On cumulative residual (past) inaccuracy for truncated random variables

TL;DR

This paper explores the properties of cumulative residual and past inaccuracy measures, extending the concepts of entropy and Kerridge inaccuracy to truncated random variables, providing theoretical insights and bounds.

Contribution

It introduces and analyzes the cumulative residual and past inaccuracy measures for truncated variables, extending existing entropy concepts with new properties and bounds.

Findings

Properties like monotonicity and bounds are established for truncated variables.

The measures are extended to left, right, and doubly truncated cases.

Theoretical framework enhances understanding of inaccuracy measures in information theory.

Abstract

To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables.