Barbour, A. D.; Lindvall, T.; Rogers, L. C. G. Stochastic ordering of order statistics. (English) Zbl 0729.62048 J. Appl. Probab. 28, No. 2, 278-286 (1991). The main result of this paper is the following: Theorem 1. Let \(X_ 1,...,X_ n\), \(Y_ 1,...,Y_ n\) be independent, non-negative random variables with distributions \[ P(X_ j>t)=\bar F(\lambda_ jt)\equiv \exp (-\int^{\lambda_ jt}_{0}r(s)ds),\quad P(Y_ j>t)=\bar F({\hat \lambda}t), \] where \(\lambda_ 1,...,\lambda_ n\) are positive constants with average \({\hat \lambda}\) and \(\bar F\) is the tail of the distribution function \(F\equiv 1-\bar F\), with failure-rate function r. Assume \( x\mapsto r(x)\) is decreasing; \(x\mapsto xr(x)\) is increasing. Then it is possible to construct on some probability space random variables \[ (X'_ 1,...,X'_ n)=^{{\mathcal D}}(X_ 1,...,X_ n)\text{ and } (Y'_ 1,...,Y'_ n)=^{{\mathcal D}}(Y_ 1,...,Y_ n) \] such that \(Y'_{(j)}\leq X'_{(j)}\) for \(j=1,...,n\) a.s. Reviewer: S.Rachev (Santa Barbara) Cited in 1 ReviewCited in 3 Documents MSC: 62G30 Order statistics; empirical distribution functions 62P10 Applications of statistics to biology and medical sciences; meta analysis 92D30 Epidemiology 60E99 Distribution theory Keywords:stochastic ordering of order statistics; independent exponential random variables; monotone coupling; order relation; comparison of properties of epidemic processes; rates of infection; homogeneous sample; heterogeneous sample; independent, non-negative random variables; tail of the distribution; failure-rate function PDFBibTeX XMLCite \textit{A. D. Barbour} et al., J. Appl. Probab. 28, No. 2, 278--286 (1991; Zbl 0729.62048) Full Text: DOI