Applied Sciences
| Open Access |
DOI: Numerical Verification Of The Rao–Cramer Inequality And Analysis Of The Efficiency Of Statistical Estimators
Abdukhakimov Saidakhmat Khazratkulovich , Associate Professor, Jizzakh Branch of the National University of Uzbekistan, Uzbekistan Abdukhakimova Maftuna Gofur qizi , PhD, Lecturer, Jizzakh Branch of the National University of Uzbekistan, Uzbekistan Ganiyeva Dilrabo Aliyevna , Master’s Student, Jizzakh Branch of the National University of Uzbekistan, UzbekistanAbstract
This paper is devoted to the analysis of the Rao–Cramer inequality and the efficiency of statistical estimators. In the theoretical part, it is shown that the sample mean obtained from a normal distribution is an unbiased and maximally efficient estimator of the parameter In the applied part, the empirical variance is computed for different sample sizes using Monte Carlo simulation and compared with the Rao–Cramer lower bound. The obtained results are visualized through graphs and tables, providing numerical evidence that the sample mean is an efficient estimator.
Keywords
Rao–Cramer inequality, probability density function, Fisher information
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Copyright (c) 2026 Abdukhakimov Saidakhmat Khazratkulovich, Abdukhakimova Maftuna Gofur qizi, Ganiyeva Dilrabo Aliyevna
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