Characterizing Distributions by Linearity of Regression of Generalized Order Statistics

Abstract

Let X1,..., Xn be a random sample from an absolutely continuous (with respect to Lebesgue measure) distribution with the corresponding generalized order statistics X(1, n, m~, k),..., X(n, n, m~, k). In this paper, we present some characterization of distributions when linearity of regression E[X(s, n, m~, k)|X(r, n, m~, k)=x]=ax+b is identified.

Keywords

• Conditional expectation; generalized order statistics; Linearity of regression.