Multivariate t-distribution

In statistics, the multivariate t -distribution is a multivariate probability distribution. It is a generalization to random vectors of the Students t -distribution, which is a distribution applicable to univariate random variables. While the cas ...

Nakagami distribution

The Nakagami distribution or the Nakagami- m distribution is a probability distribution related to the gamma distribution. The family of Nakagami distributions has two parameters: a shape parameter m ≥ 1 / 2 {\displaystyle m\geq 1/2} and a second ...

Noncentral beta distribution

In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a generalization of the beta distribution. The noncentral beta distribution Type I is the distribution of the ratio X = χ m 2 ...

Noncentral chi distribution

If X i {\displaystyle X_{i}} are k independent, normally distributed random variables with means μ i {\displaystyle \mu _{i}} and variances σ i 2 {\displaystyle \sigma _{i}^{2}}, then the statistic Z = ∑ i = 1 k X i σ i 2 {\displaystyle Z={\sqrt ...

Noncentral F-distribution

In probability theory and statistics, the noncentral F -distribution is a continuous probability distribution that is a generalization of the F -distribution. It describes the distribution of the quotient, where the numerator X has a noncentral c ...

Noncentral t-distribution

As with other probability distributions with noncentrality parameters, the noncentral t -distribution generalizes a probability distribution – Students t -distribution – using a noncentrality parameter. Whereas the central distribution describes ...

Normal-inverse Gaussian distribution

The normal-inverse Gaussian distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution. The NIG distribution was noted by Blaesild in 197 ...

Normal-inverse-gamma distribution

In probability theory and statistics, the normal-inverse-gamma distribution is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance.

PERT distribution

In probability and statistics, the PERT distribution is a family of continuous probability distributions defined by the minimum, most likely and maximum values that a variable can take. It is a transformation of the four-parameter Beta distributi ...

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 occurring in sequence, or phases. The sequence i ...

Rayleigh distribution

In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. It is essentially a chi distribution with two degrees of freedom. A Rayleigh distribution is often o ...

Reciprocal distribution

In probability and statistics, the reciprocal distribution, also known as the log-uniform distribution, is a continuous probability distribution. It is characterised by its probability density function, within the support of the distribution, bei ...

Scaled inverse chi-squared distribution

The scaled inverse chi-squared distribution is the distribution for x = 1/ s 2, where s 2 is a sample mean of the squares of ν independent normal random variables that have mean 0 and inverse variance 1/σ 2 = τ 2. The distribution is therefore pa ...

Shifted Gompertz distribution

The shifted Gompertz distribution is the distribution of the larger of two independent random variables one of which has an exponential distribution with parameter b {\displaystyle b} and the other has a Gumbel distribution with parameters η {\di ...

Shifted log-logistic distribution

The shifted log-logistic distribution is a probability distribution also known as the generalized log-logistic or the three-parameter log-logistic distribution. It has also been called the generalized logistic distribution, but this conflicts wit ...

Skew normal distribution

In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.

Slash distribution

In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate. In other words, if the random variable Z has a normal distribution with zero mean and u ...

Split normal distribution

In probability theory and statistics, the split normal distribution also known as the two-piece normal distribution results from joining at the mode the corresponding halves of two normal distributions with the same mode but different variances. ...

Studentized range distribution

In probability and statistics, studentized range distribution is the continuous probability distribution of the studentized range of an i.i.d. sample from a normally distributed population. Suppose that we take a sample of size n from each of k p ...

Sub-Gaussian distribution

In probability theory, a sub-Gaussian distribution is a probability distribution with strong tail decay. Informally, the tails of a sub-Gaussian distribution are dominated by the tails of a Gaussian. Formally, the probability distribution of a ra ...

Truncated normal distribution

In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above. The truncated normal distribu ...

Tukey lambda distribution

Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution and not used in statistical models ...

In probability theory and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and upper limit b. f x | a, b, α, β = α x − β 2, for x ∈.}

Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies betwe ...

Variance-gamma distribution

The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The ...

Von Mises distribution

In probability theory and directional statistics, the von Mises distribution is a continuous probability distribution on the circle. It is a close approximation to the wrapped normal distribution, which is the circular analogue of the normal dist ...

Von Mises–Fisher distribution

In directional statistics, the von Mises–Fisher distribution, is a probability distribution on the {\displaystyle } -sphere in R p {\displaystyle \mathbb {R} ^{p}}. If p = 2 {\displaystyle p=2} the distribution reduces to the von Mises distributi ...

Wakeby distribution

The Wakeby distribution is a five-parameter probability distribution defined by its quantile function, W p = ξ + α β 1 − 1 − p β) − γ δ 1 − 1 − p − δ) {\displaystyle Wp=\xi +{\frac {\alpha }{\beta }}1-1-p^{\beta })-{\frac {\gamma }{\delta }}1-1-p ...

Wilkss lambda distribution

In statistics, Wilks lambda distribution, is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance.

Wrapped asymmetric Laplace distribution

In probability theory and directional statistics, a wrapped asymmetric Laplace distribution is a wrapped probability distribution that results from the "wrapping" of the asymmetric Laplace distribution around the unit circle. For the symmetric ca ...

Wrapped Cauchy distribution

In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known a ...

Wrapped exponential distribution

In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the "wrapping" of the exponential distribution around the unit circle.

Wrapped Levy distribution

In probability theory and directional statistics, a wrapped Levy distribution is a wrapped probability distribution that results from the "wrapping" of the Levy distribution around the unit circle.

Wrapped normal distribution

In probability theory and directional statistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution around the unit circle. It finds application in the theory of Browni ...

Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named ...

Borel distribution

The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory. It is named after the French mathematician Emile Borel. If the number of offspring that an organism has is Poiss ...

Categorical distribution

In probability theory and statistics, a categorical distribution is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category ...

Conway–Maxwell–binomial distribution

In probability theory and statistics, the Conway–Maxwell–binomial distribution is a three parameter discrete probability distribution that generalises the binomial distribution in an analogous manner to the way that the Conway–Maxwell–Poisson dis ...

Degenerate distribution

In mathematics, a degenerate distribution is a probability distribution in a space with support only on a space of lower dimension. If the degenerate distribution is univariate it is a deterministic distribution and takes only a single value. Exa ...

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 which each of the phases occur may itself be a st ...

Discrete uniform distribution

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/ n. Another way of ...

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 family. They are the discrete analogue of the cont ...

Fishers noncentral hypergeometric distribution

In probability theory and statistics, Fishers noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified by weight factors. It can also be defined as the conditional dis ...

Geometric distribution

In probability theory and statistics, the geometric distribution is either of two discrete probability distributions: The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3. } ...

Kirkwood approximation

The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function P {\displaystyle P} is give ...

Logarithmic distribution

In probability and statistics, the logarithmic distribution is a discrete probability distribution derived from the Maclaurin series expansion − ln ⁡ 1 − p = p + p 2 + p 3 + ⋯. {\displaystyle -\ln1-p=p+{\frac {p^{2}}{2}}+{\frac {p^{3}}{3}}+\cdots ...

Noncentral hypergeometric distributions

In statistics, the hypergeometric distribution is the discrete probability distribution generated by picking colored balls at random from an urn without replacement. Various generalizations to this distribution exist for cases where the picking o ...

Parabolic fractal distribution

In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank. T ...