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

Abstract

Let $X_{{\lambda }_1},\dots ,X_{{\lambda }_n}$ be independent and non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i}{X}_{{\lambda }_i},i=1,\dots ,n$, where $I_{p_1},\dots ,I_{p_n}$ are independent Bernoulli random variables independent of $X_{{\lambda }_i}$s, with $\mathrm{E}[I_{p_i}]=p_i,i=1,\dots ,n$. In actuarial sciences, Y_i 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 ${\lambda }_1,\dots ,{\lambda }_n$ and the variables in the other set have the parameters ${\lambda }_1^{*},\dots ,{\lambda }_n^{*}$. For illustration we apply the results to transmuted exponential and the transmuted Weibull models.

ACKNOWLEDGMENT

We are grateful to the anonymous referees for their constructive suggestions and comments that helped to improve the article.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

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