On families of distributions which are characterized by some properties of ordered random variables

Abstract

New characterizations of some probability distributions by relations for different ordered random variables are obtained. Such variables include order statistics and sequential maxima. These relations also include upper record values as well as lower records. All ordered random objects are based on sequences of independent random variables having a common continuous distribution function. Equalities in distribution for sequential maxima exposed by different random shifts are investigated. These shifts (onesided or two-sided) have exponential distributions. Some theorems and consequences are suggested in which the corresponding characterizations of distributions by such kind of relations are presented. The simple properties of exponentially shifted order statistics, which characterize certain probability distributions, also are under consideration. All presented here results give a lot of characterizations of different distributions. As the partial cases of these results one can find relations, which characterize the families of the classical exponential and logistic distributions. Refs 7.