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

Let X-lambda 1,..., X-lambda n be independent and non-negative random variables belong to the transmuted-G model and let Y-i = I-pi X-lambda i, i=1,..., n, where I-p1,..., I-pn are independent Bernoulli random variables independent of X-lambda i s, with E[I-pi] = p(i), i = 1,..., 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),..., lambda(n) and the variables in the other set have the parameters lambda(1)*,..., lambda(n)*. For illustration we apply the results to transmuted exponential and the transmuted Weibull models.