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Free Content A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem

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Abstract:

The Central Limit Theorem, or CLT, is one of the most striking and useful results in probability and statistics, and explains why the normal distribution appears in areas as diverse as gambling, measurement error, sampling, and statistical mechanics. Equipped with a probabilistic "zero-bias" explanation for the appearance of the Lindeberg condition, a sufficient and nearly necessary condition for the CLT, a simplified proof of the Lindeberg-Feller Theorem, and its partial converse, is given.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/193009709X469788

Publication date: January 1, 2009

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