Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables

Peng Zhao, Xiaohu Li and N. Balakrishnan

Journal of Multivariate Analysis, 2009, vol. 100, issue 5, 952-962

Abstract: 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].

Keywords: primary; 60E15 secondary; 60K10 Majorization order Weakly majorization order p-larger order Hazard rate order (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (22)

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