Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models

Abstract

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained. Numerical simulation studies have also been provided to examine the examples presented.

Keywords

• proportional hazard rates
• proportional reversed hazard rates
• relative hazard rate order
• relative reversed hazard rate order
• stochastic order
• relative aging