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Summary: Multivariate generalizations of the multiplicative
binomial distribution: Introducing the MM package
P. M. E. Altham
University of Cambridge
Robin K. S. Hankin
Auckland University of Technology
Abstract
We present two natural generalizations of the multinomial and multivariate binomial
distributions, which arise from the multiplicative binomial distribution of (Altham 1978).
The resulting two distributions are discussed and we introduce an R package, MM,
which includes associated functionality.
Keywords: Generalized Linear Models, Multiplicative Binomial, Overdispersion, Overdis-
persed Binomial, Categorical Exponential Family, Multiplicative Multinomial Distribution,
R.
1. Introduction
The uses of the binomial and multinomial distributions in statistical modelling are very well
understood, with a huge variety of applications and appropriate software, but there are plenty
of real-life examples where these simple models are inadequate. In the current paper, we first
remind the reader of the two-parameter exponential family generalization of the binomial
distribution first introduced by Altham (1978) to allow for over- or under-dispersion:
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