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Statements

Subject Item
dbr:Beta_prime_distribution
dbo:wikiPageWikiLink
dbr:Inverted_Dirichlet_distribution
Subject Item
dbr:Inverted_Dirichlet_distribution
rdfs:label
Inverted Dirichlet distribution
rdfs:comment
In statistics, the inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first described by Tiao and Cuttman in 1965. The distribution has a density function given by The distribution has applications in statistical regression and arises naturally when considering the multivariate Student distribution. It can be characterized by its mixed moments: provided that and .
dcterms:subject
dbc:Multivariate_continuous_distributions dbc:Continuous_distributions dbc:Exponential_family_distributions dbc:Conjugate_prior_distributions
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43387431
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1086192938
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dbr:Statistical_regression dbr:Support_Vector_Machine dbr:Bayesian_inference dbr:Multivariate_Student_distribution dbr:Mixture_models dbc:Continuous_distributions dbr:Dirichlet_process dbr:Moment_(mathematics) dbr:Dirichlet_distribution dbr:Hierarchical_clustering dbr:Beta_prime_distribution dbc:Exponential_family_distributions dbr:Newton–Raphson dbc:Conjugate_prior_distributions dbc:Multivariate_continuous_distributions dbr:Statistics dbr:Negative_multinomial_distribution
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dbo:abstract
In statistics, the inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first described by Tiao and Cuttman in 1965. The distribution has a density function given by The distribution has applications in statistical regression and arises naturally when considering the multivariate Student distribution. It can be characterized by its mixed moments: provided that and . The inverted Dirichlet distribution is conjugate to the negative multinomial distribution if a generalized form of odds ratio is used instead of the categories' probabilities. T. Bdiri et al. have developed several models that use the inverted Dirichlet distribution to represent and model non-Gaussian data. They have introduced finite and infinite mixture models of inverted Dirichlet distributions using the Newton–Raphson technique to estimate the parameters and the Dirichlet process to model infinite mixtures. T. Bdiri et al. have also used the inverted Dirichlet distribution to propose an approach to generate Support Vector Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering.
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wikipedia-en:Inverted_Dirichlet_distribution?oldid=1086192938&ns=0
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dbr:Generalized_beta_distribution
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Subject Item
dbr:Dirichlet_distribution
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dbr:Inverted_Dirichlet_distribution
Subject Item
dbr:List_of_things_named_after_Peter_Gustav_Lejeune_Dirichlet
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dbr:Inverted_Dirichlet_distribution
Subject Item
dbr:Negative_multinomial_distribution
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