Entropy-based measure of uncertainty in past lifetime distributions

By A. Di Crescenzo, M. Longobardi. Journal of Applied Probability, 2002

233 citations recorded by the source corpus.

Subfields: Demography, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2c088301eeb8c70ad5e5afb0dc99c1d444487feb

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Citations in the corpus

On Weighted Residual and Past Entropies (2006, methodology): “The past entropy at time t of X is deﬁned by Di Crescenzo and Longobardi [6] as: where f ( x ) /F ( t ), 0 x t , is the pdf of the past lifetime [ X | X ≤ t ].”
On weighted extropies (2020, background): “To avoid this problem, the concept of weighted entropy has been introduced (see Di Crescenzo and Longobardi (2006)) as Hw (X) = −E [X log f(X)] = − ∫ +∞ 0 xf(x) log f(x)dx. (3) To measure the uncertainty about the residual lifetime of X at time t, Ebrahimi (1996) introduced the residual entropy…”
Quantile based entropy function (2012, background): “All rights reserved. doi:10.1016/j.spl.2012.02.005 A similar function can be obtained in terms of the inactivity time (t − X | X ≤ t) given in Di Crescenzo and Longobardi (2002).”
Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables (2009, unknown): “8), which is similar to the one given in Di Crescenzo and Longobardi (2002), can be interpreted in the following way.”
Some reliability properties of extropy for residual and past lifetime random variables (2020, methodology): “(1993), Ebrahimi (1996) and Di Crescenzo and Longobardi (2002) with reference to Shannon’s entropy. In the meantime the variant approaches of employing the quantile version of various entropies were also introduced with the objectives of providing alternative methodology, new results and different m”
Quantile based entropy function in past lifetime (2013, methodology): “…October 2012 MSC: 94A17 62E10 62N05 Keywords: Shannon entropy Past lifetime Quantile function Reliability measures Characterizations a b s t r a c t Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual…”
Some Properties of Past Entropy and their Applications (2006, methodology): “Now we recall Proposition 2.2 of Di Crescenzo and Longobardi (2002) which gives the relationship between IUL class and decreasing reversed hazard rate (DRHR) class of life distributions.”