WEIGHTED R-NORM ENTROPY FOR LIFETIME DISTRIBUTIONS: PROPERTIES AND APPLICATION.

In the field of information theory, different uncertainty measures have been introduced by various researchers. These measures are widely used in reliability and survival studies. In this article, we introduce two new weighted uncertainty measures which are known as weighted R-Norm entropy (WRNE) and weighted R-Norm residual entropy (WRNRE). WRNE and WRNRE are "lengthbiased" shift-dependent uncertainty measures in which higher weight is assigned to large values of the observed random variable. Several important properties of these measures are studied. Some significant characterization results and the relationships of WRNRE with other reliability measures are presented. We also show that the survival function is uniquely determined by the WRNRE. Finally, based on a real life data set of bladder cancer patients, we illustrate the importance of WRNE and WRNRE. [ABSTRACT FROM AUTHOR]