A new Neutrosophic Paradox Distribution with Application in Modeling Cyber Attack Uncertainty

Nahed I. Isa; Hegazy M. Zaher; Noura A. T. Abu El-Magd

Authors

Nahed I. Isa Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
Hegazy M. Zaher Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
Noura A. T. Abu El-Magd Faculty of Politics and Economics, Beni-Suef University, Beni-Suef, Egypt.

Keywords:

neutrosophic paradox distribution; Beta distribution; Exponential distribution; machine learning; cybersecurity.

Abstract

In recent years, researchers have increasingly focused on neutrosophic probability distributions to handle
incomplete data and inherent uncertainty. A novel distribution, called the Neutrosophic Paradox Distribution (NPD), will be
introduced in this paper, which is developed using neutrosophic algebra in a unique and innovative manner. The NPD is
constructed from three underlying component distributions, and we thoroughly investigate its mathematical characteristics,
such as mean, variance, and cumulative function, including a formal proof of its neutrosophic probability density function.
To illustrate its practical utility, we present detailed examples of specific NPD components such as the Beta-Neutrosophic
Paradox Distribution (Beta-NPD) and the Exponential-Neutrosophic Paradox Distribution (Exponential-NPD). Furthermore,
the proposed distribution is applied to devise robust solutions for complex cybersecurity problems. In this paper, solved
examples are presented to clarify the effectiveness and applicable to apply of NPD in real-world scenarios, highlighting its
potential as a valuable tool in uncertain and incomplete data environments.

DOI 10.5281/zenodo.17594617