Bivariate natural exponential families with quadratic diagonal of the variance function

Joanna Matysiak

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arXiv · 1504.05219

Bivariate natural exponential families with quadratic diagonal of the variance function

Joanna Matysiak

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Abstract

We characterize bivariate natural exponential families having the diagonal of the variance function of the form \[ \textrm{diag} V(m_1,m_2)=\left(Am_1^2+am_1+bm_2+e,Am_2^2+cm_1+dm_2+f\right), \] with $A<0$ and $a,\ldots,f\in\mathbb{R}$. 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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Joanna Matysiak. 2015-04-20. Bivariate natural exponential families with quadratic diagonal of the variance function. https://arxiv.org/abs/1504.05219

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