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.

• Arcsine distribution.
• Argus distribution.
• Amoroso distribution.
• Arfwedson Distribution.
• Asymptotic Normal Distribution.
• Alpha Distribution.
• Array Distribution.
• Azzalini Distribution.
• Balding-Nichols distribution.
• Bates distribution.
• Bell shaped distribution.
• Bernoulli distribution.
• Benford distribution.
• Benini distribution.
• Beta Binomial distribution.
• Beta distribution
• Beta Geometric distribution (Type I Geometric).
• Beta Prime distribution.
• Bimodal distribution.
• Bingham / Bingham-Mardia distribution).
• Bipolar Distribution.
• Binomial distribution.
• Binomials Added Distribution.
• Birnbaum-Saunders Distribution.
• Bivariate distribution.
• Bivariate normal distribution.
• Bradford distribution.
• Bravais Distribution.
• Breit–Wigner distribution. See: Cauchy Distribution.
• Burr Distribution.
• Categorical distribution.
• Cauchy Distribution.
• Cauchy-Lorentz distribution. See: Cauchy Distribution.
• Chi distribution.
• Chi-Bar-Squared Distribution.
• Chi-Squared Distribution.
• Circular distribution.
• Circular normal distribution. See: Von Mises Distribution.
• Cobb-Douglas (see Lognormal).
• Composed Distribution (see Stuttering Poisson).
• Compound Distribution.
• Compound Poisson Distribution. See Stuttering Poisson.
• Constant distribution. See degenerate distribution.
• Continuous distribution.
• Continuous joint distribution.
• Copula distribution.
• Cosine distribution.
• Cramp function Distribution.
• Cumulative distribution (function) CDF
• Cumulative frequency distribution.
• Darmois-Koopman Distribution.
• Degenerate distribution.
• Delta distribution.
• De Moivre Distribution.
• Dirac delta distribution.
• Directional distribution.
• Dirichlet distribution.
• Discrete Weibull Distribution.
• Distribution par Grappes (see Stuttering Poisson).
• Edgeworth Series Distribution.
• Elfving Distribution.
• Equinormal distribution.
• Erlang distribution.
• Eulerian Distribution.
• Exceedance Distribution.
• Exponential distribution.
• Factorial Distribution.
• Fatigue Life Distribution. See: Birnbaum-Saunders Distribution.
• Ferreri Distribution.
• Flat normal distribution.
• Frechet distribution (see Weibull).
• G-and-H distribution.
• Galton-McAlister (see Lognormal).
• Gamma distribution.
• Generalized Inverse Normal Distribution.
• Ghosh Distribution.
• Gibrat Distribution (see Lognormal).
• Gompertz-Rayleigh distribution.
• Gram-Charlier Distribution.
• Grand Unified Distribution.
• Halphen Distribution.
• Hansmann’s Distributions.
• Hard distribution.
• Helmert’s Distribution.
• Holtsmark distribution.
• Hotelling’s T-squared distribution/test.
• Hurdle distribution.
• Inverse Gamma Distribution.
• Inverse Normal Distribution.
• Irwin–Hall distribution.
• Kapetyn’s Distribution.
• Kullbach Distribution.
• Kummer distribution.
• Johnson SB Distribution.
• Joint probability distribution
• Laha distribution.
• Lexian Distribution.
• Lindley distribution.
• Linear exponential distribution.
• Lineo-Normal Distribution.
• Log-Normal Distribution.
• Log-Rayleigh distribution. See: Benini distribution.
• Lorentz distribution (or Lorentzian function). See: Cauchy Distribution.
• Macdonald distribution.
• Mallows distribution.
• Marshall-Olkin Bivariate Distribution.
• Mielke’s beta-kappa distribution.
• Mixture of Chi-Squared distribution (see Chi-Bar-Squared)
• Mixture Distribution.
• Modified normal distribution.
• Multivariate normal distribution (see: Bivariate normal).
• Nakagami distribution.
• Normal Distribution.
• Pareto distribution.
• Pearson System of Distributions.
• Poisson Distribution.
• Poisson Distribution with events in clusters (see Stuttering Poisson).
• Poisson Power Series Distribution (see Stuttering Poisson).
• Polar distribution (see Circular distribution).
• Pollaczek-Geiringer Distribution.
• Posterior Probability distribution.
• Power Function Distribution.
• Radico-Normal Distribution.
• Rayleigh distribution
• Romanovsky Distribution.
• Rutherford’s Contagious Distribution.
• Semicircle distribution
• Semi-Normal Distribution.
• Semi-Triangular Distribution.
• Skewed Distribution.
• Stable Distribution.
• Standard Normal Distribution.
• Student’s T-Distribution.
• Stuttering Poisson Distribution.
• Survival distribution.
• Symmetric Triangular Distribution.
• Tikhonov distribution. See Von Mises distribution.
• Tine Distribution.
• Triangular Distribution.
• Tweedie distribution.
• Two Rectangulars Added.
• Uniform Distribution.
• Unimodal Distribution.
• Unit Normal Distribution.
• Variance Ratio Distribution.
• Voigt distribution.
• Von Mises Distribution.
• Waring distribution.
• Weibull Distribution.
• Weibull-Gnedenko (see: Weibull distribution)
• Weibull-Rician (see: Weibull distribution)
• Wrapped (Up) Normal Distribution.
• Zero-modified distribution
• Zero-modified lognormal distribution (see: Delta distribution.)
• Zero-modified normal distribution.

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

Sargan

Schuhl

semi-normal

Severity Distribution.

Shepard

sichel

Shakil-Singh-Kibria distribution

Sine Distribution.

Skellam Distribution (Poisson Difference Distribution).

Smooth probability distribution

Snedicor

Spherical

Stacy-Mihram (see Generalized gamma)

skew(ed)-normal

slash

Special 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

Univariate Distribution.

U Power Distribution.

U-Shaped Distribution.

Variance Ratio (see F: Distribution)

Von Mises Fisher Distribution.

Wallenius Distribution.

Wilks

Wishart Distribution.

Wrapped-up normal

Wrapped up Cauchy

Yule-Simon Distribution.

Zero-inflated distribution.

Zero-truncated distribution

Zeta Distribution.

Zipf

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
2
k -2
(26) inverse chi 0 √1
2
1
2
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
2
k -1
(24) inverse chi-square 0 1
2
1
2
k -1
(22) L´evy . . 1
2
-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
2
k 1
(12) chi-square 0 2 1
2
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
2
k 2
(14) chi 0 √
2
1
2
k 2
(11) half-normal 0 . 1
2
2
(16) Rayleigh 0 . 1 2
(17) Maxwell 0 . 3
2
2
(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