Sequential Order Statistics: Ageing and Stochastic Orderings

Ordered random variables play an important role in statistics, reliability theory, and many applied areas. Sequential order statistics provide a unified approach to a variety of models of ordered random variables. We investigate conditions on the underlying distribution functions on which the sequential order statistics are based, to obtain stochastic comparisons of sequential order statistics given some well known stochastic orderings, such as the usual stochastic, the hazard rate and the likelihood ratio orders, among others. Also, we derive sufficient conditions under which the sequential order statistics are increasing hazard rate, increasing hazard rate average or decreasing hazard rate average. Applications of the main results involving nonhomogeneous pure birth processes are also given.