New Developments in Generalized Information Measures

Abstract

Publisher Summary The concept of Shannon's (1948) entropy is the central concept of information theory. Sometimes this measure is referred to as the “measure of uncertainty.” The entropy of a random variable is defined in terms of its probability distribution and can be shown to be a good measure of randomness or uncertainty. This chapter discusses new developments in generalized information measures. The entropy of a random variable is defined in terms of its probability distribution and can be shown as a good measure of randomness or uncertainty. In the past, researchers' interest tended toward one- and two-scalar parametric generalizations of the measures. The unified ( r , s )-measures are divided in two parts: (1) unified ( r , s )-information measures and (2) M-dimensional unified (r, s)-divergence measures. The measure H ( P ) is the Shannon's entropy and the measure H ( P | Q ) is the inaccuracy. The arithmetic-geometric mean divergence measure and its unified ( r , s )-generalizations are also presented in this chapter.