A measure of discrimination between two residual life-time distributions and its applications

Abstract

Hazard function, cumulative hazard function, mean residual lifetime function, NBU, IFR, Kullback-Leibler discrimination information, MDI principle,

Entropy and Residual Entropy Functions and Some Characterization Results

“…Consider the problem of finding a sufficient condition for the uniqueness of the solution of the initial value problem (IVP) 0 0 = ( , ), ( ) = , dy f x y y x y dx (11) where f is given function of two variables whose domain is a region Proof See Gupta and Kirmani (1998).…”

Generalized Measures of Divergence in Survival Analysis and Reliability

“…Appropriately chosen functions ϕ(·) give rise to special measures mentioned above, while, for α = 0, the BHHJ family reduces to the Csiszár family. Ebrahimi and Kirmani (1996b) introduced the following measure of discrepancy between X and Y at time t:…”

“…The BHHJ family depends on an index a which controls the trade-off between robustness and efficiency when the measure is used as an estimating criterion for robust parameter estimation. Ebrahimi and Kirmani (1996b) introduced a measure of discrepancy between the lifetimes X and Y of two items at time t. In survival analysis or in reliability we might know the current age t of a biomedical or technical system. We need to take this information into consideration when we compare two systems or populations.…”

“…We need to take this information into consideration when we compare two systems or populations. Ebrahimi and Kirmani (1996b) achieved this by replacing the distribution functions of the random variables X and Y in the Kullback-Leibler divergence of X and Y (see Kullback and Leibler (1951)) by the distributions of their residual lifetimes. Di Crescenzo and Longobardi (2004) defined a dual measure of divergence which constitutes a distance between past-life distributions.…”

Some Results on Dynamic Discrimination Measures of Order (alpha, beta)

“…Several researchers have studied KL discrimination measure by including the current age. In this direction we refer to Asadi et al [2], Di Crescenzo and Longobardi [7] and Ebrahimi and Kirmani [10,11]. Later the discrimination measure (1.1) was generalized, called discrimination measure of order α, as As similar measure to (1.2), discrimination measure of order α between two rv's X and Y at time t can be defined by (see Asadi et al [3]) …”