ON GENERALIZED CUMULATIVE INFORMATION OF KULLBACK-LEIBLER TYPE

In this paper generalized versions of the empirical cumulative Kullback-Leibler information are introduced, together with their alternative representations. The generalization refers to both application of a weight function and the use of Tsallis extended logarithm in the original Kullback-Leibler information measure. The original measure was extensively studied in several papers. The first information measure proposed in this paper is the weighted version of the original Kullback-Leibler information, the second one implies the use of Tsallis extended logarithm, while the third one, combines the first and second. Some properties of the new measures are also discussed.