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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.
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution , a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [ a , b ...
In probability and statistics, the class of exponential dispersion models (EDM), also called exponential dispersion family (EDF), is a set of probability distributions that represents a generalisation of the natural exponential family.
The inverse Gaussian distribution is a two-parameter exponential family with natural parameters −λ/(2μ 2) and −λ/2, and natural statistics X and 1/X.. For > fixed, it is also a single-parameter natural exponential family distribution [2] where the base distribution has density
The Bernoulli distributions for form an exponential family. The maximum likelihood estimator of 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.
Toddler nearly falls from 400-foot cliff while family visits erupting Kīlauea. Weather. Fox Weather. Multiple tornadoes strike southeastern Texas as severe storms march across South.
Pages in category "Exponential family distributions" The following 42 pages are in this category, out of 42 total. This list may not reflect recent changes. A.