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Let $X_{\lambda_1}, \ldots , X_{\lambda_n}$ be independent non-negativerandom variables belong to the transmuted-G model and let $Y_i=I_{p_i}X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1}, \ldots, I_{p_n}$ areindependent Bernoulli random variables independent of $X_{\lambda_i}$'s, with${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$corresponds to the claim amount in a portfolio of risks. In this paper wecompare the smallest and the largest claim amounts of two sets of independentportfolios belonging to the transmuted-G model, in the sense of usualstochastic order, hazard rate order and dispersive order, when the variables inone set have the parameters $\lambda_1,\ldots,\lambda_n$ and the variables inthe other set have the parameters $\lambda^{*}_1,\ldots,\lambda^{*}_n$. Forillustration we apply the results to the transmuted-G exponential and thetransmuted-G Weibull models.

Stochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model