The median of an exponential family and the normal law

2018

STATISTICS & PROBABILITY LETTERS

The median of an exponential family and the normal law

01 Pubblicazione su rivista

Letac Gérard, Mattner Lutz, Piccioni Mauro

DOI: 10.1016/j.spl.2017.10.002

ISSN: 0167-7152

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 Ptfor all t characterizes P as the standard Gaussian law N(0,1).

Characterization of the normal laws Choquet–Deny equation Median of a distribution Real exponential families statistics and probability