ON CERTAIN PROBLEMS INVOLVING ORDER STATISTICS : A UNIFIED APPROACH THROUGH ORDER STATISTICS PROPERTY OF POINT PROCESSES

Abstract

SUMMARY. It is known there are some similarities between order statistics and record values, moreover, when viewed as point processes, the two processes both share the order statistics property. These motivated us to investigate some intrinsic properties within the class of order statistics point processes, which in turn lead to some useful characterizations by using certain conditional moment of the spacings of the jump times. Our results explain not only why order statistics and record values have parallel characterizations when using the backward conditional expectations, but also generalize several existing characterization results.