Document Type : Original Article

Authors

• Ghobad Saadat Kia (Barmalzan) ¹
• Kiomars Motarjem ²
• Ali Akbar Hosseinzadeh ³

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.

Abstract

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.

Keywords

• Powered Gompertz Distribution
• Order Statistics
• $k$-out-of-$n$ Systems
• Majorization Orders
• Stochastic Orders
• Archimedean Copula