On some stochastic inequalities involving minimum of random variables
Peter Kubat · Naval Research Logistics Quarterly · 1982
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 .