Order statistics   drawn from a sample   of independent random variables with the distribution function F are considered. Excluding lattice distribution functions F, the difference   and the order statistics   have the same distribution if and only if  . This result is equivalent to a proposition on the PARETO distributions where the difference   has to be substituted by the quotient  . It is also the conditions   and   that characterize the distribution function F(X₀ + a x) = E(x). As it is shown by an example, the assumption (^*) is necessary for this proposition. - The proof of the first proposition provides also the solution of the following problem: “For which (not lattice) distribution functions F and G holds   where  .