The median of an exponential family and the normal law

Gérard Letac, Lutz Mattner and Mauro Piccioni

Statistics & Probability Letters, 2018, vol. 133, issue C, 38-41

Abstract: Let P be a probability on the real line generating a natural exponential family (Pt)t∈R. We show that the property that t is a median of Pt for all t characterizes P as the standard Gaussian law N(0,1).

Keywords: Characterization of the normal laws; Real exponential families; Median of a distribution; Choquet–Deny equation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2017.10.002

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