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Stochastic comparisons of two finite mixtures of general family of distributions

Author

Listed:
  • Raju Bhakta

    (National Institute of Technology Rourkela)

  • Priyanka Majumder

    (Indian Institute of Science Education and Research Thiruvananthapuram)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

  • Narayanaswamy Balakrishnan

    (McMaster University)

Abstract

We consider here two finite (arithmetic) mixture models (FMMs) with general parametric family of distributions. Sufficient conditions for the usual stochastic order and hazard rate order are then established under the assumption that the model parameter vectors are connected in p-larger order, reciprocal majorization order and weak super/sub majorization order. Furthermore, we establish hazard rate order and reversed hazard rate order between two mixture random variables (MRVs) when a matrix of model parameters and mixing proportions changes to another matrix in some mathematical sense. We have also considered scale family of distributions to establish some sufficient conditions under which the MRVs have hazard rate order. Several examples are presented to illustrate and clarify all the results established here.

Suggested Citation

  • Raju Bhakta & Priyanka Majumder & Suchandan Kayal & Narayanaswamy Balakrishnan, 2024. "Stochastic comparisons of two finite mixtures of general family of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(6), pages 681-712, August.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:6:d:10.1007_s00184-023-00930-4
    DOI: 10.1007/s00184-023-00930-4
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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. Hazra, Nil Kamal & Kuiti, Mithu Rani & Finkelstein, Maxim & Nanda, Asok K., 2017. "On stochastic comparisons of maximum order statistics from the location-scale family of distributions," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 31-41.
    3. 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.
    4. Omid Shojaee & Manoochehr Babanezhad, 2023. "On some stochastic comparisons of arithmetic and geometric mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 499-515, July.
    5. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    Full references (including those not matched with items on IDEAS)

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