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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 lognormal and Beta distribution are in the exponential family, but not the natural exponential family. 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 ...
Download as PDF; Printable version; In other projects ... also known as the Natural Exponential Family ... (PDF). Biometrika. 81 (2): 396–402.
Category: Exponential family distributions. ... Print/export Download as PDF; Printable version; In other projects
Download as PDF; Printable version; ... Normal distributions form an exponential family with natural parameters ... may be a value from a distribution table, ...
In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision .
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.
Toggle the table of contents. ... Download as PDF; Printable version; ... Because the Dirichlet distribution is an exponential family distribution it has a conjugate ...