM.
Bridge distribution: provided inbridgedist, as detailed in Wang and Louis (2003). The distribution of random intercept that allows a marginalized random intercept logistic regression to also be logistic regression.
Box Cox distribution:gamlss.dist provides the Box-Cox normal, the Box-Cox power exponential and the Box-Cox t distributions.rmutil provides the Box-Cox normal.
Burr distribution: see Pareto.
Cardioid distribution: provided inVGAM (d,p,q,r) andCircStats,circular (d,r).
Carthwrite’s Power-of-Cosine distribution: provided incircular (d,r).
Cauchy distribution: Base R provides the d, p, q, r functions for this distribution (see above). Other implementations are available inlmomco andsgt. The skew Cauchy distribution is provided insn.LaplacesDemon provides d, p, q, r functions for the Half-Cauchy distribution.
Chen distribution: a special case of the Extended Chen-Poisson Lifetime Distribution as found inecpdist.
Chernoff distribution:ChernoffDist provides d, p, q functions of the distribution of the maximizer of the two-sided Brownian motion minus quadratic drift, known as Chernoff’s distribution.
Chi(-squared or not) distribution: Base R provides the d, p, q, r functions for the chi-squared distribution, both central and non-central (see above). Moments, limited expected values and the moment generating function are provided inactuar.extraDistr provides d, p, q, r functions for inverse chi-squared distribution (standard and scaled). Only d,r functions are available for the inverse chi-squared distribution in packageLaplacesDemon. A fast random generator is available for the Chi distribution is implemented inRunuran as well as the density function. The non-central Chi distribution is not yet implemented. The chi-bar-squared distribution is implemented inemdbook.sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for sums of non central chi-squared raised to powers distribution and sums of log of non central chi-squared for computing d, p, q, r functions.
| Distribution name | Packages | Functions | Distribution suffix |
| Chi-squared | stats | d, p, q, r | chisq |
| Chi-squared | actuar | m, mgf, lev | chisq |
| Chi-squared | Runuran | d, r | chisq |
| Chi-bar-squared | emdbook | d, p, q, r | chibarsq |
| Chi | Runuran | d, r | chi |
| Inverse Chi-squared | extraDistr | d, p, q, r | invchisq |
| Scaled Inverse Chi-squared | extraDistr | d, p, q, r | invchisq |
| Sum of power Chi-squared | sadists | d, p, q, r | sumchisqpow |
| Sum of log Chi-squared | sadists | d, p, q, r | sumlogchisq |
Circular distributions:CircStats,circular,Directional,rvMF,VGAM provide many circular distributions, see below.Directional also proposes various fitting methods.
| Distribution name | Packages | Functions | Distribution suffix |
| Angular Gaussian | Directional | d, r | spml |
| Cardioid | CircStats | d, r | card |
| Cardioid | VGAM | d, p, q, r | card |
| Cardioid | Directional | d, r | cardio |
| circular beta | Directional | d, r | circbeta |
| circular exponential | Directional | d, r | circexp |
| circular Purkayastha | Directional | d, r | circpurka |
| von Mises | circular | d, p, q, r | vonmises |
| von Mises | CircStats | d, p, r | vm |
| von Mises | Directional | d, r | vm |
| von Mises | rvMF | r | vMF |
| wrapped Cauchy | circular | d, r | wrappedcauchy |
| wrapped Cauchy | CircStats | d, r | wrpcauchy |
| wrapped Cauchy | Directional | d, r | wrapcauchy |
| wrapped normal | circular | d, p, q, r | wrappednormal |
| wrapped normal | CircStats | d, r | wrpnorm |
| wrapped normal | Directional | d, r | wrapnormal |
Consul distribution: seermutil.
Continuous binomial distribution:cbinom provides the d/p/q/r functions for a continuous analog to the standard discrete binomial with continuous size parameter and continuous support with x in [0, size + 1].
Dagum distribution: see beta. the power log Dagum provided innew.dist.
Davies distribution: The Davies distribution is provided inDavies package.
(non-central) Dunnett’s test distribution: no longer provided.
Eta-mu distribution: provided inlmomco.sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central eta distribution for computing d, p, q, r functions.
Exponential distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above).actuar provides additional functions such as the moment generating function, moments and limited expected values. It also has the d, p, q, r for the inverse exponential distribution. The shifted (or two-parameter exponential) and the truncated exponential distributions are implemented inlmomco andtolerance packages with d, p, q, r functions. Exponential Power distribution is also known as General Error Distribution: d, p, q, r functions for the power and the skew power exponential type 1-4 distributions are implemented ingamlss.dist andlmomco. The power exponential distribution is also provided innormalp,rmutil,LaplacesDemon. The skew power exponential is providedmixSPE. A fast random generator is available for the power Exponential distribution is implemented inRunuran as well as the density function.AEP implements the Asymmetric Exponential Power Distribution.pgnorm implements the p-Generalized Normal Distribution.
| Distribution name | Packages | Functions | Distribution suffix |
| Exponential | stats | d, p, q, r | exp |
| Exponential | actuar | m, mgf, lev | exp |
| Exponential | gamlss.dist | d, p, q, r | EXP |
| Exponential | poweRlaw | d, p, q, r | exp |
| Inverse exponential | actuar | d, p, q, r, m, lev | invexp |
| Shifted exponential | lmomco | d, p, q, r, lm, tlmr | exp |
| Shifted exponential | tolerance | d, p, q, r | 2exp |
| Truncated exponential | lmomco | d, p, q, r, lm, tlmr | texp |
| Truncated exponential | ReIns | d, p, q, r | texp |
| Power exponential | normalp | d, p, q, r | normp |
| Power exponential | Runuran | d, r | exp |
| Power exponential | rmutil | d, r | powexp |
| Power exponential | LaplacesDemon | d, p, q, r | pe |
| Skew power exp. | lmomco | d, p, q, r, lm, tlmr | aep4 |
| Power and skew power exp. | mixSPE | r | pe, spe |
| Power and skew power exp. | gamlss.dist | d, p, q, r | PE, SEP |
Externally studentized midrange distribution: PackageSMR computes the studentized midrange distribution (d, p, q, r).
