The Lindeberg-Feller Theorem extends the central limit theorem to a triangular array of independent random variables that need not be identically distributed, showing that their properly normalized sum converges to a normal distribution provided a condition on the tails of their distributions, the Lindeberg condition, is satisfied. Named for Jarl Waldemar Lindeberg and William Feller, it is the standard general form of the central limit theorem used when the classical identically-distributed assumption does not hold.
Facts
StatementIf a triangular array of independent random variables satisfies the Lindeberg condition, then the normalized sum of the array converges in distribution to a standard normal random variable, giving the central limit theorem in this general setting. 1 Sources
1. Lindeberg's condition, Wikipedia
Statement section, concluding sentenceQuote, Statement section, concluding sentence
then the central limit theorem holds, i.e. the random variables Zn converge in distribution to a standard normal random variable as n approaches infinity.
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