On stochastic comparisons of largest order statistics in the scale model

Abstract

Let $X_{{\lambda }_1},X_{{\lambda }_2},\dots ,X_{{\lambda }_n}$ be independent nonnegative random variables with $X_{{\lambda }_i}\sim F({\lambda }_{i}t)$, $i=1,\dots ,n$, where ${\lambda }_i>0$, $i=1,\dots ,n$ and $F$ is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic $X_{n:n}^{\lambda }$ is smaller than another one $X_{n:n}^{\theta }$ according to likelihood ratio ordering. Furthermore, we apply these results when $F$ is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.

References in corpus (1)

• Stochastic order relations among parallel systems from Weibull distributions

Cited by in corpus (3)

• Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas
• Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions
• Ordering results of extreme order statistics from multiple-outlier scale models with dependence