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arXiv · 1708.03789

The medians for exponential families and the normal law

Gerard Letac·Lutz Mattner·Mauro Piccioni
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Abstract

Let $P$ a probability on the real line generating a natural exponential family $(P_t)_{t\in \R}$. We show that $t$ is a median of $P_t$ for all $t$ only if $P$ is the standard Gaussian law $N(0.1).$ The proof is based on the Choquet Deny equation.

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Gerard Letac, Lutz Mattner, Mauro Piccioni. 2017-08-12. The medians for exponential families and the normal law. https://arxiv.org/abs/1708.03789

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