Comparative analysis of unknown parameter estimation of the gamma distribution with right-censored data in incomplete statistical models

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.