  Let $X_{\lambda_1}, \ldots , X_{\lambda_n}$ be independent non-negative
random variables belong to the transmuted-G model and let $Y_i=I_{p_i}
X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1}, \ldots, I_{p_n}$ are
independent 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 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 usual
stochastic order, hazard rate order and dispersive order, when the variables in
one set have the parameters $\lambda_1,\ldots,\lambda_n$ and the variables in
the other set have the parameters $\lambda^{*}_1,\ldots,\lambda^{*}_n$. For
illustration we apply the results to the transmuted-G exponential and the
transmuted-G Weibull models.
