Journals Information
Mathematics and Statistics Vol. 13(4), pp. 237 - 251
DOI: 10.13189/ms.2025.130408
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Comparative Analysis of Unknown Parameters of the Normal Distribution under Right-Censoring Using MLE and Bayesian Methods
Nurmukhamedova Nargiza 1, Berdimuradov Mirkamol 2,*, Murodov Sardor 3
1 Department of Econometrics & Economical Modelling, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan
2 Department of Applied Mathematics and Intellectual Technologies, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan
3 Department of Econometrics, Tashkent State University of Economics, Tashkent, Uzbekistan
ABSTRACT
Right-censored data frequently occur in survival analysis, reliability engineering, and economic modeling, where the exact value of some observations is unknown due to time limitations or censoring mechanisms. This paper aims to conduct a comparative analysis of parameter estimation for the Normal distribution under right-censoring conditions using two approaches: Maximum Likelihood Estimation (MLE) and Bayesian inference. In the Bayesian framework, both conjugate priors and numerical techniques such as Monte Carlo integration and Gibbs sampling are employed. For MLE, the Expectation-Maximization (EM) algorithm is used to iteratively estimate the mean and variance from incomplete observations. The study is structured around four censoring scenarios, including fixed and random censoring, with either the mean or the variance assumed unknown. Simulated datasets under each scenario are analyzed to assess the accuracy, stability, and efficiency of the two methods. The performance is evaluated in terms of Mean Squared Error (MSE), 95% confidence or highest posterior density (HPD) intervals, and robustness to increasing censoring levels. Results show that Bayesian methods yield more stable and lower-error estimates in small samples and highly censored data, while MLE performs competitively or better when sample size increases, particularly under complex censoring patterns. The study contributes to statistical methodology by highlighting when and why each method is preferable under practical constraints. The implications are relevant for practitioners in applied statistics, actuarial modeling, and data science dealing with incomplete observations. Though limited to the Normal model, the findings suggest broader applicability to other distributions and future work may include Gamma extensions, adaptive priors, or hybrid Bayesian EM frameworks. This work also serves as a practical reference for selecting estimation strategies based on data characteristics, sample size, and censoring structure.
KEYWORDS
Bayesian Estimation, Maximum Likelihood Estimation, Monte-Carlo Method, Expectation-Maximization, Right Censoring, Mean Squared Error
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nurmukhamedova Nargiza , Berdimuradov Mirkamol , Murodov Sardor , "Comparative Analysis of Unknown Parameters of the Normal Distribution under Right-Censoring Using MLE and Bayesian Methods," Mathematics and Statistics, Vol. 13, No. 4, pp. 237 - 251, 2025. DOI: 10.13189/ms.2025.130408.
(b). APA Format:
Nurmukhamedova Nargiza , Berdimuradov Mirkamol , Murodov Sardor (2025). Comparative Analysis of Unknown Parameters of the Normal Distribution under Right-Censoring Using MLE and Bayesian Methods. Mathematics and Statistics, 13(4), 237 - 251. DOI: 10.13189/ms.2025.130408.