Study on the Speed of Convergence of the Central Limit Theorem by a Simulation Program

Abstract

Although sufficient mathematical tools are available to prove the correctness of the central limit theorem, it is only proved in an infinite sense, while the speed of convergence of a sum (Sn) of n independent identically distributed random variables to a normal distributed random variable is not easy to find theoretically. This paper describesa simulation program which may be used to simulate the distribution of Sn for any given n. Then the speed of convergence of the central limit theorem can be studied.