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On Countable Mixtures of Bivariate Binomial Distributions
Author(s) -
Papageorgiou H.,
David Katerina M.
Publication year - 1994
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.4710360510
Subject(s) - mathematics , bivariate analysis , factorial , binomial (polynomial) , statistics , cumulant , conditional probability distribution , continuity correction , binomial distribution , negative binomial distribution , joint probability distribution , statistical parameter , beta binomial distribution , poisson distribution , mathematical analysis
A unified treatment is given for mixtures of bivariate binomial distributions with respect to their index parameter(s). The use of probability generating functions is employed and a number of interesting properties including probabilities, factorial moments, factorial cumulants and conditional distributions are derived. Five classes of such mixtures are examined and several well known bivariate discrete distributions are used as illustrative examples. Biological applications are indicated including the fit of three bivariate distributions to an actual set of human family data.