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ON THE ELASTICITY OF EXPECTED INTEREPOCH INTERVALS IN A NON-HOMOGENEOUS POISSON PROCESS UNDER SMALL VARIATIONS OF HAZARD RATE

Published online by Cambridge University Press:  23 April 2019

Georgios Psarrakos  and
Abdolsaeed Toomaj
Georgios Psarrakos
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece E-mail: gpsarr@unipi.gr
Abdolsaeed Toomaj
Affiliation:
Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous, Iran E-mail: ab.toomaj@gonbad.ac.ir; ab.toomaj@gmail.com
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Abstract

The elasticity of life expectancy is an important feature in life tables. It is also known as life table entropy in the areas of demography and biology, and as normalized cumulative residual entropy in reliability theory. The elasticity of life expectancy provides useful information on studying the way in which small variations in the force of mortality (or hazard rate) affects the life expectancy. In this paper, a perturbation analysis of the hazard rate to the expected interepoch intervals in a non-homogeneous Poisson process is applied, and further interpretations are given by using a normalized version of the generalized cumulative residual entropy. Properties of the elasticity, including ordering results, bounds and empirical estimation, are obtained. Moreover, the dynamic version of the elasticity is studied, and some monotonicity and characterization results are given.

Keywords

elasticity of life expectancygeneralized cumulative residual entropyhazard ratemean residual lifetimeproportional hazards model
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 550 - 569
Copyright
Copyright © Cambridge University Press 2019

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