Comparative analysis of unknown parameter estimation of the gamma distribution with right-censored data in incomplete statistical models
DOI:
https://doi.org/10.71310/pcam.1_63.2025.09Keywords:
Gamma distribution, Nelder-Mead simplex algorithm, Expectation-Maximization, Maximum Likelihood Estimation, Right-censoring, Proportional hazards modelAbstract
In this article, the problem of estimating the parameters of the gamma distribution under censored data conditions in incomplete statistical models is considered. Numerical maximum likelihood methods are analyzed, including the Nelder-Mead and Expectation-Maximization (EM) algorithms, which are applied for estimating the distribution parameters. A comparison of estimation accuracy at different levels of censoring is conducted, allowing the identification of the advantages and limitations of each method. The obtained results show that the EM algorithm provides higher estimation accuracy under censoring conditions, while the Nelder-Mead method demonstrates stable results under full observation. The influence of the proportional hazards model on parameter estimation under dependent censoring is also examined. This study expands the investigation of numerical methods for estimating distribution parameters under incomplete data conditions, offering recommendations on selecting the most effective method depending on the sample characteristics and the level of censoring.
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Abdushukurov A.A., Kim L.V. 1987. Lower Cramer-Rao and Bhattacharyya bounds for randomly censored observations. Journal of Soviet Mathematics. 38(5): – P. 2171–2185.
Abdushukurov A.A., Nurmukhamedova N.S. 2020. Asymptotic Properties of Bayesian-Type Estimates in the Competing Risk Model under Random Censoring. Journal of Mathematical Sciences (United States). 245(3): – P. 341–349.
Berdimuradov M.B. 2024. Estimation of unknown parameter of gamma distribution in incomplete models of statistics. ACTA NUUz. 1(1): – P. 43–52.
Breslow N.E. 1975. Analysis of Survival Data under the Proportional Hazards Model. International Statistical Review. 43(1): – P. 45–57.
Clayton D., Cuzick J. 1985. Multivariate Generalizations of the Proportional Hazards Model. Journal of the Royal Statistical Society, Series A (General). 148(2): – P. 82–117.
Cox D.R. 1972. Regression Models and Life-Tables. Journal of the Royal Statistical Society, Series B (Methodological). 34(2): – P. 187–220.
Dempster A.P., Laird N.M., Rubin D.B. 1977. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B (Methodological). 39(1): – P. 1–38.
Kalbfleisch J.D., Prentice R.L. 1980. The Statistical Analysis of Failure Time Data. Wiley.
Klein J.P., Moeschberger M.L. 2003. Survival Analysis: Techniques for Censored and Truncated Data. Springer.
McLachlan G.J., Krishnan T. 2008. The EM Algorithm and Extensions. Wiley, – 400 p.
Nelder J.A., Mead R. 1965. A Simplex Method for Function Minimization. Computer Journal. 7(4): – P. 308–313.