Fisher-Snedecor (or F) distribution: Base R provides the d, p, q, r functions for the F distribution, possibly with a non-central parameter.sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central Fisher distribution (and product of multiple doubly non central Fisher distribution) for computing d, p, q, r functions.flexsurv provides d, p, q, r functions as well as hazard (h) and integrated hazard rate (i) functions for the generalized F distribution.fpow returns the noncentrality parameter of the noncentral F distribution if probability of type I and type II error, degrees of freedom of the numerator and the denominator are given.
Frechet distribution: provided inVGAM,RTDE,ReIns,extraDistr,distributionsrd andevd. A fast random generator is available for the Frechet distribution is implemented inRunuran as well as the density function. The truncated Frechet distribution is provided inReIns.
Friedman’s Chi distribution: provided inSuppDists.
Gamma distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above).EnvStats provides d, p, q, r functions of the gamma parametrized by the mean and the coefficient of variation.actuar provides d, p, q, r functions of the inverse, the inverse transformed and the log gamma distributions whileghyp provides those functions for the variance gamma distribution.extraDistr andLaplacesDemon provide the inverse gamma distribution.CaDENCE provides the zero-inflated gamma distribution.VarianceGamma provides d, p, q, r functions for the variance gamma distribution as well as moments (skewness, kurtosis, ...).VGAM,ggamma provide d, p, q, r functions of the log gamma and the generalized gamma distribution. The generalized gamma distribution can also be found ingamlss.dist. See Pearson III for a three-parameter gamma distribution with a location parameter.flexsurv provides d, p, q, r functions as well as hazard (h) and integrated hazard rate (i) functions for the generalized gamma distribution.coga provides d, p, r functions for a sum of independent but not identically distributed gamma distributions.MCMCpack provides d, r functions of the Inverse Gamma.rmutil provides the generalized Gamma.distTails provides the full-tail gamma distributionsglg provides the generalized log-Gamma along with various functions to fit semi-parametric regression models.ollggamma provides d, p, q, r for the Odd Log-Logistic Generalized Gamma. The d, p, q, r functions for the truncated generalised gamma distribution are found intggd.
| Distribution name | Packages | Functions | Distribution suffix |
| Gamma | stats | d, p, q, r | gamma |
| Gamma | actuar | m, mgf, lev | gamma |
| Gamma | EnvStats | d, p, q, r | gammaAlt |
| zero-inflated Gamma | CaDENCE | d, p, q, r | bgamma |
| Inverse gamma | actuar | d, p, q, r, m, lev, mgf | invgamma |
| Inverse gamma | extraDistr | d, p, q, r | invgamma |
| Inverse gamma | LaplacesDemon | d, r | invgamma |
| Inverse gamma | MCMCpack | d, r | invgamma |
| Log-gamma | actuar | d, p, q, r, m, lev | lgamma |
| Log-gamma | VGAM | d, p, q, r | lgamma |
| Variance gamma | ghyp | d, p, q, r | VG |
| Variance gamma | VarianceGamma | d, p, q, r, m | vg |
| Generalized gamma | flexsurv | d, p, q, r, h, i | gengamma |
| Generalized gamma | gamlss.dist | d, p, q, r | GG |
| Generalized gamma | VGAM | d, p, q, r | gengamma.stacy |
| Generalized gamma | rmutil | d, p, q, r | ggamma |
| Generalized gamma | ggamma | d, p, q, r | ggamma |
| convolution of gamma | coga | d, p, r | coga |
| Full-taill gamma | distTails | d, p, r | dFTG |
| Generalized log-gamma | sglg | d, p, q, r | glg |
Pólya–Gamma distribution: r function random sampling routines for the distribution are provided byBayesLogit,pg, andpgdraw.
Gaussian (or normal) distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above).actuar provides the moment generating function and moments. Thetruncnorm package provides d, p, q, r functions for the truncated gaussian distribution as well as functions for the first two moments.EnvStats provides d, p, q, r functions for the truncated normal distribution and the zero-modified distribution.extraDistr provides the truncated normal.LaplacesDemon provides d, p, q, r functions for the Half-normal distribution.lmomco implements the generalized normal distribution. The Exponentially modified Gaussian is available inemg,gamlss.dist,tsdistributions,sn implements the skew normal distribution.greybox implements the folded normal distribution.VGAM implements the folded and the skewed normal distribution, andcsn provides d, r functions for the closed skew normal distribution.NormalLaplace provides d, p, q, r functions for the sum of a normal and a Laplace random variables, whileLaplacesDemon provides d, r functions of the sum of a normal and a Laplace random variables.PSDistr provides d, p, q, r functions of transformations of the normal distribution, such as expnormal and sinh-normal distributions.
| Distribution name | Packages | Functions | Distribution suffix |
| Normal | stats | d, p, q, r | norm |
| Normal | actuar | m, mgf | norm |
| Truncated normal | truncnorm | d, p, q, r, m | truncnorm |
| Truncated normal | EnvStats | d, p, q, r | normTrunc |
| Truncated normal | extraDistr | d, p, q, r | tnorm |
| Truncated normal | crch | d, p, q, r | cnorm |
| Generalized normal | lmomco | d, p, q, r | gno |
| Zero modified Gaussian | EnvStats | d, p, q, r | zmnorm |
| Exponentially modified Gaussian | emg | d, p, q, r | emg |
| Exponentially modified Gaussian | gamlss.dist | d, p, q, r | exGAUSS |
| Folded and skew normal | gamlss.dist | d, p, q, r | SN1, SN2 |
| Folded normal | greybox | d, p, q, r | fnorm |
| Closed skew normal | csn | d, p, q, r | csn |
| Skew normal | sn | d, p, q, r | sn |
| Skew normal | snorm | d, p, q, r | tsdistributions |
General error distribution (also known as exponential power distribution): seeexponential item.
