Stochastic Aging Classes for the Maximum Statistic from Friday and Patil Bivariate Exponential Distribution Family

Abstract

Friday and Patil bivariate exponential (FPBVE) distribution family is one of the most flexible bivariate exponential distributions in the literature; among others, it contains the bivariate exponential models due to Freund, Marshall–Olkin, Block–Basu, and Proschan–Sullo as particular cases. In this article, we discuss the stochastic aging of the maximum statistic from FPBVE model in according to the log-concavity of its density function, i.e., in the increasing or decreasing likelihood ratio classes (ILR or DLR), and consequently in the IFR and DFR classes. Furthermore, a kind of DFR distributions which are not DLR is derived from our classification.

Keywords:

• Bivariate exponential
• Failure rate
• Log-concavity
• Maximum statistic
• ILR (DLR) class

Mathematics Subject Classification:

• Primary 62N05
• Secondary 60E15

Acknowledgment

The authors would like to thank the referees for their comments and careful reading of the manuscript, which have improved the presentation of this article.