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• Mixture_distribution abstract "In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.In cases where each of the underlying random variables is continuous, the outcome variable will also be continuous and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other distribution functions and density functions. The individual distributions that are combined to form the mixture distribution are called the mixture components, and the probabilities (or weights) associated with each component are called the mixture weights. The number of components in mixture distribution is often restricted to being finite, although in some cases the components may be countably infinite. More general cases (i.e. an uncountable set of component distributions), as well as the countable case, are treated under the title of compound distributions.A distinction needs to be made between a random variable whose distribution function or density is the sum of a set of components (i.e. a mixture distribution) and a random variable whose value is the sum of the values of two or more underlying random variables, in which case the distribution is given by the convolution operator. As an example, the sum of two jointly normally distributed random variables, each with different means, will still have a normal distribution. On the other hand, a mixture density created as a mixture of two normal distributions with different means will have two peaks provided that the two means are far enough apart, showing that this distribution is radically different from a normal distribution. Mixture distributions arise in many contexts in the literature and arise naturally where a statistical population contains two or more subpopulations. They are also sometimes used as a means of representing non-normal distributions. Data analysis concerning statistical models involving mixture distributions is discussed under the title of mixture models, while the present article concentrates on simple probabilistic and statistical properties of mixture distributions and how these relate to properties of the underlying distributions.".
• Mixture_distribution thumbnail Gaussian-mixture-example.svg?width=300.
• Mixture_distribution wikiPageID "708242".
• Mixture_distribution wikiPageLength "16681".
• Mixture_distribution wikiPageOutDegree "66".
• Mixture_distribution wikiPageRevisionID "675950310".
• Mixture_distribution wikiPageWikiLink Bayesian_network.
• Mixture_distribution wikiPageWikiLink Bimodal_distribution.
• Mixture_distribution wikiPageWikiLink Category:Probability_distributions.
• Mixture_distribution wikiPageWikiLink Category:Systems_of_probability_distributions.
• Mixture_distribution wikiPageWikiLink Compound_distribution.
• Mixture_distribution wikiPageWikiLink Compound_probability_distribution.
• Mixture_distribution wikiPageWikiLink Continuous_random_variable.
• Mixture_distribution wikiPageWikiLink Convex_combination.
• Mixture_distribution wikiPageWikiLink Convolution.
• Mixture_distribution wikiPageWikiLink Countable.
• Mixture_distribution wikiPageWikiLink Countable_set.
• Mixture_distribution wikiPageWikiLink Cumulative_distribution_function.
• Mixture_distribution wikiPageWikiLink Discrete_distribution.
• Mixture_distribution wikiPageWikiLink Expectation-maximization_algorithm.
• Mixture_distribution wikiPageWikiLink Expectation–maximization_algorithm.
• Mixture_distribution wikiPageWikiLink Experimental_error.
• Mixture_distribution wikiPageWikiLink Exponential_distribution.
• Mixture_distribution wikiPageWikiLink Fat-tailed_distribution.
• Mixture_distribution wikiPageWikiLink Fat_tail.
• Mixture_distribution wikiPageWikiLink Generalized_function.
• Mixture_distribution wikiPageWikiLink Graphical_model.
• Mixture_distribution wikiPageWikiLink Hierarchical_Bayes_model.
• Mixture_distribution wikiPageWikiLink Homoscedastic.
• Mixture_distribution wikiPageWikiLink Homoscedasticity.
• Mixture_distribution wikiPageWikiLink Joint_probability_distribution.
• Mixture_distribution wikiPageWikiLink Kurtosis.
• Mixture_distribution wikiPageWikiLink Linear_combination.
• Mixture_distribution wikiPageWikiLink List_of_convolutions_of_probability_distributions.
• Mixture_distribution wikiPageWikiLink Mahalanobis_distance.
• Mixture_distribution wikiPageWikiLink Manifold.
• Mixture_distribution wikiPageWikiLink Margin_of_error.
• Mixture_distribution wikiPageWikiLink Meta-analysis.
• Mixture_distribution wikiPageWikiLink Mixture_(probability).
