Abstract
In this paper, we discuss ordering properties of sample range from two independent heterogeneous exponential variables in terms of the likelihood ratio order and the hazard rate order (dispersive order). It is shown, among others, that the weakly majorization order between two parameter vectors is equivalent to the likelihood ratio order between sample ranges and that the p-larger order between two parameter vectors implies the hazard rate order (dispersive order) between sample ranges. In the case of exponential sample range, we thus highlight the close connection that exists between some classical stochastic orders and majorization-type orders. Numerical examples are also provided to illustrate the theoretic results established here.
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Zhao, P., Li, X. (2013). Sample Range of Two Heterogeneous Exponential Variables. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_6
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DOI: https://doi.org/10.1007/978-1-4614-6892-9_6
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