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Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models

Author

Listed:
  • Sangita Das

    (National Institute of Technology Rourkela)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

  • N. Balakrishnan

    (McMaster University)

Abstract

In actuarial science, it is often of interest to compare stochastically extreme claim amounts from heterogeneous portfolios. In this regard, in the present work, we compare the smallest order statistics arising from two heterogeneous portfolios in the sense of the usual stochastic, hazard rate, reversed hazard rate and likelihood ratio orderings. We also consider the multiple-outlier model and obtain some ordering results. It is assumed that the portfolios belong to the general exponentiated location-scale model. The results obtained here are based on vector majorization of parameters and multivariate chain majorization with heterogeneity in different parameters. For the purpose of illustration, the derived results are applied to some well known distributions. Various examples and counterexamples are also provided. Finally, a simulation study is conducted to validate some of the results established here.

Suggested Citation

  • Sangita Das & Suchandan Kayal & N. Balakrishnan, 2021. "Orderings of the Smallest Claim Amounts from Exponentiated Location-Scale Models," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 971-999, September.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09793-y
    DOI: 10.1007/s11009-020-09793-y
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    References listed on IDEAS

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    1. 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.
    2. Barmalzan, Ghobad & Payandeh Najafabadi, Amir T., 2015. "On the convex transform and right-spread orders of smallest claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 380-384.
    3. Barmalzan, Ghobad & Payandeh Najafabadi, Amir T. & Balakrishnan, Narayanaswamy, 2016. "Likelihood ratio and dispersive orders for smallest order statistics and smallest claim amounts from heterogeneous Weibull sample," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 1-7.
    4. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2020. "Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(3), pages 475-487, July.
    5. Nil Kamal Hazra & Mithu Rani Kuiti & Maxim Finkelstein & Asok K. Nanda, 2018. "On stochastic comparisons of minimum order statistics from the location–scale family of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 105-123, February.
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