The entropy of consecutive order statistics

Calculation of the entropy of a set of consecutive order statistics is relatively more complicated than that of the entropy of the individual order statistic, which has been studied by Wong and Chan (1990). We provide some fundamental relations occurring in the entropy of consecutive-order statistics, which are very useful for computations. We first consider the decomposition of the entropy of order statistics, and derive some recurrence relations in the first r order statistics. We also establish a dual principle for the entropy of order statistics, which yields a dual relation from a given relation in the entropy of order statistics