Let $\{Y_{1},\ldots ,Y_{n}\}$ be a collection of interdependent nonnegative random variables, with $Y_{i}$ having an exponentiated location-scale model with location parameter $\mu _i$, scale parameter $\delta _i$ and shape (skewness) parameter $\beta _i$, for $i\in \mathbb {I}_{n}=\{1,\ldots ,n\}$. Furthermore, let $\{L_1^{*},\ldots ,L_n^{*}\}$ be a set of independent Bernoulli random variables, independently of $Y_{i}$'s, with $E(L_{i}^{*})=p_{i}^{*}$, for $i\in \mathbb {I}_{n}.$ Under this setup, the portfolio of risks is the collection $\{T_{1}^{*}=L_{1}^{*}Y_{1},\ldots ,T_{n}^{*}=L_{n}^{*}Y_{n}\}$, wherein $T_{i}^{*}=L_{i}^{*}Y_{i}$ represents the $i$th claim amount. This article then presents several sufficient conditions, under which the smallest claim amounts are compared in terms of the usual stochastic and hazard rate orders. The comparison results are obtained when the dependence structure among the claim severities are modeled by (i) an Archimedean survival copula and (ii) a general survival copula. Several examples are also presented to illustrate the established results.

令$\{Y_{1},\ldots ,Y_{n}\}$是相互依赖的非负随机变量的集合，其中$Y_{i}$具有位置参数为 $\mu _i$的指数位置尺度模型，尺度参数$\delta _i$和形状（偏度）参数$\beta _i$，对于$i\in \mathbb {I}_{n}=\{1,\ldots ,n\}$。此外，令$\{L_1^{*},\ldots ,L_n^{*}\}$是一组独立的伯努利随机变量，独立于$Y_{i}$，其中$E(L_{i }^{*})=p_{i}^{*}$，对于$i\in \mathbb {I}_{n}.$在这种设置下，风险组合是集合$\{T_{1}^{*}=L_{1}^{*}Y_{1},\ldots ,T_{n}^{*}=L_{n}^{*}Y_{n}\ }$，其中$T_{i}^{*}=L_{i}^{*}Y_{i}$代表第$i$个索赔金额。然后，本文提出了几个充分条件，在这些条件下，根据通常的随机和危险率顺序比较最小的索赔金额。当索赔严重性之间的依赖结构由（i）阿基米德生存copula和（ii）一般生存copula建模时，获得了比较结果。还提供了几个例子来说明已建立的结果。