Let X1, . . . , Xn be a set of n continuous and non-negative random variables, with log-concave joint density function f, faced by a person who seeks for an optimal deductible coverage for this n risks. Let d = (d1, . . . dn) and d ∗ = (d ∗ 1 , . . . d∗ n ) be two vectors of deductibles...

Let X[lambda]1,...,X[lambda]n be independent random variables such that X[lambda]i, i=1,...,n has probability density function known as a generalized Rayleigh random variable. We show that for [nu]>=1, if majorizes , then is larger than according to likelihood ratio ordering.