A new characterization of the power distribution

A new characterization for the power function distribution is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. The result is obtained by applying a new variant of the Choquet-Deny theorem. We note that in this new result the product consists of order statistics from independent samples. This characterization result may also be interpreted in terms of some special scheme of ranked set sampling.