# Category: Types of probability distributions

Exponential family
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, incl
Tsallis distribution
In statistics, a Tsallis distribution is a probability distribution derived from the maximization of the Tsallis entropy under appropriate constraints. There are several different families of Tsallis
Univariate distribution
In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector
Wrapped distribution
In probability theory and directional statistics, a wrapped probability distribution is a continuous probability distribution that describes data points that lie on a unit n-sphere. In one dimension,
Taleb distribution
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of ca
Degenerate distribution
In mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension, and according to others a distribution with s
Utilization distribution
A utilization distribution is a probability distribution giving the probability density that an animal is found at a given point in space. It is estimated from data sampling the location of an individ
Location–scale family
In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter.
Indecomposable distribution
In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables:
Discrete-stable distribution
The discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution is distributed according to the same fami
Exchangeable random variables
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distributi
Compound probability distribution
In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a r
Ratio distribution
A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions.Given t
Super-Poissonian distribution
In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a
Infinite divisibility (probability)
In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distri
2-EPT probability density function
In probability theory, a 2-EPT probability density function is a class of probability density functions on the real line. The class contains the density functions of all distributions that have charac
Group family
In probability theory, especially as that field is used in statistics, a group family of probability distributions is a family obtained by subjecting a random variable with a fixed distribution to a s
A dyadic (or 2-adic) distribution is a specific type of discrete or categorical probability distribution that is of some theoretical importance in data compression.
Heavy-tailed distribution
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many a
Mixed Poisson distribution
A mixed Poisson distribution is a univariate discrete probability distribution in stochastics. It results from assuming that the conditional distribution of a random variable, given the value of the r
Occupancy frequency distribution
In macroecology and community ecology, an occupancy frequency distribution (OFD) is the distribution of the numbers of species occupying different numbers of areas. It was first reported in 1918 by th
NEF-QVF
No description available.
Circular distribution
In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π). A cir
Asymptotic distribution
In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea
Singular distribution
In probability, a singular distribution is a probability distribution concentrated on a set of Lebesgue measure zero, where the probability of each point in that set is zero.
Elliptical distribution
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplif
Joint probability distribution
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint
Directional statistics
Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, Rn), axes (lines through the o
List of probability distributions
Many probability distributions that are important in theory or applications have been given specific names.
Maximum entropy probability distribution
In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. A
Truncated distribution
In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statis
Natural exponential family
In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF).
Discrete phase-type distribution
The discrete phase-type distribution is a probability distribution that results from a system of one or more inter-related geometric distributions occurring in sequence, or phases. The sequence in whi
Distribution of the product of two random variables
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random
Inverse distribution
In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior dis
Symmetric probability distribution
In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for c
Probability mass function
In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the di
Phase-type distribution
A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes oc