Some charaterizations of the uniform distribution
Mohammed N. Goria · Communication in Statistics- Theory and Methods · 1987
We first prove a uniquenes property of the Uniform distribution on the unit interval and then establish its charaterization based on the structure of the expected spacings between the consecutive order statistics as also through the independence between the largest order statistics as also through the independence between the largest order statistic X(n) and the ratio [Xbar]/X(n), [Xbar] being the sample mean.