PhD Candidate of Statistics, Shahid Beheshti University
Associate Professor, Shahid Beheshti University
Suppose is a set of non-negative random variables with having the distribution function generalized exponential, for , and are independent Bernoulli random variables, independent of the 's, with , . Let , for It is of interest to note that in actuarial science, it corresponds to the claim amount in a portfolio of risks. In this paper, it’s been tried to discuss the stochastic comparison between the smallest claim amounts in the sense of the usual stochastic order using the concept of vector weakly submajorization and under certain conditions. We obtain the usual stochastic order between the smallest claim amounts when the matrix of parameters changes to another matrix in a mathematical sense and finds an upper bound for the survival function of smallest claim amount. The results established here extend some well-known results in the literature and show that larger stochastic order smallest claim amount lead to the desirable property of uniformly larger Value-at-Risk.