Mixture discrete reversed hazard rate and its main properties

The reversed hazard rate, defined as the ratio of the density to the distribution function, has recently drawn great interest in reliability and survival analysis due to its usefulness in the analysis of left-censored data. This paper develops the mixture model of discrete reversed hazard rates and studies its main properties. Similar to the continuous case, results of the bending property for the reversed hazard rate in discrete case are studied. In addition, mixtures of the mean inactivity time, which are closely related to the reversed hazard rate, are discussed and the corresponding results of its bending property are also investigated. Preservation of aging properties under both mixtures of reversed hazard rate and mean inactivity time is discussed as well. As a special case, the proportional discrete reversed hazard rate model is presented and the bending properties for this case are also discussed. Finally, stochastic comparisons of the mixture discrete reversed hazard rates of two mixed populations are addressed.