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Lindeberg-Feller Central Limit Theorem

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b,

lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a),

where Phi is the normal distribution function.

See also

Berry-Esséen Theorem, Central Limit Theorem, Feller-Lévy Condition, Normal Distribution Function

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References

Feller, W. "Über den zentralen Genzwertsatz der Wahrscheinlichkeitsrechnung." Math. Z. 40, 521-559, 1935.Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. New York: Wiley, p. 229, 1968.Lindeberg, J. W. "Eine neue Herleitung des Exponentialgesetzes in der Wahrschienlichkeitsrechnung." Math. Z. 15, 211-225, 1922.Zabell, S. L. "Alan Turing and the Central Limit Theorem." Amer. Math. Monthly 102, 483-494, 1995.

Referenced on Wolfram|Alpha

Lindeberg-Feller Central Limit Theorem

Cite this as:

Weisstein, Eric W. "Lindeberg-Feller Central Limit Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Lindeberg-FellerCentralLimitTheorem.html

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