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

natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF). The natural exponential families...

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance...

Look up exponential or exponentially in Wiktionary, the free dictionary. Exponential may refer to any of several mathematical topics related to exponentiation...

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

Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function...

plugged in. Most, but not all, common families of distributions are exponential families. Exponential families have a large number of useful properties...

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

Exponential Random Graph Models (ERGMs) are a family of statistical models for analyzing data from social and other networks. Examples of networks examined...

distribution The Marshall–Olkin exponential distribution The continuous-categorical distribution, an exponential family supported on the simplex that generalizes...

theorem, among families of probability distributions whose domain does not vary with the parameter being estimated, only in exponential families is there a...

particular since most common probability distributions—notably the exponential family—are only logarithmically concave, and concavity of the objective function...

the weights in the exponential moving average which follows. An exponential moving average (EMA), also known as an exponentially weighted moving average...

problems for which the theorem holds. In particular, the one-dimensional exponential family of probability density functions or probability mass functions with...

=g^{-1}(\eta )} . An overdispersed exponential family of distributions is a generalization of an exponential family and the exponential dispersion model of distributions...

strongly discouraged. For error distributions that belong to the exponential family, a link function may be used to transform the parameters under the...

probability and statistics, the class of exponential dispersion models (EDM), also called exponential dispersion family (EDF), is a set of probability distributions...

The family of normal distributions not only forms an exponential family (EF), but in fact forms a natural exponential family (NEF) with quadratic...

It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location...

from an exponential family with identity as its natural sufficient statistics and mild-conditions are satisfied (e.g. for normal, exponential, Poisson...

for the network. Any positive Markov random field can be written as exponential family in canonical form with feature functions f k {\displaystyle f_{k}}...

proof established the EM method's convergence also outside of the exponential family, as claimed by Dempster–Laird–Rubin. The EM algorithm is used to find...

general result whenever the prior distributions are members of the exponential family, which is the case for most of the standard distributions. The above...

communication theory. The Rényi entropies and divergences for an exponential family admit simple expressions H α ( p F ( x ; θ ) ) = 1 1 − α ( F ( α θ...

algorithm can be very inefficient. The Natural Exponential Family (if it exists), also known as exponential tilting, provides a class of proposal distributions...

cases of the Panjer distribution. They are also members of a natural exponential family. Suppose p is unknown and an experiment is conducted where it is decided...

an exponential family with sufficient statistic T = log ⁡ ( 1 + e − x ) {\displaystyle T=\log(1+e^{-x})} . In fact this is a full rank exponential family...

different exponential tiltings of a random variable X {\displaystyle X} is known as the natural exponential family of X {\displaystyle X} . Exponential Tilting...

{Beta} (p;\alpha ;\beta )=(n+1)B(k;n;p)} Beta distributions also provide a family of prior probability distributions for binomial distributions in Bayesian...

, n ) = Exponential ⁡ ( 1 ) {\displaystyle \lim _{n\to \infty }n\operatorname {Beta} (1,n)=\operatorname {Exponential} (1)} the exponential distribution...