Many probability distributions that are important in theory or applications have been given specific names.

Discrete distributions

Binomial distribution
Degenerate distribution

With finite support

Conway–Maxwell–Poisson distribution
Poisson distribution
Skellam distribution

With infinite support

Absolutely continuous distributions

Beta distribution
Kumaraswamy distribution
Continuous uniform distribution

Supported on a bounded interval

Chi-squared distribution
Gamma distribution
Pareto distribution

Supported on intervals of length 2π – directional distributions

Supported on semi-infinite intervals, usually [0,∞)

Cauchy distribution
Johnson SU distribution
Laplace distribution
Stable distribution

Supported on the whole real line

With variable support

Mixed discrete/continuous distributions

Joint distributions

For any set of independent random variables the probability density function of their joint distribution is the product of their individual density functions.

Two or more random variables on the same sample space

Distributions of matrix-valued random variables

Non-numeric distributions

Miscellaneous distributions

See also


  1. ^ Sun, Jingchao; Kong, Maiying; Pal, Subhadip (22 June 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme". Communications in Statistics - Theory and Methods: 1–23. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587.
  2. ^ Polson, Nicholas G.; Scott, James G.; Windle, Jesse (2013). "Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables". Journal of the American Statistical Association. 108 (504): 1339–1349. arXiv:1205.0310. doi:10.1080/01621459.2013.829001. ISSN 0162-1459. JSTOR 24247065. S2CID 2859721. Retrieved 11 July 2021.
  3. ^ Pal, Subhadip; Gaskins, Jeremy (23 May 2022). "Modified Pólya-Gamma data augmentation for Bayesian analysis of directional data". Journal of Statistical Computation and Simulation: 1–22. doi:10.1080/00949655.2022.2067853.