Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

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In this article, we study reliability measures such as geometric vitality function and conditional Shannon's measures of uncertainty proposed by Ebrahimi (1996 Ebrahimi , N. ( 1996 ). How to measure uncertainty in the residual lifetime distribution . Sankhya A 58 : 48 – 56 . [Google Scholar]) and Sankaran and Gupta (1999 Sankaran , P. G. , Gupta , R. P. ( 1999 ). Characterization of lifetime distributions using measure of uncertainty . Calcutta Statist. Assoc. Bull. 49 : 195 – 196 . [Google Scholar]), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.