Generalized extreme value distribution: d, p, q provided inlmomco; d, p, q, r, provided inVGAM,evd,evir,FAdist,extraDistr,EnvStats,TLMoments,rmutil,QRM,ROOPSD andfExtremes.revdbayes provide d, p, q, r functions of the GEV distribution in a Bayesian setting.bgev provide d, p, q, r functions of the bimodal GEV distribution.PGaGEV provide d, p, q, r functions of the Power Garima-Generalized Extreme Value Distribution.
Gompertz distribution: provided inflexsurv,extraDistr.flexsurv also provides hazard (h) and integrated hazard rate (i) functions. The shifted Gompertz distribution is implemented inextraDistr. The unit-Gompertz is provided inugomquantreg.
Govindarajulu distribution: provided inlmomco.
Gumbel distribution: provided in packageslmomco,VGAM,gamlss.dist,FAdist,extraDistr,QRM,TLMoments,dgumbel,EnvStats andevd.actuar provides the raw moments and the moment generating function (mgf) in addition to the d, p, q, r functions. A fast random generator is available for the Gumbel distribution is implemented inRunuran as well as the density function. The reverse Gumbel distribution is implemented inlmomco andgamlss.dist.bgumbel provides the bimodel Gumbel distribution.
Hjorth distribution: provided inrmutil.
Huber distribution: Huber’s least favourable distribution provided in packagesmoothmest (d, r), and inVGAM,marg,extraDistr (d, p, q, r).
(generalized) G-and-K, G-and-H distributions:gk provides d, p, q, r functions for the g-and-k and generalized g-and-h distributions which are nonlinear transforms of the Gaussian variables.
(generalized) Hyperbolic distribution:fBasics,ghyp,tsdistributions ,GeneralizedHyperbolic andHyperbolicDist packages provide d, p, q, r functions for the generalized hyperbolic distribution.QRM provides d, r functions for the generalized hyperbolic distribution.SkewHyperbolic provides the skewed Hyperbolic Student t-Distribution.fBasics also implements the standardized generalized Hyperbolic distribution. A fast random generator is available for the hyperbolic distribution is implemented inRunuran as well as the density function.
Hyperbolic sine distribution and extension:gamlss.dist provides the sinh and the asinh distributions. Generalized Power Hyperbolic sine distributions are provided inFatTailsR.
Inverse Gaussian (also known Wald) distribution: d, p, q, and r functions of the inverse Gaussian are provided instatmod,extraDistr,SuppDists,rmutil.LaplacesDemon provides d, r functions for the inverse Gaussian distribution.actuar provides d, p, q, r, m, lev, mgf functions for the Inverse Gaussian distribution.SuppDists also provides a function that returns moments, skewness, kurtosis.fBasics the normal inverse Gaussian and standardized normal inverse Gaussian distributions.tsdistributions provides the normal inverse Gaussian distribution. The generalized inverse gaussian (GIG) distribution can be found ingamlss.dist,ginormal,HyperbolicDist,QRM,rmutil. The truncated GIG is also available inginormal. A random generator is available for the (generalized) Inverse Gaussian distribution is implemented inRunuran as well as the density function.GIGrvg generates random variables from the generalized inverse Gaussian distribution. Unit inverse Gaussian provided innew.dist.
Johnson distribution: provided inSuppDists,ForestFit,tsdistributions provides d, p of Johnson SB distribution.skewunit provides d, p, and r of Johnson SB distribution.
Jones and Pewsey distribution: provided incircular (d).
K-prime distribution:sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for K-prime distribution for computing d, p, q, r functions.
Kappa distribution: A 4-parameter Kappa distribution is provided inlmomco andFAdist.
Kappa-mu distribution: provided inlmomco.
Kato-Jones distribution: provided incircular (d, r).
Kendall’s tau distribution: provided inSuppDists.
Kiener distribution: a family of distributions generalizing hyperbolic sine distributions (see hyperbolic sine section), d, p, q, r, m provided inFatTailsR.
Kruskal Wallis distribution: provided inSuppDists.
Kumaraswamy distribution: provided in packagesVGAM,extraDistr,gkwdist,lmomco,new.dist.elfDistr provides the Kumaraswamy Complementary Weibull Geometric Probability Distribution.
(Tukey) Lambda distribution and its extensions: The generalized Lambda distribution (GLD) is well known for its wide range of shapes. The original Tukey Lambda distribution can be obtained as a special case of the generalized Lambda distribution. There exists different parametrization of GLD in the literature: RS (Ramberg-Schmeiser or tail-index param), FMKL (Freimer-Mudholkar-Kollia-Lin), FM5 (Five-parameter version of FKML by Gilchrist), GPD (gen. Pareto dist.) and AS (Asymmetry-steepness). The following packages implement such distributions (with d, p, q, r functions):gld (RS, FKML, FM5, GPD),Davies (RS),gb (RS),lmomco (FMKL),extraDistr (original Tukey).
Tukey’s G/H distribution: provided inTukeyGH77, and Tukey’s H distribution is provided as a special case of Lambert W x F distribution.
Lambda-prime distribution:sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for K-prime distribution for computing d, p, q, r functions.
Lambert W x F distribution:LambertW package provides d, p, q, r functions as well as the first 4 central moments and a qqplot.
Laplace (also called double exponential distribution) and asymmetric Laplace distribution: provided indistr,lmomco,LaplacesDemon,L1pack,VGAM,sgt,extraDistr,greybox,rmutil,Rsubbotools,joker andHyperbolicDist packages.LaplacesDemon provides the Laplace distribution parametrized by the precision parameter as well as the skew Laplace distribution. Asymmetric Laplace distribution is implemented inald,Rsubbotools,greybox. A fast random generator is available for the Laplace distribution is implemented inRunuran as well as the density function.smoothmest implements the density and the random generator. The skew Laplace distribution is available insgt.LaplacesDemon provides the log-Laplace distribution.ExtendedLaplace provides the extended Laplace distribution.
