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Table Of Integrals Series And Products

Tables of integrals

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

On cumulative entropies

As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

Entropy-based measure of uncertainty in past lifetime distributions

Some results on the proportional reversed hazards model

We consider a “length-biased” shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of “weighted residual entropy” and “weighted past entropy”, that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively. The obtained results include their behaviors under monotonic transformations. AMS Classification: 62N05, 62B10

Antonio Di Crescenzo

Papers

On cumulative entropies

Entropy-based measure of uncertainty in past lifetime distributions

Some results on the proportional reversed hazards model

On weighted residual and past entropies

A measure of discrimination between past lifetime distributions