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The Structure of Compounded Trivariate Binomial Distributions
Author(s) -
Papageorgiou H.,
David Katerina M.
Publication year - 1995
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.4710370107
Subject(s) - mathematics , factorial , poisson distribution , negative binomial distribution , binomial (polynomial) , logarithm , binomial distribution , statistics , negative multinomial distribution , poisson binomial distribution , cumulant , logarithmic distribution , beta binomial distribution , mathematical analysis
A family of trivariate binomial mixtures with respect to their exponent parameter is introduced and its structure is studied by the use of probability generating functions. Expressions for probabilities, factorial moments and factorial cumulants are given. Conditional distributions are also examined. Illustrative examples include the trivariate Poisson, binomial, negative binomial and modified logarithmic series distributions. In addition, properties of the compounded trivariate Poisson distribution are discussed. Finally biological, medical and ecological applications are indicated.