• Mixture_distribution wikiPageWikiLink Mixture_model.
• Mixture_distribution wikiPageWikiLink Multimodal_distribution.
• Mixture_distribution wikiPageWikiLink Multivariate_distribution.
• Mixture_distribution wikiPageWikiLink Multivariate_normal_distribution.
• Mixture_distribution wikiPageWikiLink Multivariate_random_variable.
• Mixture_distribution wikiPageWikiLink Normal_distribution.
• Mixture_distribution wikiPageWikiLink Observational_error.
• Mixture_distribution wikiPageWikiLink Outlier.
• Mixture_distribution wikiPageWikiLink Outliers.
• Mixture_distribution wikiPageWikiLink Overdispersion.
• Mixture_distribution wikiPageWikiLink Parametric_family.
• Mixture_distribution wikiPageWikiLink Probability.
• Mixture_distribution wikiPageWikiLink Probability_density_function.
• Mixture_distribution wikiPageWikiLink Probability_distribution.
• Mixture_distribution wikiPageWikiLink Random_variable.
• Mixture_distribution wikiPageWikiLink Random_vector.
• Mixture_distribution wikiPageWikiLink Robust_statistics.
• Mixture_distribution wikiPageWikiLink Sampling_bias.
• Mixture_distribution wikiPageWikiLink Sampling_error.
• Mixture_distribution wikiPageWikiLink Skewness.
• Mixture_distribution wikiPageWikiLink Statistical_model.
• Mixture_distribution wikiPageWikiLink Statistical_population.
• Mixture_distribution wikiPageWikiLink Statistical_survey.
• Mixture_distribution wikiPageWikiLink Statistics.
• Mixture_distribution wikiPageWikiLink Study_heterogeneity.
• Mixture_distribution wikiPageWikiLink Subpopulation.
• Mixture_distribution wikiPageWikiLink Survey_methodology.
• Mixture_distribution wikiPageWikiLink Uncountable.
• Mixture_distribution wikiPageWikiLink Uncountable_set.
• Mixture_distribution wikiPageWikiLink Unimodality.
• Mixture_distribution wikiPageWikiLink File:Gaussian-mixture-example.svg.
• Mixture_distribution wikiPageWikiLinkText "Mixture distribution".
• Mixture_distribution wikiPageWikiLinkText "finite mixture distribution".
• Mixture_distribution wikiPageWikiLinkText "mixed distribution".
• Mixture_distribution wikiPageWikiLinkText "mixture distribution".
• Mixture_distribution wikiPageWikiLinkText "mixture model".
• Mixture_distribution wikiPageWikiLinkText "mixture".
• Mixture_distribution wikiPageWikiLinkText "mixtures".
• Mixture_distribution wikiPageWikiLinkText "the mixtures of densities".
• Mixture_distribution hasPhotoCollection Mixture_distribution.
• Mixture_distribution wikiPageUsesTemplate Template:=.
• Mixture_distribution wikiPageUsesTemplate Template:Citation_needed.
• Mixture_distribution wikiPageUsesTemplate Template:Cite.
• Mixture_distribution wikiPageUsesTemplate Template:Details.
• Mixture_distribution wikiPageUsesTemplate Template:Expand_section.
• Mixture_distribution wikiPageUsesTemplate Template:Main.
• Mixture_distribution wikiPageUsesTemplate Template:Reflist.
• Mixture_distribution wikiPageUsesTemplate Template:See_also.
• Mixture_distribution subject Category:Probability_distributions.
• Mixture_distribution subject Category:Systems_of_probability_distributions.
• Mixture_distribution hypernym Distribution.
• Mixture_distribution type Article.
• Mixture_distribution type Software.
• Mixture_distribution type Article.
• Mixture_distribution type Thing.
• Mixture_distribution comment "In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.".
• Mixture_distribution label "Mixture distribution".
• Mixture_distribution seeAlso Mixture_model.
• Mixture_distribution sameAs m.034lf0.
• Mixture_distribution sameAs Q17157111.
• Mixture_distribution sameAs Q17157111.

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