Quantile cumulative distribution function and its applications

Abstract

In this article, we consider functions having the properties of both the cumulative distribution function and the quantile function. Due to these characteristics, we term such functions quantile cumulative distribution functions. The comparison distribution function defined by Parzen (1982) for comparing the probability distributions of two populations is an example of such a function. We discuss some properties of the quantile cumulative distribution function and its usefulness in generating new continuous probability distributions on the unit interval. An overview of some of their applications is also presented to emphasize the importance of the quantile cumulative distribution function.

KEYWORDS:

• Cumulative distribution function
• quantile function
• quantile density function
• comparison distribution

2020 Mathematics Subject Classification:

• 60E05
• 62E10

Acknowledgments

The author thanks the reviewers for their valuable comments, which have considerably improved the content and presentation of the manuscript.