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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, an exponential family is a set of probability distributions of 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 sets of 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. For more information, see below.".
- Exponential_family wikiPageExternalLink e.html.
- Exponential_family wikiPageExternalLink mathword.html.
- Exponential_family wikiPageExternalLink jMEF.
- Exponential_family wikiPageExternalLink 04dpp117.pdf.
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- Exponential_family wikiPageRevisionID "705099353".
- Exponential_family wikiPageWikiLink Absolute_continuity.
- Exponential_family wikiPageWikiLink Bayesian_network.
- Exponential_family wikiPageWikiLink Bayesian_statistics.
- Exponential_family wikiPageWikiLink Bernard_Koopman.
- Exponential_family wikiPageWikiLink Bernoulli_distribution.
- Exponential_family wikiPageWikiLink Beta-binomial_distribution.
- Exponential_family wikiPageWikiLink Beta_distribution.
- Exponential_family wikiPageWikiLink Bijection.
- Exponential_family wikiPageWikiLink Binomial_distribution.
- Exponential_family wikiPageWikiLink Calculus_of_variations.
- Exponential_family wikiPageWikiLink Canonical_form.
- Exponential_family wikiPageWikiLink Categorical_distribution.
- Exponential_family wikiPageWikiLink Category:Continuous_distributions.
- Exponential_family wikiPageWikiLink Category:Discrete_distributions.
- Exponential_family wikiPageWikiLink Category:Exponentials.
- Exponential_family wikiPageWikiLink Category:Types_of_probability_distributions.
- Exponential_family wikiPageWikiLink Cauchy_distribution.
- Exponential_family wikiPageWikiLink Chi-squared_distribution.
- Exponential_family wikiPageWikiLink Compound_probability_distribution.
- Exponential_family wikiPageWikiLink Conjugate_prior.
- Exponential_family wikiPageWikiLink Convex_set.
- Exponential_family wikiPageWikiLink Counting_measure.
- Exponential_family wikiPageWikiLink Cumulant.
- Exponential_family wikiPageWikiLink Cumulative_distribution_function.
- Exponential_family wikiPageWikiLink Derivative.
- Exponential_family wikiPageWikiLink Differential_geometry_of_curves.
- Exponential_family wikiPageWikiLink Digamma_function.
- Exponential_family wikiPageWikiLink Dimension.
- Exponential_family wikiPageWikiLink Dirichlet-multinomial_distribution.
- Exponential_family wikiPageWikiLink Dirichlet_distribution.
- Exponential_family wikiPageWikiLink Dot_product.
- Exponential_family wikiPageWikiLink E._J._G._Pitman.
- Exponential_family wikiPageWikiLink Entropy_(information_theory).
- Exponential_family wikiPageWikiLink Exponential_dispersion_model.
- Exponential_family wikiPageWikiLink Exponential_distribution.
- Exponential_family wikiPageWikiLink Exponential_family.
- Exponential_family wikiPageWikiLink Exponentiation.
- Exponential_family wikiPageWikiLink F-distribution.
- Exponential_family wikiPageWikiLink Factorization.
- Exponential_family wikiPageWikiLink Gamma_distribution.
- Exponential_family wikiPageWikiLink Gamma_function.
- Exponential_family wikiPageWikiLink Generalized_linear_model.
- Exponential_family wikiPageWikiLink Generalized_logistic_distribution.
- Exponential_family wikiPageWikiLink Geometric_distribution.
- Exponential_family wikiPageWikiLink Georges_Darmois.
- Exponential_family wikiPageWikiLink Gibbs_measure.
- Exponential_family wikiPageWikiLink Heavy-tailed_distribution.
- Exponential_family wikiPageWikiLink Hypergeometric_distribution.
- Exponential_family wikiPageWikiLink Hyperparameter.
- Exponential_family wikiPageWikiLink Hyperprior.
- Exponential_family wikiPageWikiLink Identifiability.
- Exponential_family wikiPageWikiLink Independence_(probability_theory).
- Exponential_family wikiPageWikiLink Independent_and_identically_distributed_random_variables.
- Exponential_family wikiPageWikiLink Inverse-Wishart_distribution.
- Exponential_family wikiPageWikiLink Inverse-gamma_distribution.
- Exponential_family wikiPageWikiLink Inverse_Gaussian_distribution.
- Exponential_family wikiPageWikiLink Iverson_bracket.
- Exponential_family wikiPageWikiLink Kernel_(statistics).
- Exponential_family wikiPageWikiLink Lagrange_multiplier.
- Exponential_family wikiPageWikiLink Laplace_distribution.
- Exponential_family wikiPageWikiLink Lebesgue–Stieltjes_integration.
- Exponential_family wikiPageWikiLink Likelihood_function.
- Exponential_family wikiPageWikiLink Log-normal_distribution.
- Exponential_family wikiPageWikiLink Logarithm.
- Exponential_family wikiPageWikiLink Logistic_distribution.
- Exponential_family wikiPageWikiLink Logistic_function.
- Exponential_family wikiPageWikiLink Logit.
- Exponential_family wikiPageWikiLink Matrix_calculus.
- Exponential_family wikiPageWikiLink Matrix_multiplication.
- Exponential_family wikiPageWikiLink Maximum_entropy_probability_distribution.
- Exponential_family wikiPageWikiLink Mean.
- Exponential_family wikiPageWikiLink Measure_(mathematics).
- Exponential_family wikiPageWikiLink Mixture_distribution.
- Exponential_family wikiPageWikiLink Mixture_model.
- Exponential_family wikiPageWikiLink Moment-generating_function.
- Exponential_family wikiPageWikiLink Moment_(mathematics).
- Exponential_family wikiPageWikiLink Multinomial_distribution.
- Exponential_family wikiPageWikiLink Multivariate_gamma_function.
- Exponential_family wikiPageWikiLink Multivariate_normal_distribution.
- Exponential_family wikiPageWikiLink Multivariate_random_variable.
- Exponential_family wikiPageWikiLink Natural_exponential_family.
- Exponential_family wikiPageWikiLink Negative_binomial_distribution.
- Exponential_family wikiPageWikiLink Normal-gamma_distribution.
- Exponential_family wikiPageWikiLink Normal_distribution.
- Exponential_family wikiPageWikiLink Normalization_(statistics).
- Exponential_family wikiPageWikiLink Normalizing_constant.
- Exponential_family wikiPageWikiLink Parametrization.
- Exponential_family wikiPageWikiLink Pareto_distribution.
- Exponential_family wikiPageWikiLink Partition_function_(mathematics).
- Exponential_family wikiPageWikiLink Poisson_distribution.
- Exponential_family wikiPageWikiLink Posterior_predictive_distribution.