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Stochastic properties of generalized finite α-mixtures

Published online by Cambridge University Press:  15 July 2021

Omid Shojaee
Affiliation:
Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81744, Iran. E-mail: o.shojaee@sci.ui.ac.ir
Majid Asadi
Affiliation:
Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81744, Iran. E-mail: o.shojaee@sci.ui.ac.ir School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran. E-mail: m.asadi@sci.ui.ac.ir
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics, University of the Free State, P.O. Box 339, Bloemfontein 9300, South Africa Department of Management Science, University of Strathclyde, Glasgow, UK. E-mail: finkelm@ufs.ac.za

Abstract

Most of the real-life populations are heterogeneous and homogeneity is often just a simplifying assumption for the relevant statistical analysis. Mixtures of lifetime distributions that correspond to homogeneous subpopulations were intensively studied in the literature. Various distributional and stochastic properties of finite and continuous mixtures were discussed. In this paper, following recent publications, we develop further a mixture concept in the form of the generalized α-mixtures that include all mixture models that are widely explored in the literature. We study some main stochastic properties of the suggested mixture model, that is, aging and appropriate stochastic comparisons. Some relevant examples and counterexamples are given to illustrate our findings.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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