LASSO distribution: provided inLaplacesDemon.
Lévy distribution: provided inrmutil.
Linear failure rate distribution: no longer implemented.
Loglog distribution: no longer implemented.
Lomax distribution: see beta.
Logistic distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above).actuar andVGAM provide d, p, q, r functions for the log-logistic (also called Fisk), the paralogistic and the inverse paralogistic distributions.FAdist the log-logistic distribution with two and three parameters.llogistic provides the log-logistic parametrized by the median.trdist provides the log-logistic distribution. The generalized logistic distribution (Type I, also known as skew-logistic distribution) is provided inlmomco,sld,rmutil,SCI andglogis.GTDL implements generalized Time-Dependent Logistic distribution.
| Distribution name | Packages | Functions | Distribution suffix |
| Logistic | stats | d, p, q, r | logis |
| Logistic | actuar | m, mgf | logis |
| Log logistic | actuar | d, p, q, r, m, lev | llogis |
| Log logistic | VGAM | d, p, q, r | fisk |
| Log logistic | FAdist | d, p, q, r | llog, llog3 |
| Paralogistic | actuar | d, p, q, r, m, lev | paralogis |
| Paralogistic | VGAM | d, p, q, r | paralogistic |
| Inv. paralogistic | actuar | d, p, q, r, m, lev | invparalogis |
| Inv. paralogistic | VGAM | d, p, q, r | inv.paralogistic |
| Truncated logistic | crch | d, p, q, r | tlogis |
| Generalized logistic | glogis | d, p, q, r | glogis |
| Generalized logistic | SCI | d, p, q | genlog |
| Generalized logistic | lmomco | d, p, q, r | glo |
| Generalized logistic | sld | d, p, q, r | sl |
| Generalized logistic | rmutil | d, p, q, r | glogis |
Logit-normal distribution: provided inlogitnorm.
Log-normal distribution and its extensions: The log normal distribution is implemented in Base R (see above) andpoweRlaw. The log normal distribution parametrized by its mean and its coefficient of variation is also provided inEnvStats.LaplacesDemon provides the lognormal parametrized by the precision parameter. The truncated lognormal distribution is provided inEnvStats with two possible parametrizations as well as inReIns. The 3-parameter lognormal distribution is available inlmomco,greybox,TLMoments,EnvStats andFAdist. The packageloglognorm implements d, p, q, r functions for the double lognormal distribution, as well as the raw moment, the expected value and the variance functions.EnvStats provides d, p, q, r functions for the zero-modified lognormal distribution with two possible parametrizations.distributionsrd provides the double Pareto-lognormal distribution, the left Pareto-lognormal distribution, the truncated lognormal distribution.
Makeham distribution: provided inVGAM.
Minimax distribution: provided inminimax.
Mittag-Leffler distribution: d, p, q, r functions provided inMittagLeffleR.
Muth distribution: provided innew.dist.
Nakagami distribution: provided inVGAM.
Neutrosophic: provided inntsDists.
Pareto distribution: d, p, q, r functions are implemented inVGAM for the Pareto distribution type IV (which includes Burr’s distribution, Pareto type III, Pareto type II (also called the lomax distribution) and Pareto type I) and the (upper/lower) truncated Pareto distribution. In an actuarial context,actuar provides d, p, q, r functions as well as moments and limited expected values for the Pareto I and II, the inverse Pareto, the ‘generalized pareto’ distributions, the Burr and the inverse Burr distributions, all special cases of the transformed beta II distribution. A fast random generator for the Burr and the Pareto II distribution is implemented inRunuran as well as the density.EnvStats andLaplacesDemon provides d, p, q, r functions for Pareto I distribution.extremefit provides the Burr, the Pareto II, mixture of Pareto I distributions and a composite distribution of two Pareto I distributions.lmomco,evd,fExtremes,extraDistr,QRM,Renext,revdbayes,FAdist,LaplacesDemon,TLMomentsqrmtools andevir packages implement the Generalized Pareto Distribution (from Extreme Value Theory), which is depending the shape parameter’s value a Pareto II distribution, a shifted exponential distribution or a generalized beta I distribution.ParetoPosStable implements the Pareto positive stable distribution. The extended Pareto distribution is implemented inRTDE and the shifted truncated (to unit interval) Pareto is implemented inmbbefd.ReIns provides Burr, extended Pareto, generalized Pareto, Pareto 1 distributions and their truncated version.CaDENCE provides the Pareto 2 and the zero-inflated Pareto 2 distribution.Pareto provides the Pareto 1, piecewise Pareto and the generalized Pareto (from actuarial theory). The gamma-Lomax distribution is provided innew.dist.
