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Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model

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  • Hossein Nadeb
  • Hamzeh Torabi
  • Ali Dolati

Abstract

Let Xλ1,…,Xλn be independent and non-negative random variables belong to the transmuted-G model and let Yi=IpiXλi,i=1,…,n, where Ip1,…,Ipn are independent Bernoulli random variables independent of Xλis, with E[Ipi]=pi,i=1,…,n. In actuarial sciences, Yi corresponds to the claim amount in a portfolio of risks. In this article, we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of the usual stochastic order, hazard rate order, and dispersive order, when the variables in one set have the parameters λ1,…,λn and the variables in the other set have the parameters λ1*,…,λn*. For illustration we apply the results to transmuted exponential and the transmuted Weibull models.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uaajxx:v:24:y:2020:i:3:p:475-487
    DOI: 10.1080/10920277.2019.1671203
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    Cited by:

    1. Catana, Luigi-Ionut, 2022. "Stochastic orders of multivariate Jones–Larsen distribution family with empirical applications in physics, economy and social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    2. 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.

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