On some stochastic inequalities involving minimum of random variables

Peter Kubat

Naval Research Logistics Quarterly, 1982, vol. 29, issue 3, 399-402

Abstract: Let Xi be independent IFR random variables and let Yi be independent exponential random variables such that E[Xi]=E[Yi] for all i=1, 2, ⃛ n. Then it is well known that E[min (Xi)] ≥E[min (Xi)]. Nevertheless, for 1≤i≤n exponentially distributed Xi's and for a decreasing convex function ϕ(.). it is shown that \documentclass{article}\pagestyle{empty}\begin{document}$$ E[\Phi (\mathop {\min }\limits_{1\le i\le n}\,(X_i))]\,\, \le\,\,E[\Phi (\mathop {\min}\limits_{1\le i \le n} \,(X_i))] $$\end{document} .

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:29:y:1982:i:3:p:399-402

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