Distribution Properties#

Continuous#

These distributions are defined over a continuous range of values.

Discrete#

These distributions are defined over a discrete range of values.

Symmetric#

These distributions are symmetric about their center (or can be symmetric under parameter choices):

Laplace
Normal
Cauchy
Student’s t
Beta (when α = β)
Beta Scaled (when α = β)
Uniform
Logistic
Von Mises (Note: circular distributions such as Von Mises are symmetric on the circle.)
Multivariate Normal

Note: PreliZ distributions have a `skewness()` method.

For more information on symmetric distributions, see: Symmetric distribution.

Asymmetric#

Distributions with skewed (non‐symmetric) shapes include:

Note: PreliZ distributions have a `skewness()` method.

For more on skewness and asymmetry, see: Skewness.

Bounded#

Distributions whose support is bounded (i.e. defined only on a finite interval). Continuous: - Beta - Beta Scaled - Triangular - Uniform - Logit-Normal - Kumaraswamy - Truncated Normal - Dirichlet

Discrete: - Beta Binomial - Binomial - Categorical - Discrete Uniform - Hypergeometric - Zero-Inflated Binomial

For more on distributions with bounded support, see: Support (statistics).

Unbounded#

Distributions defined over the entire real line (or “two‐sided” with infinite support):

For more on distributions with unbounded support, see: Support (statistics).

Non‐Negative#

Distributions supported on the non‐negative real numbers.

Continuous: - Exponential - Gamma - Chi-Squared - Weibull - Pareto - Half-Cauchy - Half-Normal - Half-Student’s t - Inverse Gamma - Log-Normal - Rice - Wald - Log-Logistic - Logit-Normal - Scaled Inverse Chi-Squared

Discrete: - Bernoulli - Binomial - Negative Binomial - Poisson - Zero-Inflated Binomial - Zero-Inflated Negative Binomial - Zero-Inflated Poisson - Discrete Weibull - Geometric

For more on non‐negative random variables and distributions, see: Support (statistics).

Multivariate#

Distributions with more than one dimension:

For more on multivariate probability distributions, see: Joint probability distribution.

Univariate#

The following distributions are univariate (one-dimensional).

Continuous: - Asymmetric Laplace - Beta - Beta Scaled - Cauchy - Chi-Squared - Ex-Gaussian - Exponential - Gamma - Gumbel - Half-Cauchy - Half-Normal - Half-Student’s t - Inverse Gamma - Kumaraswamy - Laplace - Log-Normal - Logistic - Log-Logistic - Logit-Normal - Moyal - Normal - Pareto - Rice - Scaled Inverse Chi-Squared - Skew-Normal - Student’s t - Skew-Student’s t - Triangular - Truncated Normal - Uniform - Von Mises - Wald - Weibull

Discrete: - Bernoulli - Beta Binomial - Binomial - Categorical - Discrete Uniform - Discrete Weibull - Geometric - Hypergeometric - Negative Binomial - Poisson - Zero-Inflated Binomial - Zero-Inflated Negative Binomial - Zero-Inflated Poisson

For more on univariate probability distributions, see: Probability distribution.

Modifiers (Special Cases)#

For more details on distribution modifications, see: Censoring (statistics), Hurdle model, Mixture model, and Truncated distribution.

Heavy-Tailed#

Distributions with tails that decay slowly (i.e. they allow for large outliers) include:

Note: PreliZ distributions have a `kurtosis()` method.

For more on heavy-tailed distributions, see: Heavy-tailed distribution.

Light-Tailed#

Distributions with tails that decay relatively quickly include:

Note: PreliZ distributions have a `kurtosis()` method.

For more on tail behavior and light-tailed distributions, see: Heavy-tailed distribution.

Extreme Value#

Distributions commonly used in the modeling of extreme events:

For more on extreme value theory, see: Extreme value theory.

Zero-Inflated#

These distributions have been augmented to allow for extra zeros:

For more on zero-inflated models, see: Zero-inflated model.