| Distribution name | Packages | Functions | Distribution suffix |
| Pareto I | VGAM | d, p, q, r | paretoI |
| Pareto I | actuar | d, p, q, r, m, lev | pareto1 |
| Pareto I | EnvStats | d, p, q, r | pareto |
| Pareto I | extraDistr | d, p, q, r | pareto |
| Pareto I | ReIns | d, p, q, r | pareto |
| Pareto I | LaplacesDemon | d, p, q, r | pareto |
| Pareto I | distributionsrd | d, p, q, r | pareto |
| Pareto I | Pareto | d, p, q, r | Pareto |
| Trunc. Pareto I | ReIns | d, p, q, r | tpareto |
| Pareto II | VGAM | d, p, q, r | paretoII |
| Pareto II | actuar | d, p, q, r, m, lev | pareto, pareto2 |
| Pareto II | Runuran | d, r | pareto |
| Pareto II | extraDistr | d, p, q, h | lomax |
| Pareto II | extremefit | d, p, q, h | pareto |
| Pareto II | Renext | d, p, q, r | lomax |
| Pareto II | rmutil | d, p, q, r | pareto |
| Pareto II | CaDENCE | d, p, q, r | pareto2 |
| zero-inflated Pareto II | CaDENCE | d, p, q, r | bpareto2 |
| Pareto III | VGAM | d, p, q, r | paretoIII |
| Pareto III | actuar | d, p, q, r | pareto3 |
| Pareto IV | VGAM | d, p, q, r | paretoIV |
| Pareto IV | actuar | d, p, q, r | pareto4 |
| Inverse Pareto | actuar | d, p, q, r, m, lev | invpareto |
| Inverse Pareto | distributionsrd | d, p, q, r, m, lev | invpareto |
| Extended Pareto | RTDE | d, p, q, r | EPD |
| Extended Pareto | ReIns | d, p, q, r | epd |
| Shift. trunc. Pareto | mbbefd | d, p, q, r, m, ec | stpareto |
| Gen. Pareto (actuarial) | actuar | d, p, q, r, m, lev | genpareto |
| Gen. Pareto (actuarial) | Pareto | d, p, q, r | GenPareto |
| Gen. Pareto (EVT) | lmomco | d, p, q, r | gpa |
| Gen. Pareto (EVT) | evd | d, p, q, r | gpd |
| Gen. Pareto (EVT) | fExtremes | d, p, q, r | gpd |
| Gen. Pareto (EVT) | evir | d, p, q, r | gpd |
| Gen. Pareto (EVT) | extraDistr | d, p, q, r | gpd |
| Gen. Pareto (EVT) | QRM | d, p, q, r | GPD |
| Gen. Pareto (EVT) | ReIns | d, p, q, r | gpd |
| Gen. Pareto (EVT) | LaplacesDemon | d, r | gpd |
| Gen. Pareto (EVT) | TLMoments | d, p, q, r | gpd |
| Trunc. Gen. Pareto (EVT) | ReIns | d, p, q, r | tgpd |
| Gen. Pareto (EVT) | revdbayes | d, p, q, r | gp |
| Gen. Pareto (EVT) | Renext | d, p, q, r | GPD |
| Gen. Pareto (EVT) | qrmtools | d, p, q, r | GPD |
| Gen. Pareto (EVT) | ROOPSD | d, p, q, r | gpd |
| Feller-Pareto | actuar | d, p, q, r, m, lev | fpareto |
| Burr | actuar | d, p, q, r, m, lev | burr |
| Burr | extremefit | d, p, q, r | burr |
| Burr | ReIns | d, p, q, r | burr |
| Burr | rmutil | d, p, q, r | burr |
| Trunc. Burr | ReIns | d, p, q, r | tburr |
| Inverse Burr | actuar | d, p, q, r, m, lev | invburr |
Pearson’s distribution: Pearson type III available inlmomco andFAdist. A log-Pearson type III distribution is also available inFAdist.PearsonDS provides the d, p, q, r functions as well as the first four moments for the Pearson distributions: types I, II, III, IV, V, VI, VII.cpd provides d, p, q, r for complex bi/triparametric Pearson distributions.
Pearson’s Rho distribution: provided inSuppDists.
Perks distribution: provided inVGAM.
Planck’s distribution: a random generator is available inRunuran.
Phase-type distribution: provided inactuar,mapfit,matrixdist,PhaseTypeR.
Power distribution: r pkg(“poweRlaw”)`,Rsubbotools implement the exponential power distribution. Two-sided power distribution provided inrmutil.Rsubbotools provides the skewed exponential power distribution and a three-parameter version known as Subbotin distribution.
Proportion distribution: this is the distribution for the difference between two independent beta distributions. d, p, q, r functions intolerance.
Omega distribution: provided innew.dist.
Quadratic forms and their ratios:CompQuadForm provides several exact and approximate methods to evaluate the distribution function of quadratic forms in normal variables.Qapprox provides fast approximations for the distribution function in nonnegative definite cases.QF provides d, p, q, r for nonnegative definite quadratic forms in normal variables and their ratios where the numerator and denominator are independent, as well as p for ratios of central quadratic forms in the same normal variables.qfratio provides d, p, q, r for the distribution of ratios of potentially noncentral quadratic forms in the same normal variables, as well as moment.
Rayleigh distribution: provided in packagesVGAM,extraDistr andlmomco. The slashed generalized Rayleigh distribution provided innew.dist. The two-parameter Rayleigh provided innew.dist.
Ram Awadh: provided innew.dist.
Response time distribution:rtdists provides d, p, q, r functions for the (Ratcliff) diffusion distribution and for the linear ballistic accumulator (LBA) with different underlying drift-distributions (Normal, Gamma, Frechet, and log-normal).
Simplex distribution: provided inrmutil.
Singh-Maddala distribution: see beta.
Slash distribution: provided inlmomco,extraDistr andVGAM.
Spearman’s Rho distribution: provided inSuppDists.
Stable distribution: d, p, q, r functions are available infBasics andstabledist, the functions use the approach of J.P. Nolan for general stable distributions.stable (d, p, q, r, h) is also used for general stable and uses a modified Buck parametrization.MixedTS provides mixed tempered stable distribution (d, p, q, r).FMStable provides (d, p, q) the extremal or maximally skew stable and the finite moment log stable distributions.SymTS provides d, p, q, r functions for symmetric stable, symmetric classical tempered stable, and symmetric power tempered stable distributions.TempStable provides d, p, q, r functions for tempered stable distributions.libstable4u provides d, p, q, r functions for skew stable distributions.dstabledist provides d, p, r functions for skew stable distributions.StableEstim provides fitting functions, characteristic functions, and simulation capabilities for 4-parameter stable distributions.
