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Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components

Author

Listed:
  • Raju Bhakta

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India)

  • Pradip Kundu

    (School of Computer Science and Engineering, XIM University, Bhubaneswar 752050, Odisha, India)

  • Suchandan Kayal

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India)

  • Morad Alizadeh

    (Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran)

Abstract

In this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic order between the FMMs is established when heterogeneity presents in one parameter as well as two parameters. In addition, we also study ageing faster order in terms of the reversed hazard rate between two FMMs when heterogeneity is in two parameters. For the case of heterogeneity in three parameters, we obtain the comparison results based on reversed hazard rate and likelihood ratio orders. The theoretical developments are illustrated using several examples and counterexamples.

Suggested Citation

  • Raju Bhakta & Pradip Kundu & Suchandan Kayal & Morad Alizadeh, 2024. "Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components," Mathematics, MDPI, vol. 12(6), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:852-:d:1357043
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    References listed on IDEAS

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    1. Nil Kamal Hazra & Maxim Finkelstein, 2018. "On stochastic comparisons of finite mixtures for some semiparametric families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 988-1006, December.
    2. Jorge Navarro, 2016. "Stochastic comparisons of generalized mixtures and coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 150-169, March.
    3. Mostafa Sattari & Ghobad Barmalzan & Narayanaswamy Balakrishnan, 2021. "Stochastic comparisons of finite mixture models with generalized Lehmann distributed components," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(22), pages 7767-7782, September.
    4. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, October.
    5. Hossein Nadeb & Hamzeh Torabi, 2022. "New results on stochastic comparisons of finite mixtures for some families of distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(10), pages 3104-3119, May.
    6. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.
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