Feller-Lévy Condition

Given a sequence of independent random variates X_1, X_2, ..., if sigma_k^2=var(X_k) and




This means that if the Lindeberg condition holds for the sequence of variates X_1, ..., then the variance of an individual term in the sum S_n of X_k is asymptotically negligible. For such sequences, the Lindeberg condition is necessary as well as sufficient for the Lindeberg-Feller central limit theorem to hold.

See also

Berry-Esséen Theorem, Central Limit Theorem, Lindeberg Condition

Explore with Wolfram|Alpha


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

Feller-Lévy Condition

Cite this as:

Weisstein, Eric W. "Feller-Lévy Condition." From MathWorld--A Wolfram Web Resource.

Subject classifications