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Fisher Information Matrix of the Dirichlet‐multinomial Distribution
Author(s) -
Paul Sudhir R.,
Balasooriya Uditha,
Banerjee Tathagata
Publication year - 2005
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200410103
Subject(s) - multinomial distribution , mathematics , dirichlet distribution , fisher information , statistics , negative multinomial distribution , econometrics , beta binomial distribution , negative binomial distribution , mathematical analysis , poisson distribution , boundary value problem
Abstract In this paper we derive explicit expressions for the elements of the exact Fisher information matrix of the Dirichlet‐multinomial distribution. We show that exact calculation is based on the beta‐binomial probability function rather than that of the Dirichlet‐multinomial and this makes the exact calculation quite easy. The exact results are expected to be useful for the calculation of standard errors of the maximum likelihood estimates of the beta‐binomial parameters and those of the Dirichlet‐multinomial parameters for data that arise in practice in toxicology and other similar fields. Standard errors of the maximum likelihood estimates of the beta‐binomial parameters and those of the Dirichlet‐multinomial parameters, based on the exact and the asymptotic Fisher information matrix based on the Dirichlet distribution, are obtained for a set of data from Haseman and Soares (1976), a dataset from Mosimann (1962) and a more recent dataset from Chen, Kodell, Howe and Gaylor (1991). There is substantial difference between the standard errors of the estimates based on the exact Fisher information matrix and those based on the asymptotic Fisher information matrix. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)