Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables
Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than Y2:n, the second order statistic of Y1,...,Yn, in terms of the likelihood ratio order if and only if with . Also, it is shown that X2:n is smaller than Y2:n in terms of the likelihood ratio order if and only if These results form nice extensions of those on the hazard rate order in Pa[caron]lta[caron]nea [E. Pa[caron]lta[caron]nea, On the comparison in hazard rate ordering of fail-safe systems, Journal of Statistical Planning and Inference 138 (2008) 1993-1997].
Volume (Year): 100 (2009)
Issue (Month): 5 (May)
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References listed on IDEAS
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- Chang, Kuo-Hwa, 2001. "Stochastic orders of the sums of two exponential random variables," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 389-396, February. Full references (including those not matched with items on IDEAS)
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