Hazard Measure and Mean Residual Life Ordering: A Unified Approach

摘要

The hazard rate ordering is applied frequently in reliability to compare two probability distributions on R(+) such that they are both absolutely continuous (w.r.t. Lebesgue measure) or both purely discrete (concentrated on the set of non-negative integers) via their hazard rates. Kotz and Shanbhag (1980) extended the concept of hazard rate introducing new concept of hazard measure, applicable to any arbitrary distribution on the real line; in particular, this concept avoids the restriction that the distribution be absolutely continuous or purely discrete. These latter authors have also extended the concept of mean residual life function and have given related representations for distributions. In this paper, we introduce the concepts of hazard measure ordering and mean residual life ordering to compare two arbitrary probability distributions and study their basic properties.