Geometric dispersion models with real quadratic v-functions

Geometric dispersion models, characterized by their v-functions, are recently introduced arising from geometric sums of exponential dispersion models and they exhibit many potential applications. In this paper, we classify all the real quadratic v-functions. Up to affinity, there are only six types of such models with unbounded domain: asymmetric Laplace, geometric and the four remaining ones are obtained by the exponential mixtures of Poisson, gamma, negative binomial and generalized hyperbolic secant distributions. Further, we find the seventh one which is geometric hybrid distribution, purely a quadratic v-function on bounded domain and, classically steep as well as unbounded ones but not geometric-steep. (C) 2018 Elsevier B.V. All rights reserved.