On the Rotar central limit theorem for sums of a random number of independent random variables

Tran Loc Hung

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arXiv · 2309.13988

On the Rotar central limit theorem for sums of a random number of independent random variables

Tran Loc Hung

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Abstract

The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and Lindeberg-Feller's in the classical version. The Rotar central limit theorem generalizes the classical Lindeberg-Feller central limit theorem since the Rotar condition is weaker than Lindeberg's. The main aim of this paper is to introduce the Rotar central limit theorem for sums of a random number of independent (not necessarily identically distributed) random variables and the conditions for its validity. The order of approximation in this theorem is also considered in this paper.

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Tran Loc Hung. 2023-09-25. On the Rotar central limit theorem for sums of a random number of independent random variables. https://arxiv.org/abs/2309.13988

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