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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 ...
List of representations of e; Euler's identity; Exponential decay; Exponential distribution; Exponential factorial; Exponential family; Exponential formula; Exponential function; Exponential growth; Exponential integral; Exponential minus 1; Exponential sum; Exponentiation; Exponentiation by squaring
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.
The natural exponential family of a distribution may be realized by shifting or translating K(t), and adjusting it vertically so that it always passes through the origin: if f is the pdf with cumulant generating function () = (), and | is its natural exponential family, then () = (), and () = (+) ().
This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. ... Exponential family; Exponential field; Exponential formula;
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.
These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF). More general distributions can be defined by fixing some initial values of p j and applying the recursion to define subsequent values. This can be of use in fitting distributions to empirical data.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
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