Lorenz ordering of order statistics

Let Xi:nXi:n denote the ith order statistic of a random sample of size n from a continuous distribution with cdf F. Sufficient conditions are obtained on F   so that Xj:m⩽⋆Xi:nXj:m⩽⋆Xi:n (hence Xj:m⩽LorenzXi:nXj:m⩽LorenzXi:n) for i⩽ji⩽j and n-i⩾m-jn-i⩾m-j.