Bernoulli: Any random variable taking values in \(\{0, 1\}\).

BetaBinomial: A sum of \(n\) iid Bernoulli variables, with a marginalized Beta prior on the success probability. Values in \(\{0, 1, 2, \dots, n\}\).

BetaNegativeBinomial: Negative Binomial Distribution with a marginalized Beta prior. Values in \(\{0, 1, 2, \dots\}\).

Binomial: A sum of \(n\) iid Bernoulli variables. Values in \(\{0, 1, 2, \dots, n\}\).

Categorical: Any random variable over a finite set \(\{0, 1, 2, \dots, n-1\}\).

DiscreteUniform: Uniform random variable over the contiguous set of integers \(\{m, m+1, \dots, M-1\}\).

Geometric: The number of unsuccessful Bernoulli trials until a success. Values in \(\{0, 1, 2, \dots\}\)

HyperGeometric: A population of size \(N\), \(K\) of which are marked, and drawing without replacement \(n\) samples from the population; the HyperGeometric models the number in the sample that are marked.

NegativeBinomial: Number of successes in a sequence of iid Bernoulli until \(r\) failures occur. Values in \(\{0, 1, 2, \dots\}\).

Poisson: Poisson random variable. Values in \(0, 1, 2, \dots\)

YuleSimon: An exponential-geometric mixture.


Beta: Beta random variable on the open interval \((0, 1)\).

ChiSquared: Chi Squared random variable. Values in \((0, \infty)\).

ContinuousUniform: Uniform random variable over a close interval \([m, M]\).

Exponential: Exponential random variable. Values in \((0, \infty)\)

F: The F-distribution. Also known as Fisher-Snedecor distribution. Values in \((0, +\infty) \)

Gamma: Gamma random variable. Values in \((0, \infty)\).

Gompertz: The Gompertz distribution. Values in \([0, \infty) \).

Gumbel: The Gumbel Distribution. Values in \( \mathbb{R} \)

HalfStudentT: HalfStudentT random variable. Values in \((0, \infty)\)

Laplace: The Laplace Distribution over \(\mathbb{R}\)

Logistic: A random variable with a cumulative distribution given by the logistic function. Values in \( \mathbb{R} \)

LogLogistic: A log-logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution. Values in \([0, +\infty) \)

LogUniform: The random variable \(X = b^Y\) where \(Y \sim \text{ContinuousUniform}[m, M]\).

LnUniform: The random variable \(X = e^Y\) where \(Y \sim \text{ContinuousUniform}[m, M]\).

Normal: Normal random variables. Values in \(\mathbb{R}\)

StudentT: Student T random variable. Values in \(\mathbb{R}\)

Weibull: The Weibull Distribution. Values in \((0, \infty)\).


Dirichlet: The Dirichlet distribution over vectors of probabilities \((p_0, p_1, \dots, p_{n-1})\). \(p_i \in (0, 1), \sum_i p_i = 1.\)

MultivariateNormal: Arbitrary linear transformations of \(n\) iid standard normal random variables.

NormalField: A mean-zero normal, sparse-precision Markov random field.

SimplexUniform: \(n\) dimensional Dirichlet with all concentrations equal to one.

SymmetricDirichlet: \(n\) dimensional Dirichlet with all concentrations equal to \(\alpha / n\).


LogPotential: Not really a distribution, but rather a way to handle undirected model (AKA random fields). See Ising under the Examples page.