A Novel of Bounded Zeghdoudi Distribution: Estimations, Simulation and Applications

Abstract

 In this article, we introduce a new unit Zeghoudi distribution, which is called the bounded Zeghoudi distribution (BZD), an innovative modification of the Zeghoudi distribution (ZD). This new suggested distribution retains the original ZD’s simplicity while improving modeling flexibility and accuracy for data constrained to the unit interval. The BZD displays numerous significant characteristics, including decreased, left-skewed, right-skewed, and unimodal probability density functions, but the hazard rate function can be J-shaped, U-shaped, and bathtub-shaped. Some important statistical features of the BZD, such as moments, mean, variance, moment generating function, lower and upper incomplete moments, mean residual life, mean inactivity time, some inequality measures, and order statistics, are computed. We demonstrate the effectiveness and reliability of the BZD using sixteen standard techniques for parameter estimation, supported by an extensive simulation analysis. Beyond its general statistical usefulness, the BZD is particularly relevant for cybersecurity analytics, where many key indicators such as intrusion detection rates, anomaly scores, attack probabilities, packet loss ratios, and vulnerability exploitability. The implementation of the BZD on four actual proportional datasets concerning failure rate, engineering, and medical data illustrates its efficacy and superiority compared to many well-known statistical models, such as ZD, unit Lindley distribution, the unit Teissier distribution, the reduced Kies distribution, exponentiated reduced Kies distribution, the Kumaraswamy distribution, beta distribution, and the unit Burr-III distribution.