Student distribution and its extensions: Base R provides the d, p, q, r functions for Student and non central Student distribution (see above).extraDistr andLaplacesDemon provides the Student distribution with location and scale parameters.LaplacesDemon provides d, p, q, r functions for the Half-Student distribution.sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for doubly non central Student distribution for computing d, p, q, r functions. The skewed Student distribution is provided inskewt,sn,tsdistributions andgamlss.dist packages. The generalized skew distribution is provided insgt. d, p, q, r functions for the generalized t-distribution can be found ingamlss.dist.fBasics provides d, p, q, r functions for the skew and the generalized hyperbolic t-distribution. The L-moments of the Student t (3-parameter) are provided inlmomco.crch provides d, p, q, r functions for the truncated student distribution.
| Distribution name | Packages | Functions | Distribution suffix |
| Student | stats | d, p, q, r | t |
| Student with loc. and scal. | extraDistr | d, p, q, r | lst |
| Student with loc. and scal. | LaplacesDemon | d, p, q, r | st |
| Doubly non central St. | sadists | d, p, q, r | dnt |
| Skew Student | skewt | d, p, q, r | skt |
| Skew Student | sn | d, p, q, r | st |
| Skew St. Type 1-5 | gamlss.dist | d, p, q, r | ST1, ST2, ST3, ST4, ST5 |
| Gen. Student | gamlss.dist | d, p, q, r | GT |
| Gen. Hyp. Student | fBasics | d, p, q, r | ght |
| Skew Gen. Student | sgt | d, p, q, r | sgt |
Topp-Leone Cauchy Rayleigh (TLCAR) distribution: provided inTLCAR (d, p, q, r).
Triangle/trapezoidal distribution: packagestriangle,extraDistr,mc2d,EnvStats andVGAM provide d, p, q, r functions for the triangle or triangular distribution, while the packagetrapezoid provides d, p, q, r functions for the Generalized Trapezoidal Distribution.CircStats,circular provide d, r functions for triangular distribution. A fast random generator is available for the triangle distribution is implemented inRunuran as well as the density function.skewunit provides d, p, r functions for the triangle distribution.
Tsallis or q-Exponential distribution:tsallisqexp provides d, p, q, r functions for two parametrizations of the Tsallis distribution and also implements a left-censored version.
Tweedie distribution: the Tweedie distribution is implemented in packagetweedie. Let us note that the Tweedie distribution is not necessarily continuous, a special case of it is the Poisson distribution.
U-quadratic distribution: d, p, r functions are found inskewunit.
Uniform distribution: d, p, q, r functions are of course provided in R. See section RNG for random number generation topics.KScorrect provides d, p, q, r functions for the log-uniform distribution.
Unit-garima distribution: d, p, q, r functions provided inUGarima.
Upsilon distribution:sadists implements Gram Charlier, Edgeworth and Cornish-Fisher approximations for Upsilon distribution for computing d, p, q, r functions.
Vasicek distribution:vasicek implements d, p, r functions.vasicekreg implements d, p, q, r functions.
voigt distribution:voigt implements d, r functions.
Wakeby distribution: A 5-parameter Wakeby is provided inlmomco.
Weibull distribution and its extensions: Base R provides the d, p, q, r functions for this distribution (see above). The inverse Weibull is provided inactuar package and also the moments and the limited expected value for both the raw and the inverse Weibull distribution.FAdist implements the three-parameter Weibull distribution. Furthermore,lmomco implements the Weibull distribution whileevd implements the reverse Weibull distribution. The reverse generalized extreme value distribution are provided ingamlss.dist (d, p, q, r) and the shifted left truncated Weibull distribution is provided inRenext. The right truncated Weibull is provided inReIns. The generalized Weibull is provided inrmutil. The tail Weibull is provided indistTails.CaDENCE provides the zero-inflated Weibull distribution. The bimodal Weibull distribution is provided innew.dist. The Marshal–Olkin Generalized Inverse Weibull Distribution is provided inmogiw.
First-passage time of a Wiener process:WienR provides d, p functions of the first-passage time of a diffusion model.
Bivariate Pareto:Bivariate.Pareto provides a random generator for the bivariate Pareto distribution.
Multivariate beta distribution:NonNorMvtDist provides d, p, q, r, s functions for inverted beta distribution.
Multivariate Burr distribution:NonNorMvtDist provides d, p, q, r, s functions.
Multivariate Cauchy distribution:sn provide d, p, r functions for the multivariate skew Cauchy distribution, whileLaplacesDemon provides d, r functions for the multivariate Cauchy distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega.multvardiv provides d, p, r functions of the multivariate Cauchy distribution..
Cook-Johnson’s Multivariate Uniform Distribution:NonNorMvtDist provides d, p, q, r, s functions.
Multivariate Dirichlet distribution:Compositional,LaplacesDemon,MCMCpack packages provide d, r functions as well as a fitting function forCompositional.compositions,bayesm provide r function.SGB provides a generalization of the Dirichlet distribution called Simplicial Generalized Beta distribution.
Multivariate exponential distribution: whileLaplacesDemon provides d, r functions for the multivariate power exponential distribution parametrized either by sigma, or by the Cholesky decomposition of sigma.
Multivariate F distribution:NonNorMvtDist provides d, p, q, r, s functions.
Multivariate gamma distribution:joker provides d, r functions.
