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

Ghobad Barmalzan and Amir Payandeh

Insurance: Mathematics and Economics, 2015, vol. 64, issue C, 380-384

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.

Keywords: Smallest claim amount; Convex transform order; Right-spread order; Increasing convex order; Weibull distribution; Coefficient of variations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:64:y:2015:i:c:p:380-384

DOI: 10.1016/j.insmatheco.2015.07.001

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