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The alpha-mixture of survival functions

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  11 December 2019

Majid Asadi ,
Nader Ebrahimi  and
Ehsan S. Soofi
Majid Asadi*
Affiliation:
University of Isfahan and IPM
Nader Ebrahimi*
Affiliation:
Northern Illinois University
Ehsan S. Soofi*
Affiliation:
University of Wisconsin-Milwaukee
*
*Postal address: Department of Statistics, University of Isfahan, Isfahan 81744, Iran. Email address: m.asadi@stat.ui.ac.ir
***Postal address: Department of Statistics, Northern Illinois University, DeKalb, IL 60155, USA. Email address: nebrahimi@niu.edu
****Postal address: Lubar School of Business, University of Wisconsin-Milwaukee, PO Box 742, Milwaukee, WI 53201, USA. Email address: esoofi@uwm.edu
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Abstract

This paper presents a flexible family which we call the $\alpha$ -mixture of survival functions. This family includes the survival mixture, failure rate mixture, models that are stochastically closer to each of these conventional mixtures, and many other models. The $\alpha$ -mixture is endowed by the stochastic order and uniquely possesses a mathematical property known in economics as the constant elasticity of substitution, which provides an interpretation for $\alpha$ . We study failure rate properties of this family and establish closures under monotone failure rates of the mixture’s components. Examples include potential applications for comparing systems.

Keywords

Arithmetic mixturegeometric mixtureharmonic mixturefailure ratestochastic orderweighted power mean

MSC classification

Primary: 60E05: Distributions 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 4 , December 2019 , pp. 1151 - 1167
Copyright
© Applied Probability Trust 2019 

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