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Stochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model. (English) Zbl 1454.91203

Summary: 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 \(E[I_{p_i}]=p_i\), \(i=1,\dots,n\). 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.

MSC:

91G05 Actuarial mathematics
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References:

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