Numerical Verification Of The Rao–Cramer Inequality And Analysis Of The Efficiency Of Statistical Estimators
Keywords:
Rao–Cramer inequality, probability density function, Fisher informationAbstract
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.
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Copyright (c) 2026 Abdukhakimov Saidakhmat Khazratkulovich, Abdukhakimova Maftuna Gofur qizi, Ganiyeva Dilrabo Aliyevna
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