Central limit theorem for signed distributions

Author:
Kenneth J. Hochberg

Journal:
Proc. Amer. Math. Soc. **79** (1980), 298-302

MSC:
Primary 60F05

DOI:
https://doi.org/10.1090/S0002-9939-1980-0565358-9

MathSciNet review:
565358

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Abstract: This paper contains an improved version of existing generalized central limit theorems for convergence of normalized sums of independent random variables distributed by a signed measure. It is shown that under reasonable conditions, the normalized sums converge in distribution to ``higher-order'' analogues of the standard normal random variable, in the sense that the density of the limiting signed distribution is the fundamental solution of a higher-order parabolic partial differential equation that is a generalization of the heat equation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0565358-9

Keywords:
Central limit theorem

Article copyright:
© Copyright 1980
American Mathematical Society