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On an ageing class based on the moment generating function order

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  26 July 2018

Shyamal Ghosh  and
Murari Mitra
Shyamal Ghosh*
Affiliation:
Indian Institute of Engineering Science and Technology, Shibpur
Murari Mitra*
Affiliation:
Indian Institute of Engineering Science and Technology, Shibpur
*
* Postal address: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O. Botanic Garden, Howrah, 711103, West Bengal, India.
* Postal address: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O. Botanic Garden, Howrah, 711103, West Bengal, India.
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Abstract

We develop shock model theory in different scenarios for the ℳ-class of life distributions introduced by Klar and Müller (2003). We also study the cumulative damage model of A-Hameed and Proschan (1975) in the context of ℳ-class and establish analogous results. We obtain moment bounds and explore weak convergence issues within the ℳ-class of life distributions.

Keywords

Moment generating function orderNHPPnonstationary pure-birth processcumulative damage modelweak convergencemoment convergence

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 402 - 415
Copyright
Copyright © Applied Probability Trust 2018 

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