Multivariate Gaussian (or normal) distribution: The multivariate Gaussian distribution is provided in the packagesmvtnorm (d, p, r),mnormt (d, p, r),mnorm (d, p, r),mniw (d, r),Compositional (r),compositions (r).pbv provides d, p functions for bivariate normal distributions.symmoments computes central and non-central moments of the multivariate Gaussian distribution.LaplacesDemon provides d, r functions for the multivariate normal distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega. Futhermore, the multivariate truncated normal is implemented inTruncatedNormal for d, p, r functions;tmvtnorm for p, q, r, m(oments) functions;tmvmixnorm for a fast RNG;nntmvn for RNG using SNN method.sparseMVN implements very fast algorithms to compute the density and generate random variates of a multivariate normal distribution for which the covariance matrix or precision matrix is sparse.cmvnorm implements the complex multivariate normal distribution (d, r). Furthermore,condMVNorm implements d, p, r functions for the conditional multivariate normal distribution.condTruncMVN implements d, p, r functions of the conditional truncated multivariate normal distribution. Finally,sn besides providing facilities for their distribution functions,sn allows the creation of S4 objects which encapsulate these distributions and provide facilities for plotting, summary, marginalization, conditioning, affine transformations of these S4 objects.Compositional provides random generator for the multivariate normal distribution on the simplex and multivariate skew normal distribution on the simplex. A random generator of the multivariate normal is provided inMultiRNG.multvardiv provides d, r function of the multivariate generalized Gaussian distribution.nvmix provides d, p, q, r function of the Multivariate Normal Variance Mixtures as well as the multivariate normal distribution.hdtg provides efficient sampling from high-dimensional multivariate truncated normal.
Multivariate generalized hyperbolic distribution:QRM provides d, r functions of the standard and the symmetric multivariate generalized hyperbolic distribution.ghyp provides d, p, r functions of the standard multivariate generalized hyperbolic distribution.
Multivariate generalized extreme value distribution: Both bivariate and multivariate Extreme Value distributions as well as order/maxima/minima distributions are implemented inevd (d, p, r).
Multivariate inverse Gaussian distribution:mig provides (d, p, r) functionality as well as a fitting function.
Multivariate Laplace distribution:LaplacesDemon provides d, r functions for the multivariate Laplace distribution parametrized either by sigma, or by the Cholesky decomposition of sigma. r is provided inMultiRNG.L1pack provides d, r functions of the multivariate Laplace distribution.
Multivariate logistic distribution:VGAM package implements the bivariate logistic distribution, whileNonNorMvtDist implements the multivariate logistic distribution.
Multivariate lognormal distribution:compositions provides r function.
Multivariate Pareto distribution:evd provides the density for the multivariate generalized Pareto type I.NonNorMvtDist provides d, p, q, r, s functions for multivariate Lomax (type II) distributions and its generalized version.NonNorMvtDist provides d, p, q, r, s functions for Mardia’s Multivariate Pareto Type I Distribution
Multivariate Stable distribution: For elliptically contoured (subgaussian stable),alphastable provides d, r functions as well as a fitting function,mvgb provides p function. The multivariate subgaussian stable distribution (d, p, r) is available inmvpd.
Multivariate Student distribution: The multivariate Student distribution is provided in the packagesmvtnorm (d, r),mnormt (d, p, r),Compositional (r),tmvmixnorm (r),QRM (d, r),bayesm (r),MVT (r).TruncatedNormal for d, p, r functions;tmvtnorm for d, p, q, r functions.sn provides d, p, r functions for the multivariate skew t distribution.LaplacesDemon provides d, r functions for the multivariate Student distribution parametrized either by sigma, by the Cholesky decomposition of sigma, by the precision matrix omega or by the Cholesky decomposition of omega. Random generator r is provided inMultiRNG. Distance between multivariate t distributions are provided inmultvardiv.nvmix provides d, r function of the multivariate Student distribution.
Multivariate Uniform distribution: r is provided inMultiRNG.compositions provides a random generator on the simplex.
Spherical distributions and other:Directional provides many spherical distributions, see below, and proposes various fitting methods.simdd provides a generator for the Fisher Bingham distribution on the unit sphere, the matrix Bingham distribution on a Grassmann manifold, the matrix Fisher distribution on SO(3), and the bivariate von Mises sin model on the torus.uniformly provides uniform sampling on various geometric shapes, such as spheres, ellipsoids, simplices.watson allows simulating mixtures of Watson distributions.
| Distribution name | Packages | Functions | Distribution suffix |
| uniform | uniformly | r | runif_on_sphere |
| Bingham | simdd | r | Bingham |
| Bingham | Directional | r | bingham |
| Ellip. Sym. Ang. Gaussian | Directional | d, r | ESAG |
| Fisher Bingham | simdd | r | FisherBingham |
| Kent | Directional | d, r | kent |
| Purkayastha | Directional | d, r | purka |
| spherical Cauchy | Directional | d, r | spcauchy |
| von Mises - Fisher | Directional | d, r | vmf |
| Wood | Directional | d. | wood |
Huang-Wan distribution: provided inLaplacesDemon.
Inverse matrix gamma distribution: provided inLaplacesDemon.
Inverse Wishart distribution:LaplacesDemon provides inverse Wishart distribution parametrized either by Sigma or by its Cholesky decomposition.LaplacesDemon provides the scaled inverse Wishart distribution.MCMCpack andmniw provides the inverse Wishart distribution.wishmom allows to computes the theoretical moments of the inverse beta-Wishart distribution.
Marcenko-Pastur distribution: provided inRMTstat,MCMCpack andbayesm.
Matrix gamma distribution: provided inLaplacesDemon.
Matrix normal distribution:MBSP (r) provides a random generator using a Cholesky decomposition;matrixsampling (r) provides a random generator using a spectral decomposition;LaplacesDemon andmniw (d, r);matrixNormal (d, p, r) collects these forms in one place and allows users to be flexible in simulating random variates (Cholesky, spectral, SVD).
Matrix student distribution: provided inmniw.
Normal Inverse Wishart distribution: provided inLaplacesDemon,mniw.
Normal Wishart distribution: provided inLaplacesDemon.
Tracy-Widom distribution: provided inRMTstat,MCMCpack andbayesm: supported beta values are 1 (Gaussian Orthogonal Ensemble), 2 (Gaussian Unitary Ensemble), and 4 (Gaussian Symplectic Ensemble).
Sparse matrix:spam provides functionalities to draw random numbers from a user-supplied RNG (e.g. rexp) or from a multivariate normal distribution for large sparse matrices: typically for sparse covariance matrices.
Spiked Wishart Maximum Eigenvalue Distribution: provided inRMTstat,MCMCpack andbayesm.
