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SHARP BOUNDS FOR SURVIVAL PROBABILITY WHEN AGEING IS NOT MONOTONE

Published online by Cambridge University Press:  06 April 2018

Ruhul Ali Khan  and
Murari Mitra
Ruhul Ali Khan
Affiliation:
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O. - Botanic Garden, Howrah-711103, West Bengal, India E-mail: ruhulali.khan@gmail.com
Murari Mitra
Affiliation:
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O. - Botanic Garden, Howrah-711103, West Bengal, India E-mails: murarimitra@yahoo.com, mmitra@math.iiests.ac.in
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Abstract

We exploit a novel bounding argument to obtain sharp bounds for survival functions belonging to the Increasing initially then Decreasing Mean Residual Life (IDMRL) class introduced by Guess, Hollander and Proschan (1986) [8]. The bounds obtained are in terms of the mean, change point and pinnacle of the mean residual life function. The bounds for the monotonic ageing classes Decreasing Mean Residual Life (DMRL) and Increasing Mean Residual Life (IMRL) are obtained as special cases. Discussions on the bounds as well as two concrete illustrative examples are included.

Keywords

Life Distribution and Survival Function and Sharp Bounds and MRL Function and IDMRL Class and Change Point and Pinnacle
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 2 , April 2019 , pp. 205 - 219
Copyright
Copyright © Cambridge University Press 2018 

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