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On the convex transform and right-spread orders of smallest claim amounts

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  • Barmalzan, Ghobad
  • Payandeh Najafabadi, Amir T.

Abstract

Suppose Xλ1,…,Xλn is a set of Weibull random variables with shape parameter α>0, scale parameter λi>0 for i=1,…,n and Ip1,…,Ipn are independent Bernoulli random variables, independent of the Xλi’s, with E(Ipi)=pi, i=1,…,n. Let Yi=XλiIpi, for i=1,…,n. In particular, in actuarial science, it corresponds to the claim amount in a portfolio of risks. In this paper, under certain conditions, we discuss stochastic comparison between the smallest claim amounts in the sense of the right-spread order. Moreover, while comparing these two smallest claim amounts, we show that the right-spread order and the increasing convex orders are equivalent. Finally, we obtain the results concerning the convex transform order between the smallest claim amounts and find a lower and upper bound for the coefficient of variation. The results established here extend some well-known results in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:380-384
    DOI: 10.1016/j.insmatheco.2015.07.001
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    References listed on IDEAS

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    1. Barmalzan, Ghobad & Najafabadi, Amir T. Payandeh & Balakrishnan, Narayanaswamy, 2015. "Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 235-241.
    2. Kochar, Subhash & Xu, Maochao, 2010. "On the right spread order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 165-176, January.
    3. Kochar, Subhash C. & Carrière, K. C., 1997. "Connections among various variability orderings," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 327-333, November.
    4. Frostig, Esther, 2001. "A comparison between homogeneous and heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 59-71, August.
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    Cited by:

    1. 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.
    2. Sangita Das & Suchandan Kayal, 2021. "Ordering results between the largest claims arising from two general heterogeneous portfolios," Papers 2104.08605, arXiv.org.
    3. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.08343, arXiv.org.
    4. Mansour Shrahili & Abdulhakim A. Albabtain & Mohamed Kayid & Zahra Kaabi, 2020. "Stochastic Aspects of Proportional Vitalities Model," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    5. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.06166, arXiv.org.

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