Some distributional results through past entropy

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

“…This measure is also named 'past entropy' of X; it has been investigated in Di Crescenzo and Longobardi [28], Nanda and Paul [29], Kundu et al [30]. Other results and applications of these dynamic information measures can be found in Sachlas and Papaioannou [31], Kundu and Nanda [32], and Ahmadi et al [33].…”

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

“…R e m a r k 2.9. Kundu and Ghosh [18] showed that inequalities (2.12) and (2.14) remain true when MRL is replaced by EIT, and equality characterizes the finite range distribution and three distributions as given in Theorem 2.1 of Kundu et al [19] for suitable values of p = r * (t)m * (t) respectively.…”

“…It is pointed out that the functions considered by them are defined for left truncated random variables. For characterizations of distributions using EIT function, we refer to Chandra and Roy [7], Kundu et al [19], and Asadi and Berred [1]. For the characterization of right truncated distributions, Kundu and Ghosh [18] have used the reversed hazard rate, expected inactivity time and reversed aging intensity functions.…”

Further results on closure properties of LPQE order

“…The role of differential entropy as a measure of uncertainty of the inactivity time X (t) has attracted increasing attention in recent years, furthermore, some researchers gave extensions for past entropy. One may refer to Di Crescenzo and Longobardi [6,7], Nanda and Paul [23,24], Maiti and Nanda [21], Kundu and Nanda [19], Gupta and Nanda [13] and the references therein.…”