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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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DOI: https://doi.org/10.1090/S0002-9939-1980-0565358-9
Keywords: Central limit theorem
Article copyright: © Copyright 1980 American Mathematical Society