Cumulative α-Jensen–Shannon measure of divergence: Properties and applications

Abstract

The problem of quantifying the distance between distributions arises in various fields, including cryptography, information theory, communication networks, machine learning, and data mining. In this article, the analogy with the cumulative Jensen–Shannon divergence, defined in Nguyen and Vreeken (2015), we propose a new divergence measure based on the cumulative distribution function and call it the cumulative α-Jensen–Shannon divergence, denoted by ${\mathit{\text{CJS}}}_{(\alpha )}$. Properties of ${\mathit{\text{CJS}}}_{(\alpha )}$ are studied in detail, and also two upper bounds for ${\mathit{\text{CJS}}}_{(\alpha )}$ are obtained. The simplified results under the proportional reversed hazard rate model are given. Various illustrative examples are analyzed.

KEYWORDS:

• Distribution function
• Entropy
• Kullback–Leibler divergence
• proportional reversed hazard rate model

2020 MSC:

• 94A17
• 62B10

Authors contributions

Riyahi: Conceptualization, Methodology, Software, Validation, Writing- Original draft preparation, Writing- Reviewing and Editing. M. Baratnia: Conceptualization, Software, Validation, Reviewing and Editing. M. Doostparast: Conceptualization, Methodology, Supervision, Writing- Original draft preparation, Writing- Reviewing and Editing. Authors contributions

Riyahi: Conceptualization, Methodology, Software, Validation, Writing- Original draft preparation, Writing- Reviewing and Editing. M. Baratnia: Conceptualization, Software, Validation, Reviewing and Editing. M. Doostparast: Conceptualization, Methodology, Supervision, Writing- Original draft preparation, Writing- Reviewing and Editing.

Disclosure statement

No potential conflict of interest was reported by the authors.