Resolution of a conjecture on variance functions for one-parameter natural exponential families

Xiongzhi Chen

Statistics & Probability Letters, 2016, vol. 118, issue C, 107-109

Abstract: We prove a conjecture of Bar-Lev, Bshouty and Enis stating that a polynomial with a simple root at 0 and a complex root with positive imaginary part is the variance function of a one-parameter natural exponential family with mean domain (0,∞) if and only if the real part of the complex root is not positive.

Keywords: Natural exponential family; Polynomial variance functions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2016.06.016

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