Wishart distributions: Base R provides the r function for the Wishart distribution.MCMCpack,RMTstat,bayesm,mniw provides d, r functions,bayesm provides r function.LaplacesDemon provides Wishart distribution parametrized either by Sigma or by its Cholesky decomposition.wishmom allows to computes the theoretical moments of the beta-Wishart distribution.
White Wishart Maximum Eigenvalue Distribution: provided inRMTstat,MCMCpack andbayesm.
Yang-Berger distribution: provided inLaplacesDemon.
Zellner distribution: provided inLaplacesDemon.
Absolute value or half distribution: Half-Cauchy, half normal and half-student are implemented both inextraDistr and inLaplacesDemon.
Composite distribution also known as spliced distribution: Split-normal (also known as the two-piece normal distribution) not yet implemented. Split-student provided in packagedng.evmix provides d, p, q, r of the following composite distributions: gamma-GPD, lognormal GPD, normal-GPD, Weibull-GPD as well as bulk models such as GPD-normal-GPD distribution.gendist provides d, p, q, r functions for composite models working with any distribution defined by its d, p, q, r functions.
Compound distribution:kdist provides d, p, q, r functions of the K distribution.
Discretized distribution:distcrete allows discretised versions of continuous distribution by mapping continuous values to an underlying discrete grid, based on a (uniform) frequency of discretisation, a valid discretisation point, and an integration range. Consult the packagecctools for uniform scaled beta distribution and the continuous convolution kernel density estimator implementations.
Quantile-based asymmetric (QBA) family of distributions: no longer implemented.
Transformed distribution:Newdistns provides G-transformed distributions for a selected number of distributions which includes Marshall Olkin G distribution, exponentiated G distribution, beta G distribution, gamma G distribution, Kumaraswamy G distribution, generalized beta G distribution, beta extended G distribution, gamma G distribution, gamma uniform G distribution, beta exponential G distribution, Weibull G distribution, log gamma G1/G2 distribution, exponentiated generalized G distribution, exponentiated Kumaraswamy G distributions, geometric exponential Poisson G distribution, truncated-exponential skew-symmetric G distribution, modified beta G distribution, and exponentiated exponential Poisson G distribution.MPS provides also G-transformed distributions, such as beta exponential G distribution, beta G distribution, exponentiated exponential Poisson G distribution, exponentiated G distribution, exponentiated generalized G distribution, exponentiated Kumaraswamy G distribution, gamma uniform G distribution, gamma uniform type I/II G distribution, generalized beta G distribution, geometric exponential Poisson G distribution, gamma-X family of modified beta exponential G distribution, exponentiated exponential Poisson G distribution, gamma-X generated of log-logistic-X familiy of G distribution, Kumaraswamy G distribution, log gamma G type I/II distribution, modified beta G distribution, Marshall-Olkin Kumaraswamy G distribution, odd log-logistic G distribution, truncated-exponential skew-symmetric G distribution, T-X{log-logistic}G distribution, Weibull G distribution.gkwdist provides the beta-Kumaraswamy, the exponentiated-Kumaraswamy, the generalized Kumaraswamy, Kumaraswamy-Kumaraswamy distributions.gendist provides d, p, q, r functions for composite models, folded models, skewed symmetric models and arctan models working with any distribution defined by its d, p, q, r functions.ComRiskModel provides also G-transformed such as binomial-G, complementary negative binomial-G and complementary geometric-G families of distributions taking baseline models such as exponential, extended exponential, Weibull, extended Weibull, Fisk, Lomax, Burr-XII and Burr-X.geppe provides exponential-Poisson (EP), the generalised EP (GEP) and the Poisson-exponential (PE) distributions.
Truncated distribution: A generic code snippet is availablein the JSS . This code is now available in two packages:truncdist,trdist are dedicated packages providing d, p, q, r, m(oments) functions of a univariate truncated distribution for a base distribution and a user-supplied distribution;LaplacesDemon provides a generic function in a Bayesian environment.TruncExpFam provides d, r functions for truncated distributions of the exponential family, e.g. truncated gamma or truncated Poisson as well as fitting procedures. It also provides functions to retrieve the original distribution parameters from a truncated sample by maximum-likelihood estimation. The d, p, q, r functions for the truncated generalised gamma distribution are found intggd.
mean(),sd(),var() functions to compute the mean, standard deviation and variance, respectively.set.seed and the kind of RNG can be specified usingRNGkind. The default RNG is the Mersenne-Twister algorithm. Other generators include Wichmann-Hill, Marsaglia-Multicarry, Super-Duper, Knuth-TAOCP, Knuth-TAOCP-2002, as well as user-supplied RNGs. For normal random numbers, the following algorithms are available: Kinderman-Ramage, Ahrens-Dieter, Box-Muller, Inversion (default). In addition to the tools above,setRNG provides an easy way to set, retain information about the setting, and reset the RNG.stats (andactuar) distributions to a tidytibble which allows to work with the rest of thetidyverse.density()), (2) the empirical cumulative distribution function (seeecdf()), (3) the empirical quantile (seequantile()) and (4) random sampling with or without replacement (seesample()).distributionsrd provides d, p, q, r user-friendly functions for the empirical distributions as well as moments.distfromq provides d, p, q, r user-friendly functions for the empirical distributions and options for estimating the tails.mded provides a function for measuring the difference between two independent or non-independent empirical distributions and returning a significance level of the difference.random(),pdf(),cdf() andquantile() provide replacements for base R’sr/d/p/q style functions.distributional also provides tools to create and to manipulate probability distributions using S3, withcdf(),density(),hdr(),mean(),median(),quantile(),...fitdistr function for parameter estimations.fitdistrplus greatly enlargesfitdistr and enhances the tools to fit any user-supplied probability distribution.OneStep is based uponfitdistrplus to provide one-step estimation procedures.EnvStats,ExtDist,