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A Strengthened Central Limit Theorem for Smooth Densities

✍ Scribed by P.L. Lions; G. Toscani

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
548 KB
Volume
129
Category
Article
ISSN
0022-1236

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✦ Synopsis

We consider the central limit theorem for the probability density function (f_{n}(x)) of the standardized sum of independent and identically distributed random variables with finite variance and regular probability density function. By showing boundedness of different convex functionals along the sequence (\left{f_{n}\right}) we prove convergence in various norms to the normal density. " 1995 Academic Press. Inc.

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