Stochastic orders for spacings of heterogeneous exponential random variables
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
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
On sample ranges from two sets of heterogenous random variables
Journal of Multivariate Analysis
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In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent characterizations of stochastic comparisons of sample ranges with respect to various stochastic orders are established. In this process, two open problems mentioned in Mao and Hu (2010) [16] are solved. The main results established here extend and strengthen several known results in the literature including those of Khaledi and Kochar (2000) [8], Zhao and Li (2009) [22] and Genest et al. (2009) [7].