Template:Probability distributions

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Probability distributions

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Probability distributions (List)

Discrete
univariate

with finite support	Benford Bernoulli beta-binomial binomial categorical hypergeometric negative Poisson binomial Rademacher soliton discrete uniform Zipf Zipf–Mandelbrot
with infinite support	beta negative binomial Borel Conway–Maxwell–Poisson discrete phase-type Delaporte extended negative binomial Flory–Schulz Gauss–Kuzmin geometric logarithmic mixed Poisson negative binomial Panjer parabolic fractal Poisson Skellam Yule–Simon zeta

Continuous
univariate

supported on a bounded interval	arcsine ARGUS Balding–Nichols Bates beta beta rectangular continuous Bernoulli Irwin–Hall Kumaraswamy logit-normal noncentral beta PERT raised cosine reciprocal triangular U-quadratic uniform Wigner semicircle
supported on a semi-infinite interval	Benini Benktander 1st kind Benktander 2nd kind beta prime Burr chi chi-squared noncentral inverse scaled Dagum Davis Erlang hyper exponential hyperexponential hypoexponential logarithmic F noncentral folded normal Fréchet gamma generalized inverse gamma/Gompertz Gompertz shifted half-logistic half-normal Hotelling's T-squared inverse Gaussian generalized Kolmogorov Lévy log-Cauchy log-Laplace log-logistic log-normal log-t Lomax matrix-exponential Maxwell–Boltzmann Maxwell–Jüttner Mittag-Leffler Nakagami Pareto phase-type Poly-Weibull Rayleigh relativistic Breit–Wigner Rice truncated normal type-2 Gumbel Weibull discrete Wilks's lambda
supported on the whole real line	Cauchy exponential power Fisher's z Gaussian q generalized normal generalized hyperbolic geometric stable Gumbel Holtsmark hyperbolic secant Johnson's S_U Landau Laplace asymmetric logistic noncentral t normal (Gaussian) normal-inverse Gaussian skew normal slash stable Student's t type-1 Gumbel Tracy–Widom variance-gamma Voigt
with support whose type varies	generalized chi-squared generalized extreme value generalized Pareto Marchenko–Pastur q-exponential q-Gaussian q-Weibull shifted log-logistic Tukey lambda

Mixed
univariate

continuous- discrete	Rectified Gaussian

Multivariate
(joint)

Univariate (circular) directional: Circular uniform; univariate von Mises; wrapped normal; wrapped Cauchy; wrapped exponential; wrapped asymmetric Laplace; wrapped Lévy
Bivariate (spherical): Kent
Bivariate (toroidal): bivariate von Mises
Multivariate: von Mises–Fisher; Bingham

Degenerate
and singular

Degenerate: Dirac delta function
Singular: Cantor

Families

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