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Monotonic approach to central limits

Author(s): Jonathan M. Kane
Journal: Proc. Amer. Math. Soc. 129 (2001), 2127-2133.
MSC (2000): Primary 62E20, 62F12, 62F05
Posted: November 22, 2000
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Abstract | References | Similar articles | Additional information

Abstract:

The approach to limits guaranteed by the Central Limit Theorem appears to be monotonic in many cases. A variety of empirical examples are discussed. Proofs are given for some special cases of the binomial, gamma, and Poisson distributions.

References:

[1994]: J. Chover, Recall via Transient Neuronal Firing, Neural Networks, 7 (1994), 233-250.
[1996]: J. Chover, Neural Correlation via Random Connections, Neural Computation 8 #8, (1996), 1711-1729.
[1968]: Kumar Jogdeo and S. M. Samuels, Monotone Convergence of Binomial Probabilities and a Generalization of Ramanujan's Equation, Ann. Math. Stat. 39 (1968), 1191-1195.

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Additional Information:

Jonathan M. Kane
Affiliation: Department of Mathematical and Computer Sciences, University of Wisconsin, Whitewater, 800 West Main Street, Whitewater, Wisconsin 53190-1790
Email: kanej@mail.uww.edu

DOI: 10.1090/S0002-9939-00-05776-2
PII: S 0002-9939(00)05776-2
Keywords: Central limit, binomial distribution, gamma distribution.
Received by editor(s): May 24, 1999
Received by editor(s) in revised form: November 15, 1999
Posted: November 22, 2000
Communicated by: Wei-Yin Loh
Copyright of article: Copyright 2000, American Mathematical Society


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