On characterization of a generalized ‘useful’ information measure

In this communication a generalized measure of ‘useful’ information is defined which has a utility scheme and two probability distributions respectively. The recent development in information theory is described to the study of characterization results based on the purely functional equation approach. In this paper, a characterization theorem is proved here with help of a functional equation. A generalized information measure of Ahmad and Khan (1977), the relative ‘useful’ information of jain and Tuteja (1986), the directed divergence of Rathie and Kannappan (1972), relative information of Kullback’s (1959) and Pearson’s - statistic is a measure of discrepancy between the two distributions and are special cases of the measure defined here.