Entropy properties of record statistics

Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. They are closely connected with the occurrence times of a corresponding non-homogenous Poisson process and reliability theory. In this paper, the information properties of record values are presented based on Shannon information. Several upper and lower bounds for the entropy of record values are obtained. It is shown that, the mutual information between record values is distribution free and is computable using the distribution of the record values of the sequence from the uniform distribution.