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Stochastic properties of generalized finite mixture models with dependent components

Part of: Special processes Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  16 September 2021

Ebrahim Amini-Seresht  and
Narayanaswamy Balakrishnan
Ebrahim Amini-Seresht*
Affiliation:
Bu-Ali Sina University
Narayanaswamy Balakrishnan*
Affiliation:
McMaster University
*
*Postal address: Department of Statistics, Bu-Ali Sina University, Hamedan, Iran. Email address: e.amini64@yahoo.com
**Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada. Email address: bala@mcmaster.ca
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Abstract

In this paper we consider a new generalized finite mixture model formed by dependent and identically distributed (d.i.d.) components. We then establish results for the comparisons of lifetimes of two such generalized finite mixture models in two different cases: (i) when the two mixture models are formed from two random vectors $\textbf{X}$ and $\textbf{Y}$ but with the same weights, and (ii) when the two mixture models are formed with the same random vectors but with different weights. Because the lifetimes of k-out-of-n systems and coherent systems are special cases of the mixture model considered, we used the established results to compare the lifetimes of k-out-of-n systems and coherent systems with respect to the reversed hazard rate and hazard rate orderings.

Keywords

Coherent systemk-out-of-n systemstochastic ordergeneralized mixture modelcopula function

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 3 , September 2021 , pp. 794 - 804
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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