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

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.