Dirichlet-multinomial distribution

http://dbpedia.org/resource/Dirichlet-multinomial_distribution an entity of type: WikicatMultivariateDiscreteDistributions

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It i rdf:langString

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rdf:langString Dirichlet-multinomial distribution

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rdf:langString Dirichlet-Multinomial

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xsd:integer 9169137

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xsd:integer 1089112307

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rdf:langString June 2021

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rdf:langString By the same reasoning, the z_1, \dots, z_N also enter into the multinomial distribution too. The multinomial distribution is literally the distribution of the vector of the n_k's. So either the purported distinction between Dirichlet-Multinomial and Multinomial does not exist, or the given reason for the distinction is incorrect.

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rdf:langString In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected. The compounding corresponds to a Pólya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large α. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively.

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