Feller-Lévy Condition
المؤلف:
Zabell, S. L.
المصدر:
"Alan Turing and the Central Limit Theorem." Amer. Math. Monthly 102
الجزء والصفحة:
...
23-4-2021
1552
Feller-Lévy Condition
Given a sequence of independent random variates 
, 
, ..., if 
and
then
This means that if the Lindeberg condition holds for the sequence of variates 
, ..., then the variance of an individual term in the sum 
of 
is asymptotically negligible. For such sequences, the Lindeberg condition is necessary as well as sufficient for the Lindeberg-Feller central limit theorem to hold.
REFERENCES:
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.
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