Some results on the odds rate order along with its statistical testing

Abstract

Recently, Lando, et al. [2022. Properties of increasing odds rate distributions with a statistical application. Journal of Statistical Planning and Inference 221,313–-325 ] define the odds rate order and show that it is stronger than the usual stochastic order, but weaker than the hazard rate order. The purpose of this paper is to investigate the other properties of this new stochastic order. Some characterization and preservation results and its relationship with other well-known stochastic orders are given. In addition, two relative ordering based on the odds rate functions are also defined and their relation with the odds rate order is investigated. Applications in statistical theory of reliability and a statistical test for the odds rate order are also included.