كليدواژه :
Smallest Claim Amounts , Exponentiated Weibull Distribution , Matrix Majorization , Schur , Convexity , Schur , Concavity.
چكيده فارسي :
Suppose X_1,…,X_n is a set of non-negative random variables with X_i having Exponentiated Weibull distribution for i=1,…,n and I_1,…,I_n are independent Bernoulli random variables, independent of the X_i s, respectively, with E(I_i )=p_i, i=1,…,n. Let Y_i=I_i X_i, for i=1,…,n. In applications, actuarial science thus Y_i corresponds to claim amount in a portfolio of risks. In this paper, We obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters (α,λ) changes to another matrix in a mathematical sense. We also show that, under some conditions on the common copula, the usual stochastic order of smallest claim amounts with heterogeneous claims is smaller than the smallest claim amounts with homogeneous claims having a common survival function, which is equal to the average of the survival functions of the heterogeneous claims. The results established here extend some well-known results in the literature.
