Comparisons of order statistics from heterogeneous negative binomial variables with applications

摘要

This paper studies the ordering properties of extreme order statistics arising from independent negative binomial random variables. Employing the useful tool of majorization-type orders, sufficient conditions are given for comparing extreme negative binomial order statistics according to the usual stochastic order. Some numerical examples are provided to illustrate the theoretical results. Applications in Poisson-Gamma shock model in reliability engineering and claim frequency in insurance are presented to show the practicability of our results as well.