The Entropy of Consecutive Order Statistics

Calculations 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 [1]. We provide some fundamental relations occuring 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.