Some New Results of Residual and Past Entropy Measures

In this paper, two new generalized entropies have been introduced with their respective properties. The results of these entropies have been verified for the exponential and weighted exponential distributions. These two entropies produce the results in the form of simple entropy, generalized entropy, residual entropy, cumulative entropy and mixtures of all these entropies. Some characteristics of residual & past entropy have been derived and special cases have also been obtained. These cases indicate that new generalized entropies are more comprehensive and useful. The main advantage of this study is to derive different types of generalization of entropies using the different parameter values of α and β.

Characterization Results Based on Generalized Dynamic Information Measure

In this paper, we consider a generalized past entropy of order [Formula: see text] and type [Formula: see text] and have characterized some distributions of random lifetimes in continuous and discrete situations. Further, we propose a weighted version of generalized past entropy for continuous and discrete cases and have proved the characterization results. Also, we study a generalized weighted residual entropy for the discrete case. At the end, the concept of generalized cumulative past entropy are also discussed.