Abstract
In this paper, we give an overview of recent results in the concept of reversed residual lifetime. We focus on properties of the reversed variance residual lifetime (RVR) and study the interrelations among reversed residual lifetime classes. We mention the most important results in the literature that are related to the RFR function for both continuous and discrete life distributions. We give properties of the reversed mean residual lifetime (RMR) and the RVR functions. Reversed entropy is briefly discussed. We study the relationships among the reversed classes.
Highlights
Properties of the so-called reversed residual lifetime have gained the interest of many researchers who have studied, for example, properties of the reversed failure rate (RFR)
We focus on properties of the reversed variance residual lifetime (RVR) and study the interrelations among reversed residual lifetime classes
Andersen et al (1993), Chandra and Roy (2001) and Block et al (1998) showed that the RFR function plays the same role in the analysis of left censored data as the failure rate function plays in the analysis of right censored data
Summary
Properties of the so-called reversed residual lifetime have gained the interest of many researchers who have studied, for example, properties of the reversed failure rate (RFR). The reversed failure rate function, denoted by r(x), is the ratio of probability density function and the corresponding distribution function. A nonnegative random variable X, having distribution F, is said to have DRFR, if the function r(t), t > 0 is decreasing. A nonnegative random variable X, having distribution F, is said to have IRFR, if the function r(t), t > 0 is increasing. A nonnegative random variable X, having distribution F, is said to have DRFRA, if the following averaged function is increasing:. A discrete lifetime X with a distribution P is said to be discrete decreasing reversed failure rate (D-DRFR) if the function rk, k ∈ N is decreasing. We end this section by mentioning an observation by Nanda and Sengupta (2005) that there is no discrete life distribution with domain in N, with an increasing reversed failure rate (D-IRFR)
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