A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem
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
Publication date: January 1, 2009
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- American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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