Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions
Journal of Multivariate Analysis
Stochastic comparisons of parallel systems when components have proportional hazard rates
Probability in the Engineering and Informational Sciences
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
Equivalent characterizations on orderings of order statistics and sample ranges
Probability in the Engineering and Informational Sciences
Bounds for mixtures of order statistics from exponentials and applications
Journal of Multivariate Analysis
Stochastic comparisons of largest order statistics from multiple-outlier exponential models
Probability in the Engineering and Informational Sciences
On sample ranges from two sets of heterogenous random variables
Journal of Multivariate Analysis
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In this paper, we investigate the ordering properties of sample ranges arising from multiple-outlier models in terms of the reversed hazard rate order and the usual stochastic order. Under the setup of an exponential model, it is shown that the weak majorization order between the two hazard rate vectors is equivalent to the reversed hazard rate order between exponential sample ranges; the p-larger order between two hazard rate vectors implies the usual stochastic order between exponential sample ranges. Under the setup of a proportional hazard rate (PHR) model, we prove that the majorization order between two parameter vectors implies the usual stochastic order between sample ranges. The results established here strengthen and generalize some of the results known in the literature. Some numerical examples are provided to illustrate the theoretical results.