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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 gamma distribution with two parameters is an exponential family but not a NEF and the chi-squared distribution is a special case of the gamma distribution with fixed scale parameter, and thus is also an exponential family but not a NEF (note that only a gamma distribution with fixed shape parameter is a NEF).
This page was last edited on 17 December 2023, at 04:18 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
Print/export Download as PDF; ... Exponential family; Exponential formula; ... This page was last edited on 23 January 2021, ...
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
Download as PDF; Printable version; ... is an exponential family with natural parameters ... This page was last edited on 14 December 2024, ...
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 ...
This page was last edited on 7 December 2016, at 21:07 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.