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).
The median of an exponential family and the normal law / Letac, Gérard; Mattner, Lutz; Piccioni, Mauro. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 133:(2018), pp. 38-41. [10.1016/j.spl.2017.10.002]
The median of an exponential family and the normal law
Piccioni, Mauro
2018
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 Ptfor all t characterizes P as the standard Gaussian law N(0,1).File allegati a questo prodotto
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