Let X_(λ_1 ),…,X_(λ_n ) be independent random variables such that X_(λ_i ),i=1,…,n has a probability density function f_(ν,σ,λ_i ) (x)= (2〖λ_i〗^ν)/(Γ(ν/2)〖(2σ^2)〗^(ν/2) ) x^(ν-1) exp(-(λ_i x)^2/(2σ^2 )), ν>0,σ>0,λ_i>0, Known as generalized Rayleigh random variable. We show that for ν≥1, if (〖λ_1^*〗^2,…,〖λ_n^*〗^2) majorizes (〖λ_1〗^2,…,〖λ_n〗^2), then ∑_(i=1)^n▒X_(λ_i^* ) larger than ∑_(i=1)^n▒X_(λ_i ) according to likelihood ratio ordering.
