Stochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model
share
Let X_λ_1, ... , X_λ_n be independent non-negative random variables belong to the transmuted-G model and let Y_i=I_p_i X_λ_i, i=1,...,n, where I_p_1, ..., I_p_n are independent Bernoulli random variables independent of X_λ_i's, with E[I_p_i]=p_i, i=1,...,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 λ_1,...,λ_n and the variables in the other set have the parameters λ^*_1,...,λ^*_n. For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.
READ FULL TEXT
