A generalization of the Binomial distribution based on the dependence ratio

Gianfranco Lovison

Statistica Neerlandica, 2015, vol. 69, issue 2, 126-149

Abstract: type="main" xml:id="stan12053-abs-0001"> We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Correlated-Binomial distribution, we believe its introduction is useful, both in terms of interpretability and mathematical tractability and in terms of generalizability to the Multinomial case.

Date: 2015
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