Quantile-based cumulative Kullback-Leibler divergence in past lifetime: Some properties and applications

Abstract

This article introduces a quantile-based cumulative Kullback-Leibler (KL) divergence measure for past lifetimes (QPCKL divergence) and studies its various properties. Unlike the cumulative KL divergence using the distribution function, the proposed measure offers an alternative method for computing the divergence between two random variables, especially when one lacks a closed-form distribution function but possesses a closed-form quantile function. A characterization property of a distribution is derived using the constant QPCKL divergence model. Subsequently, a comparison of some important reliability characteristics using the proposed measure is discussed. The QPCKL divergence for a general family of transformation models is derived. We also propose a non parametric estimator for the measure, and simulation studies are carried out for validation. Finally, the importance of the estimator is also illustrated through real data sets useful in survival studies.

Keywords:

• Quantile function
• general transformation models
• characterization
• non parametric estimation

Acknowledgments

The authors wish to thank the editor and referees for their constructive comments.

Disclosure statement

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

Additional information

Funding

The first author wishes 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) for the financial support. The second author wishes to thank Cochin University of Science and Technology, India, for the financial support.