An Extension of the Lack of Memory Property with Characterization Results

Abstract

Summary

In the reliability analysis the lack of memory property plays a pivotal role in conceptualizing some life distribution classes and in unique determination of the exponential distribution. On the other hand quite a few results like constancy of the coefficient of variation of the residual life, linearity of the mean residual life characterize the exponential distribution along with the Lomax distribution. Question that arises is - can there be an extended version of the lack of memory property to tie together the exponential and the Lomax distributions through characterization. The present paper presents an affirmative claim and extends the lack of memory property based on standardization technique. It also presents a stochastic version of this extended property with unique determination of the same life distributions. Attempts have also been made to define this extended lack of memory property in the bivariate set up and indicate the bivariate distributions that satisfy the same.