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Probability distributions

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The Nematrian website contains information and analytics on a wide range of probability distributions, including:

 

Discrete (univariate) distributions

 

-          Bernoulli, see also binomial distribution

-          Binomial

-          Geometric, see also negative binomial distribution

-          Hypergeometric

-          Negative binomial

-          Poisson

-          Uniform (discrete)

 

Continuous (univariate) distributions

 

-          Beta

-          Beta prime

-          Burr

-          Cauchy

-          Chi-squared

-          Dagum

-          Degenerate

-          Error function

-          Exponential

-          F

-          Fatigue, also known as the Birnbaum-Saunders distribution

-          Fréchet, see also generalised extreme value (GEV) distribution

-          Gamma

-          Generalised extreme value (GEV)

-          Generalised gamma

-          Generalised inverse Gaussian

-          Generalised Pareto (GDP)

-          Gumbel, see also generalised extreme value (GEV) distribution

-          Hyperbolic secant

-          Inverse gamma

-          Inverse Gaussian

-          Johnson SU

-          Kumaraswamy

-          Laplace

-          Lévy

-          Logarithmic

-          Logistic

-          Log-logistic

-          Lognormal

-          Nakagami

-          Non-central chi-squared

-          Non-central t

-          Normal

-          Pareto

-          Power function

-          Rayleigh

-          Reciprocal

-          Rice

-          Student’s t

-          Triangular

-          Uniform

-          Weibull, see also generalised extreme value (GEV) distribution

 

Continuous multivariate distributions

 

-          Inverse Wishart

 

Copulas (a copula is a special type of continuous multivariate distribution)

 

-          Clayton

-          Comonotonicity

-       Countermonotonicity (only valid for , where  is the dimension of the input)

-          Frank

-          Generalised Clayton

-          Gumbel

-          Gaussian

-          Independence

-          t

 

The Nematrian website functions for fitting univariate distributions, creating random variates and calculating moments etc. now cover most of the above probability distributions, see ProbabilityDistributionsFunctions. In many cases these functions can cater for the traditional (textbook) forms of these distributions and variants that include additional shift and scale parameters.

 

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