ESTIMATION OF THE DEVIATION FROM THE NORMAL LAW IN THE CENTRAL LIMIT THEOREM

Bessarabskaya Irina Eduardovna

This work investigates the rate of convergence in the Central Limit Theorem for sums of independent and identically distributed random variables. Numerical experiments are conducted for the uniform, exponential, and beta distributions to evaluate the Kolmogorov distance between the distribution of the standardized sum and the standard normal law for various numbers of summands. A logarithmic regression approach is used to estimate the convergence order and a empirical analogue of the Berry–Esseen constant. The obtained estimates are consistent with the leading terms of the Edgeworth expansion and demonstrate the influence of the asymmetry of the underlying distribution on the rate of normal approximation. The proposed approach provides quantitative characteristics of the asymptotic behavior of distributional convergence and can be applied to assess the quality of normal approximation for a wide class of distributions.

Keywords:Central Limit Theorem, Edgeworth Expansion, Berry–Esseen inequality, Continuous Distributions, Rate of Convergence