The Lindeberg-Feller central limit theorem states that if the random variates 
,
,
... satisfy the Lindeberg condition, then
for all 
,
 |
where 
is the normal
distribution function.
Lindeberg-Feller Central Limit Theorem
See also
Berry-Esséen Theorem, Central Limit Theorem, Feller-Lévy Condition, Normal Distribution FunctionExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Lindeberg-Feller Central Limit Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Lindeberg-FellerCentralLimitTheorem.html