Evaluating Security Systems from Statistical Perspectives Based on Censored Data: An Application to Cybersecurity

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.