Properties of Shannon Entropy for Double Truncated Random Variables and its Applications

Abstract

Doubly truncated data are sometimes encountered in several applications, mainly in survival and astronomical data analysis. This occurs when the data falls between two points. In this study, we focus on the Shannon entropy measure of doubly truncated random variables. We propose ordering and various aging properties based on this measure. Characterizations of some useful life distributions are obtained. It is showed that under certain condition, the proposed measure determines the distribution function uniquely. Some results on discrete distributions are presented. Finally, applications are given.

Keywords

• Shannon entropy
• Generalized failure rate function
• Generalized conditional mean
• Stochastic ordering
• Doubly truncated entropy ordering
• Aging classes