Results and applications of a new inaccuracy measure based on cumulative Tsallis entropy

Abstract

Non-additive measures are important for many applications. In this paper we propose an extension of the non-additive measure using the concept of Kerridge inaccuracy and cumulative Tsallis entropy. Several properties including non-linear transformation, bounds and characterizations are obtained using this measure. We also study different properties of the quantile version of the proposed measure. Finally, we numerically illustrate the usefulness of the measure and its quantile form using kernel density estimators.

Keywords:

• Cumulative Tsallis entropy
• inaccuracy measure
• reliability measures
• Kernel density estimation

2010 Mathematics Subject Classification:

• 94A17
• 62N05

Acknowledgments

The authors wish to thank the editor and anonymous reviewers for their constructive comments in the earlier draft of the paper. The first author wishes to thank Cochin University of Science and Technology, India, for the financial support.

Conflict of interest statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Funding

The second and third authors wish to thank the Science and Engineering Research Board (SERB), Government of India (FILE NO.MTR/2020/000051 vide Diary No.SERB/F/5424/2020-2021 dated 10-12-2020 and FILE NO.MTR/2019/000203 vide Diary No.SERB/F/9880/2019-2020 dated 06-02-2020) for the financial support.