Let X λ1 , . . . , X λn be dependent non-negative random variables and Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi '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 paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters λ 1 , . . . , λ n and p 1 , . . . , p n and the variables in the other set have the parameters λ

No abstract

Let X λ1 , . . . , X λn be independent non-negative random variables belong to the transmuted-G model and let Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi '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 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.

Abstract. This paper considers the estimation of the stress-strength parameter, say R, based on two independent Type-I progressively hybrid censored samples from exponential populations with different parameters. The maximum likelihood estimator and asymptotic confidence interval for R are obtained. Bayes estimator of R is also derived under the assumption of independent gamma priors. A Monte Carlo simulation study is used to evaluate the performance of maximum likelihood estimator, Bayes estimator and asymptotic confidence interval. Finally, a pair of real data sets is analyzed for illustrative purposes.

No abstract