Characterizations of Populations Using Regression Properties
利用回归性质刻画总体分布
In the present work, we study characterizations of populations obtained by using regression properties of one statistic on another. We extend some of the results of Lukacs and Laha by considering the cubic regression (polynomial regression of order 3) of a cubic statistic $S$ on a linear one $L$. This assumption of cubic regression is used to derive a third order non-linear differential equation in the characteristic function $h(t)$ of a set of $n$ independently and…