In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. They were...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

Gaussian distribution, a convolution of a normal distribution with an exponential distribution, and the Gaussian minus exponential distribution, a convolution...

information matrix. "1/p" is Jeffreys' (1946) invariant prior for the exponential distribution, not for the Bernoulli or binomial distributions). However...

gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and...

chi-squared distribution simplifies to an exponential distribution with mean equal to two (rate equal to half). The complementary cumulative distribution function...

In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special...

to exponentiation, including: Exponential function, also: Matrix exponential, the matrix analogue to the above Exponential decay, decrease at a rate proportional...

multivariate normal distribution and for matrices in the matrix normal distribution. The simplest case of a normal distribution is known as the standard...

and the exponential distribution which has coefficient of variation of one. The Erlang distribution is a series of k exponential distributions all with...

underlying distribution is normal. Unlike more widely known distributions such as the normal distribution and the exponential distribution, the chi-squared...

normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random...

equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Exponential formula...

first formulated the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually...

A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system...

about properties of the Dirichlet distribution. Because the Dirichlet distribution is an exponential family distribution it has a conjugate prior. The conjugate...

Lie group is the exponential map, which is defined using the standard matrix exponential series for eA For any skew-symmetric matrix A, exp(A) is always...

that empirical distribution p ^ {\displaystyle {\hat {p}}} deviates from the actual distribution p {\displaystyle p} decays exponentially, at a rate n D...

parameter of the distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to...

construction can be generalized by starting with a normal distribution with a general covariance matrix, in which case conditioning on ‖ x ‖ = 1 {\displaystyle...

otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models...

through exponential growth and exponential diffusion of innovations Population sizes of cities in a region or urban network, Zipf's law. Distribution of artists...

eigenvalues), one can derive a relation between the trace function, the matrix exponential function, and the determinant: det ( exp ⁡ ( A ) ) = exp ⁡ ( tr ⁡...

hypergeometric distribution Poisson distribution, for the number of occurrences of a Poisson-type event in a given period of time Exponential distribution, for...

space, a transition matrix describing the probabilities of particular transitions, and an initial state (or initial distribution) across the state space...

vector-valued and matrix-valued parameters. (See the general article on the exponential family, and also consider the Wishart distribution, conjugate prior...

as Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The same result is used when approximating the posterior with...

may also refer to: List of exponential topics Exponential function, a function of a certain form Matrix exponential, a matrix function on square matrices...

Binomial distribution Compound Poisson distribution Conway–Maxwell–Poisson distribution Erlang distribution Exponential distribution Gamma distribution Hermite...

can be used to compute the matrix exponential eA, a need frequently arising in solving linear differential equations, matrix logarithms and square roots...