Probability Distributions List

This list was compiled during my research into archaic and unusual probability distributions (or unusual names for well-known distributions). Many of these are not mentioned in traditional textbooks or found on the major websites.

In addition, you’ll find common distributions which are referenced by the more unusual distributions.

Please leave me a comment if there’s a distribution you want to see on the list.

In the works!

Pearson distribution.

Perks distribution.

PERT distribution.

Phase Type distribution.

Pólya distribution.

Poisson difference distribution (see: Skellam Distribution).

Power function distribution.

Power gamma distribution.

Power normal distribution.

Power law distribution.

Power series distributions.

Quadri-normal distribution.

Rademacher distribution.

Radico-normal distribution.

Random walk distribution.

Reciprocal distribution.

Rectangular distribution (see normal).

Relative frequency distribution.

Rice (see noncentral chi-squared)

Rician distribution.

Right triangular

Robust Soliton Distribution.

Romanowski’s modified normal distribution

Run Length

Rutherford Contagious




Severity Distribution.



Shakil-Singh-Kibria distribution

Sine Distribution.

Skellam Distribution (Poisson Difference Distribution).

Smooth probability distribution



Stacy-Mihram (see Generalized gamma)



Special Distribution.

Standard Power Distribution.



student bivariate

stuttering Poisson distribution


Symmetric Distribution.


Trapezoidal Distribution.

Triangular Distribution.

Truncated exponential.

Truncated Normal Distribution.

Truncated Poisson

Truncated Type III

Tukey g- and h-

Tukey Lambda Distribution.

Type Harmonique

Univariate Distribution.

U Power Distribution.

U-Shaped Distribution.

Variance Ratio (see F: Distribution)

Von Mises Fisher Distribution.

Wallenius Distribution.


Wishart Distribution.

Wrapped-up normal

Wrapped up Cauchy

Yule-Simon Distribution.

Zero-inflated distribution.

Zero-truncated distribution

Zeta Distribution.


Zip (Zero-inflated Poisson)

For completeness, I’ll eventually add more common distributions because the “unusual” distributions tend to reference these.

Beta-rectangular distribution
Beta prime distribution
Birthday distribution
Borel distribution
Burr distribution
Cantor distribution
Categorical distribution
Circular uniform distribution
Compound Poisson distribution
Conway-Maxwell-Poisson distribution
Coupon collector distribution
Dagum distribution
Davis distribution
de la Vallee-Poussin distribution
Delaporte distribution
Dickman distribution
Dirac delta distribution
Discrete phase-type distribution
Elliptical distribution
Exponential family

Exponential-logarithmic distribution
Extended negative binomial distribution
Fiducial distribution
Fisher’s Z distribution
Flory-Schulz distribution
Folded normal distribution
Frechet distribution
Gamma-exponential distribution
Gamma/Gompertz distribution
Gauss-Kuzmin distribution
Gaussian q-distribution
Generalized beta distribution

Half logistic distribution
Half normal distribution
Hyper-Erlang distribution
Inverse chi-squared distribution
Inverse Weibull distribution
Irwin-Hall (uniform sum) distribution
Johnson SU distribution
Kent distribution
Kolmogorov-Smirnov distribution
Kumaraswamy distribution
Kummer beta distribution
Laha distribution
Landau distribution
Levy distribution
Location scale family
Log Cauchy distribution
Log gamma distribution (alternative parameterization)
Log Laplace distribution
Logarithmic series distribution
Logit-normal distribution
Marchenko-Pastur distribution
Matrix-exponential distribution
Maximum entropy distribution
Maxwell-Boltzmann distribution
Maxwell-Juttner distribution
Metalog distribution
Mittag-Leffler distribution
Mixture distribution
Natural exponential family
Noncentral beta distribution
Noncentral hypergeometric distribution Liao, J.G., Rosen, O. (2001), Fast and Stable Algorithms for Computing and Sampling from the Noncentral Hypergeometric Distribution, The American Statistician, Vol. 55, No. 4, 366-369.
Normal inverse Gaussian distribution
Panjer recursion
Parabolic fractal distributions
Pearson system of distributions
PERT distribution
Phase-type distribution
Poisson-binomial distribution
Poly-Weibull distribution
Polya-Eggenberger distribution
Prentice distribution
Q-exponential distribution
Q-Gaussian distribution
Q-Weibull distribution
Quantile functions
Quantile-parametrized distributions
Rademacher distribution
Raised cosine distribution
Reciprocal distribution
Rectified Gaussian distribution (mixed discrete-continuous)
Relativistic Breit-Wigner distribution
Rice distribution
Scaled inverse chi-squared distribution
Seba curves
Shifted Gompertz distribution
Shifted log logistic distribution
Sinh-Arcsinh distribution
Skellam distribution
Skewed generalized t distribution
Skew normal distribution
Slash distribution
Soliton distribution
Theta distribution
Tracy-Widom distribution
Truncated normal distribution
Tukey g-and-h distribution 1; Tukey g-and-h distribution 2
Tukey lambda distribution
Tukey studentized range distribution
Type I Gumbel distribution
Type II Gumbel distribution
U-quadratic distribution
Variance gamma distribution
Wigner semicircle distribution
Wilk’s lambda distribution
Wrapped distribution
Wrapped asymmetirc Laplace distribution
Wrapped Cauchy distribution
Wrapped exponential distribution
Wrapped Levy distribution
Wrapped normal distribution
Yule-Simon distribution

scaled inverse chi 0 . 1
k -2
(26) inverse chi 0 √1
k -2
(27) inverse Rayleigh 0 . 1 -2
(19) Pearson type V . . . -1
(20) inverse gamma 0 . . -1
(23) scaled inverse chi-square 0 . 1
k -1
(24) inverse chi-square 0 1
k -1
(22) L´evy . . 1
(21) inverse exponential 0 . 1 -1
(7) Pearson type III . . . 1
(5) gamma 0 . . 1
(5) Erlang 0 >0 n 1
(6) standard gamma 0 1 . 1
(13) scaled chi-square 0 . 1
k 1
(12) chi-square 0 2 1
k 1
(9) shifted exponential . . 1 1
(8) exponential 0 . 1 1
(8) standard exponential 0 1 1 1
(5) Wien 0 . 4 1
(15) scaled chi 0 . 1
k 2
(14) chi 0 √
k 2
(11) half-normal 0 . 1
(16) Rayleigh 0 . 1 2
(17) Maxwell 0 . 3
(18) Wilson-Hilferty 0 . . 3
(30) generalized Weibull . . n >0
(31) Weibull . . 1 >0
(4) pseudo-Weibull . . 1+ 1
β >0
(3) stretched exponential

Zero inflated Poisson (ZIP) distribution
Zipf-Mandelbrot distribution