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

Abstract

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On cumulative residual (past) inaccuracy for truncated random variables

“…This led several authors to deal with dynamic information measures. See, for instance, Asadi and Zohrevand (2007), Chamany and Baratpour (2014), Di Crescenzo and Longobardi (2009), Kundu and Nanda (2015), Yari (2011), Navarro et al (2010), Sunoj et al (2009). Dynamic versions of CRE and CPE have also been proposed in the literature.…”

Interval Entropy and Informative Distance

“…The entropy (4) has been used to characterize and ordering random lifetime distributions. See Misagh and Yari [8] and Sunoj et al [1].…”

“…Now Recall that the probability density function of ሺܺȁ‫ݐ‬ ଵ ൏ ܺ ൏ ‫ݐ‬ ଶ ሻ for all Ͳ ൏ ‫ݐ‬ ଵ ൏ ‫ݐ‬ ଶ is given by ݂ሺ‫ݔ‬ሻ ൫‫ܨ‬ሺ‫ݐ‬ ଶ ሻ െ ‫ݐ‪ሺ‬ܨ‬ ଵ ሻ൯ Τ . Sunoj et al [1] considered the notion of interval entropy of ܺ in the interval ሺ‫ݐ‬ ଵ ǡ ‫ݐ‬ ଶ ሻ as the uncertainty contained in ሺܺȁ‫ݐ‬ ଵ ൏ ܺ ൏ ‫ݐ‬ ଶ ሻwhich is denoted by:…”

“…Sunoj et al [1] have explored the use of information measures for doubly truncated random variables which plays a significant role in studying the various aspects of a system when it fails between two time points. In reliability theory and survival analysis, the residual entropy was considered in Ebrahimi and Pellerey [2], which basically measures the expected uncertainty contained in remaining lifetime of a system.…”

Some Characterization Results on Dynamic Cumulative Past Inaccuracy Measure

“…If X denotes the lifetime of a unit, then the random variables X t 1 ,t 2 = (X − t 1 |t 1 ≤ X ≤ t 2 ) and X * t 1 ,t 2 = (t 2 − X|t 1 ≤ X ≤ t 2 ) are called doubly truncated (interval) residual lifetime and doubly truncated (interval) past lifetime, respectively. Sunoj et al (2009) and Misagh and Yari (2011 have introduced the interval Shannon entropy by…”