Quantile-based cumulative Kullback–Leibler divergence

ABSTRACT

The paper introduces a quantile-based cumulative Kullback–Leibler divergence and study its various properties. Unlike the distribution function approach, the quantile-based measure possesses some unique properties. The quantile functions used in many applied works do not have any tractable distribution functions where the proposed measure is a useful tool to compute the distance between two random variables. Some useful bounds are obtained for quantile-based residual cumulative Kullback–Leibler divergence and quantile-based reliability measures. Characterization results based on the functional forms of quantile-based residual Kullback–Leibler divergence are obtained for some well-known life distributions, namely exponential, Pareto II and beta.

KEYWORDS:

• Cumulative residual Kullback–Leibler divergence
• quantile function
• reliability measures
• characterizations
• stochastic ordering

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 94A17
• 94Axx

Acknowledgements

The first two authors would like to thank the support of the University Grants Commission, India, under the Special Assistance Programme.

Disclosure statement

No potential conflict of interest was reported by the authors.