Numerical Verification Of The Rao–Cramer Inequality And Analysis Of The Efficiency Of Statistical Estimators

The American Journal of Applied Sciences 2026 Open access

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Authors: Abdukhakimov Saidakhmat Khazratkulovich, Abdukhakimova Maftuna Gofur qizi, Ganiyeva Dilrabo Aliyevna
DOI: 10.37547/tajas/volume08issue01-06
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Statistical Distribution Estimation and Applications Probability and Statistical Research Advanced Statistical Methods and Models

Publication details

Journal / source
The American Journal of Applied Sciences
Volume
8
Issue
1
Pages
39–45
Publication date
1 January 2026
Language
EN