On characterizing distributions via regression of functions of generalized order statistics

Let X(1,n,m1,k),X(2,n,m2,k),…,X(n,n,m,k)X(1,n,m1,k),X(2,n,m2,k),…,X(n,n,m,k) be nn generalized order statistics from a continuous distribution FF which is strictly increasing over (a,b),−∞≤a