Central limit theorem for signed distributions
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- by Kenneth J. Hochberg PDF
- Proc. Amer. Math. Soc. 79 (1980), 298-302 Request permission
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.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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