Evaluating security systems from statistical perspectives based on censored data: An application to cybersecurity

Mohamed, Nagwa; Mansour, Mahmoud; Hussam, Eslam

doi:10.21608/cjmss.2025.376922.1159

Evaluating security systems from statistical perspectives based on censored data: An application to cybersecurity

Articles in Press

Document Type : Original Article

Authors

¹ Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez 43221, Egypt

² Department of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherouk 11837, Egypt

³ Department of Accounting, College of Business Administration in Hawtat bani Tamim, Prince Sattam bin Abdulaziz University, Hawtat bani Tamim 11941, Saudi Arabia

⁴ Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt

10.21608/cjmss.2025.376922.1159

Abstract

We propose statistical methods to estimate the geometric distribution parameter when collected data are progressively Type-II censored during time-limited trials such as a Cybersecurity experiment. Maximum likelihood estimation (MLE) and Bayesian estimators are derived while the Bayesian estimator utilizes a Beta distribution prior to estimation through simulated performance assessment. The proposed method applies to simulated login attempt data that track authentication attempts until success due to brute-force attacks. The application of progressive censoring techniques saves $70\%$ of testing duration regarding conventional approaches but preserves measurement precision. By incorporating prior knowledge, Bayesian estimation outperforms MLE in precision, especially for small samples. A simulation study establishes model reliability for different censoring scenarios while providing coverage probability evidence for accurate confidence intervals. The method is exceptional for security system design because it enables quick but precise parameter estimation. The research reveals the balancing act between the degree of censorship and accuracy levels and experimental budget constraints, providing operational benefits for Cybersecurity studies.

Keywords