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Analyzing variance in central limit theorems

Mynbayev, Kairat and Darkenbayeva, Gulsim (2019): Analyzing variance in central limit theorems. Published in: Kazakh Mathematical Journal , Vol. 19, No. 3 (2019): pp. 30-39.

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Abstract

Central limit theorems deal with convergence in distribution of sums of random variables. The usual approach is to normalize the sums to have variance equal to 1. As a result, the limit distribution has variance one. In most papers, existence of the limit of the normalizing factor is postulated and the limit itself is not studied. Here we review some results which focus on the study of the normalizing factor. Applications are indicated.

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