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Tests for Laplace order dominance with applications to insurance data

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  • Bhattacharyya, Dhrubasish
  • Khan, Ruhul Ali
  • Mitra, Murari

Abstract

Tests for Laplace order dominance are proposed in the contexts of both one-sample and two-sample problems utilizing a weighted integral as measure of deviation. The concerned test statistics are shown to be asymptotically normal and consistency of both the tests is established. The performance of the proposed test procedures is assessed by means of a simulation study. Finally, the tests are applied to insurance data for illustrative purposes and actuarial implications derived from the tests are also presented.

Suggested Citation

  • Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2021. "Tests for Laplace order dominance with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 163-173.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:163-173
    DOI: 10.1016/j.insmatheco.2021.04.005
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    References listed on IDEAS

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    1. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
    2. Hadi Ahmed & Mohamed Kayid, 2004. "Preservation properties for the Laplace transform ordering of residual lives," Statistical Papers, Springer, vol. 45(4), pages 583-590, October.
    3. Teresa Ledwina & Grzegorz Wyłupek, 2012. "Nonparametric tests for stochastic ordering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 730-756, December.
    4. Belzunce, Felix & Ortega, Eva-Maria & Ruiz, Jose M., 2007. "On non-monotonic ageing properties from the Laplace transform, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 1-14, January.
    5. Belzunce, Félix & Ortega, Eva & Ruiz, José M., 1999. "The Laplace order and ordering of residual lives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 145-156, April.
    6. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
    7. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2020. "A nonparametric test for comparison of mean past lives," Statistics & Probability Letters, Elsevier, vol. 161(C).
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    Cited by:

    1. Walid B. H. Etman & Mohamed S. Eliwa & Hana N. Alqifari & Mahmoud El-Morshedy & Laila A. Al-Essa & Rashad M. EL-Sagheer, 2023. "The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data," Mathematics, MDPI, vol. 11(13), pages 1-22, June.
    2. Lisa Parveen & Ruhul Ali Khan & Murari Mitra, 2024. "A two sample nonparametric test for variability via empirical likelihood methods," Statistical Papers, Springer, vol. 65(7), pages 4243-4265, September.
    3. Denuit, Michel & Trufin, Julien, 2022. "Tweedie dominance for autocalibrated predictors and Laplace transform order," LIDAM Discussion Papers ISBA 2022040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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