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

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• 作者：Ghobad Barmalzan ; Amir T. Payandeh Najafabadi ; ^{amirtpayandeh@sbu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Smallest claim amount ; Convex transform order ; Right-spread order ; Increasing convex order ; Weibull distribution ; Coefficient of variations
• 刊名：Insurance: Mathematics and Economics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：64
• 期：Complete
• 页码：380-384
• 全文大小：387 K

文摘

Suppose X_位1,…,X_位n$X_{{位}_1},\dots ,X_{{位}_n}$ is a set of Weibull random variables with shape parameter 伪>0$\mathrm{<font\; color="red">伪</font>}>0$, scale parameter 位_i>0${位}_i>0$ for i=1,…,n$i=1,\dots ,n$ and I_p1,…,I_pn$I_{p_1},\dots ,I_{p_n}$ are independent Bernoulli random variables, independent of the X_位i$X_{{位}_i}$’s, with E(I_pi)=p_i$E\left(I_{p_i}\right)=p_i$, i=1,…,n$i=1,\dots ,n$. Let Y_i=X_位iI_pi$Y_i=X_{{位}_i}{I}_{p_i}$, for i=1,…,n$i=1,\dots ,n$. 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.