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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
MathSciNet review:
1825926
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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:
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- [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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