On the mean residual life order of convolutions of independent uniform random variables

Abstract

Let Xλi,i=1,…,n be n independent random variables such that Xλi has uniform distribution over the interval (0,1/λi),i=1,…,n. It is proved that if (λ1,…,λn) is larger than (λ1⁎,…,λn⁎) according to reciprocal order, then ∑i=1nXλi is larger than ∑i=1nXλi⁎ according to mean residual life order as well as increasing convex order. This result gives convenient bounds for mean residual life function of ∑i=1nXλi in terms of harmonic mean of λi's. It is shown that these bounds are sharper than those given in the literature in terms of geometric mean and arithmetic mean of λi's.