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- Exponential_family abstract ""Natural parameter" links here. For the usage of this term in differential geometry, see differential geometry of curves.In probability and statistics, the exponential family is an important class of probability distributions sharing a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural distributions to consider. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–36. The term exponential class is sometimes used in place of "exponential family".The exponential families include many of the most common distributions, including the normal, exponential, gamma, chi-squared, beta, Dirichlet, Bernoulli, categorical, Poisson, Wishart, Inverse Wishart and many others. A number of common distributions are exponential families only when certain parameters are considered fixed and known, e.g. binomial (with fixed number of trials), multinomial (with fixed number of trials), and negative binomial (with fixed number of failures). Examples of common distributions that are not exponential families are Student's t, most mixture distributions, and even the family of uniform distributions with unknown bounds. See the section below on examples for more discussion.Consideration of exponential-family distributions provides a general framework for selecting a possible alternative parameterisation of the distribution, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family. See below for more information.".
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- Exponential_family wikiPageExternalLink mathword.html.
- Exponential_family wikiPageExternalLink jMEF.
- Exponential_family wikiPageExternalLink 04dpp117.pdf.
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- Exponential_family wikiPageRevisionID "598833575".
- Exponential_family hasPhotoCollection Exponential_family.
- Exponential_family subject Category:Continuous_distributions.
- Exponential_family subject Category:Discrete_distributions.
- Exponential_family subject Category:Exponentials.
- Exponential_family subject Category:Types_of_probability_distributions.
- Exponential_family type Abstraction100002137.
- Exponential_family type Arrangement105726596.
- Exponential_family type Cognition100023271.
- Exponential_family type ContinuousDistributions.
- Exponential_family type DiscreteDistributions.
- Exponential_family type Distribution105729036.
- Exponential_family type Exponential113789462.
- Exponential_family type Exponentials.
- Exponential_family type Function113783816.
- Exponential_family type MathematicalRelation113783581.
- Exponential_family type PsychologicalFeature100023100.
- Exponential_family type Relation100031921.
- Exponential_family type Structure105726345.
- Exponential_family comment ""Natural parameter" links here. For the usage of this term in differential geometry, see differential geometry of curves.In probability and statistics, the exponential family is an important class of probability distributions sharing a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural distributions to consider.".
- Exponential_family label "Exponential family".
- Exponential_family label "Exponentialfamilie".
- Exponential_family label "Exponentiële familie".
- Exponential_family label "Familia exponencial".
- Exponential_family label "Famille exponentielle".
- Exponential_family label "أسرة الأسس".
- Exponential_family sameAs Exponentialfamilie.
- Exponential_family sameAs Familia_exponencial.
- Exponential_family sameAs Famille_exponentielle.
- Exponential_family sameAs 지수족.
- Exponential_family sameAs Exponentiële_familie.
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