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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, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a ...
The natural exponential families (NEF) are a subset of the exponential families.A NEF is an exponential family in which the natural parameter η and the natural statistic T(x) are both the identity.
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Parameter plane of the complex exponential family f(z)=exp(z)+c with 8 external ( parameter) rays. In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system. [1]
The Bernoulli distributions for form an exponential family. The maximum likelihood estimator of p {\displaystyle p} based on a random sample is the sample mean . The probability mass distribution function of a Bernoulli experiment along with its corresponding cumulative distribution function.
A pair of Saturday NFL games drew a larger viewing audience than college football for the rollout of the sport's 12-team playoff. The playoff game between SMU and Penn State averaged 6.4 million ...
In the univariate case, a real-valued random variable belongs to the additive exponential dispersion model with canonical parameter and index parameter , (,), if its probability density function can be written as
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