A generalized maximum likelihood characterization of the normal distribution

Abstract

Let P be a probability measure on ℝ and Ix be the set of all n-dimensional rectangles containing x. If for all x ∈ ℝn and θ ∈ ℝ the inequality(Formula presented.) holds, P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher's (1961) maximum likelihood characterization of the normal density to a characterization of N(0, σ2) among all distributions (including those without density). The m.l. principle used is that of Scholz (1980). © 1988, Physica-Verlag Ges.m.b.H. All rights reserved.