Schur properties of convolutions of exponential and geometric random variables
Journal of Multivariate Analysis
On stochastic orders for sums of independent random variables
Journal of Multivariate Analysis
Majorization and matrix-monotone functions in wireless communications
Foundations and Trends in Communications and Information Theory
Journal of Multivariate Analysis
Stochastic order of sample range from heterogeneous exponential random variables
Probability in the Engineering and Informational Sciences
On the range of heterogeneous samples
Journal of Multivariate Analysis
Mean residual life order of convolutions of heterogeneous exponential random variables
Journal of Multivariate Analysis
On the right spread order of convolutions of heterogeneous exponential random variables
Journal of Multivariate Analysis
On hazard rate ordering of the sums of heterogeneous geometric random variables
Journal of Multivariate Analysis
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Let Sn(a1, …, an) be the sum of n independent exponential random variables with respective hazard rates a1, …, an or the sum of n independent geometric random variables with respective parameters a1, …, an. In this article, we investigate sufficient conditions on parameter vectors (a1, …, an) and $(a_{1}^{\ast},\ldots,a_{n}^{\ast})$ under which Sn(a1, …, an) and $S_{n}(a_{1}^{\ast},\ldots,a_{n}^{\ast})$ are ordered in terms of the increasing convex and the reversed hazard rate orders for both exponential and geometric random variables and in terms of the mean residual life order for geometric variables. For the bivariate case, all of these sufficient conditions are also necessary. These characterizations are used to compare fail-safe systems with heterogeneous exponential components in the sense of the increasing convex and the reversed hazard rate orders. The main results complement several known ones in the literature.