Stochastic comparisons of extreme order statistic from dependent and heterogeneous lower-truncated Weibull variables under Archimedean copula

Abstract

This article studies the stochastic comparisons of order statistics with dependent and heterogeneous lower-truncated Weibull samples under Archimedean copula. To begin, we obtain the usual stochastic and hazard rate orders of the largest and smallest order statistics from heterogeneous and dependent lower-truncated Weibull samples under Archimedean copula. Second, under Archimedean copula, we get the convex transform and the dispersive orders of the largest and smallest order statistics from dependent and heterogeneous lower-truncated Weibull samples. Finally, several numerical examples are given to demonstrate the theoretical conclusions.

Keywords

• order statistic
• archimedean copula
• majorization
• lower-truncated weibull
• stochastic orders