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.

  • Benford distribution.
  • Bernoulli distribution.
  • Beta Binomial distribution.
  • Beta Geometric distribution (Type I Geometric).
  • Beta Prime distribution.
  • Binomial distribution.
  • Bimodal distribution.
  • Bivariate distribution.
  • Bivariate normal distribution.
  • Bradford distribution.
  • Burr Distribution.
  • Categorical distribution.
  • Chi distribution.
  • Chi-squared distribution.
  • Circular normal distribution.
  • Compound distribution.
  • Continuous distribution.
  • Copula distribution.
  • Cosine distribution.
  • Cumulative frequency distribution.
  • Cumulative distribution function.
  • Degenerate distribution.
  • Delta distribution.
  • Dirichlet Distribution.
  • Discrete Probability distribution.
  • Empirical distribution function.
  • Erlang distribution.
  • Equinormal distribution.
  • Exponential-logarithmic distribution.
  • Exponential power distribution.
  • Exponential-type distribution.
  • Exponentially modified normal distribution.
  • Extended power distribution.
  • Extreme value distribution.
  • F distribution.
  • Factorial distribution.
  • Fat Tail distribution.
  • Fisher’s z distribution.
  • Fisk distribution.
  • Flat normal distribution.
  • Folded normal / Half normal distribution.
  • G-and-H distribution.
  • Gamma distribution.
  • Gamma-normal distribution.
  • Gamma Poisson distribution.
  • Gaussian distribution (see normal)
  • Gaussian mixture distribution
  • Generalized Error distribution.
  • Generalized F distribution.
  • Generalized gamma distribution.
  • Generalized gamma convolution distribution.
  • Generalized hyperbolic distribution.
  • Generalized hyperexponential distribution.
  • Generalized inverse gamma distribution.
  • Generalized inverse Gaussian distribution.
  • Generalized lognormal distribution.
  • Generalized Pareto distribution.
  • Generalized Weibull distribution.
  • Geometric distribution.
  • Gompertz distribution.
  • Gompertz-Makeham distribution.
  • Half-Cauchy distribution.
  • Half-Logistic distribution.
  • Heavy Tailed distribution.
  • Hybrid lognormal distribution.
  • Hyperbolic distribution.
  • Hyperbolic Secant distribution.
  • Hyperexponential distribution.
  • Hypergeometric distribution.
  • Inflated distribution.
  • Inverse Gaussian distribution.
  • Inverse Normal / Gaussian.
  • Inverse Gaussian-Weibull.
  • Inverted gamma distribution.
  • Irwin–Hall distribution.
  • J Shaped distribution.
  • Johnson SU distribution.
  • Kappa (Mielke) distribution.
  • Kent distribution.
  • Koopman-Darmois distribution.
  • Kumaraswamy distribution.
  • Lagged normal
  • Laha distribution.
  • Landau distribution.
  • Laplace distribution.
  • Laplace-normal
  • Lévy distribution.
  • Lindley distribution.
  • Lineo-normal distribution.
  • Location-scale family of distributions.
  • Log gamma distribution.
  • Logarithmic distribution.
  • Logistic distribution.
  • Lognormal distribution.
  • Lomax distribution.
  • Long Tail distribution.
  • Macdonald distribution.
  • Makeham-Gompertz distribution.
  • Mallows distribution.
  • Marginal distribution.
  • Marshall-Olkin (bivariate exponential) distribution.
  • Maxwell-Boltzmann distribution.
  • Modified geometric distribution.
  • Multimodal distribution.
  • Multinomial distribution.
  • Multivariate distribution.
  • Multivariate gamma distribution.
  • Multivariate normal distribution.
  • Muth distribution.
  • Nakagami distribution.
  • Negative binomial distribution.
  • Non-central distribution.
  • Non-central beta distribution.
  • Non-central chi-square distribution.
  • Non-central F distribution.
  • Non-central T distribution.
  • Normal-gamma distribution.
  • Odd Frechet power distribution.
  • Open ended distribution.
  • Parabolic distribution.
  • Pareto distribution.
  • 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.
  • Rayleigh distribution.
  • Reciprocal distribution.
  • Rectangular distribution (see normal).
  • Relative frequency distribution.
  • Rice (see noncentral chi-squared)
  • Rician distribution.
  • Right triangular
  • Robust Soliton Distribution.
  • Romanovsky
  • Romanowski’s modified normal distribution
  • Run Length
  • Rutherford Contagious
  • Sargan
  • Schuhl
  • Semicircle Distribution.
  • semi-normal
  • Severity Distribution.
  • Shepard
  • Sine Distribution.
  • Skellam Distribution (Poisson Difference Distribution).
  • Snedicor
  • Spherical
  • Stacy-Mihram (see Generalized gamma)
  • Skewed Distribution.
  • skew(ed)-normal
  • slash
  • Special Distribution.
  • Stable Distribution.
  • Standard Power Distribution.
  • Stevens-Craig
  • Stevens-Fisher
  • student bivariate
  • stuttering Poisson distribution
  • subexponential
  • Symmetric Distribution.
  • Toranzos
  • Trapezoidal Distribution.
  • Triangular Distribution.
  • Truncated exponential.
  • Truncated Normal Distribution.
  • Truncated Poisson
  • Truncated Type III
  • Tukey g- and h-
  • Tukey Lambda Distribution.
  • Type Harmonique
  • Tweedie Distribution.
  • Uniform Distribution.
  • Univariate Distribution.
  • U Power Distribution.
  • U-Shaped Distribution.
  • Variance Ratio (see F: Distribution)
  • Von Mises Distribution.
  • Von Mises Fisher Distribution.
  • Wallenius Distribution.
  • Waring Distribution.
  • Weibull Distribution.
  • Weibull-Gnedenko (see Weibull)
  • Weibull-Rician
  • Wilks
  • Wishart Distribution.
  • Wrapped-up normal
  • Wrapped up Cauchy
  • Yule-Simon Distribution.
  • Zero-modified distribution
  • Zeta Distribution.
  • Zipf

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