Orderings of Extreme Order Statistics with Archimedean Copula and Powered Gompertz Random Variables

Document Type : Original Article


1 Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran

2 Department of Statistics, Tarbiat Modaress University, Tehran, Iran.

3 Department of Mathematics, University of Zabol, Sistan and Baluchestan, Iran.


Bathtub shaped failure rate distributions are of special interest in reliability theory, survival analysis and many other fields. The so-called power Gompertz distribution is one of the popular lifetime distributions that possesses the bathtub shaped failure rate function. In this paper, we study some stochastic comparisons results for extreme order statistics from dependent powered Gompertz distributed random variables under Archimedean copula. The study has been carried out in the sense of the usual stochastic order and the dispersive order.


Volume 21, Issue 2
December 2022
Pages 197-216
  • Receive Date: 24 April 2022
  • Revise Date: 08 June 2023
  • Accept Date: 22 August 2023