Bivariate natural exponential families with quadratic diagonal of the variance function

2015/04/20 by Matysiak, Joanna
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1504.05219

Abstract

We characterize bivariate natural exponential families having the diagonal of the variance function of the form \textrmdiag V(m₁,m₂)=(Am₁²+am₁+bm₂+e,Am₂²+cm₁+dm₂+f), with A<0 and a,…,f∈ℝ. The solution of the problem relies on finding the conditions under which a specific parametric family of functions consists of Laplace transforms of some probability measures.

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