About: Dirichlet negative multinomial distribution

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In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands. If parameters of the Dirichlet distribution are , and if where

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  • In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands. If parameters of the Dirichlet distribution are , and if where then the marginal distribution of X is a Dirichlet negative multinomial distribution: In the above, is the negative multinomial distribution and is the Dirichlet distribution. (en)
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  • where is the Lauricella function (en)
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  • for (en)
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  • does not exist (en)
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  • where , and Γ is the Gamma function and B is the beta function. (en)
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  • for (en)
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  • In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands. If parameters of the Dirichlet distribution are , and if where (en)
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  • Dirichlet negative multinomial distribution (en)
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