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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fibonacci numbers, Lucas numbers
and integrals of certain Gaussian processes


Author: Ludwig Baringhaus
Journal: Proc. Amer. Math. Soc. 124 (1996), 3875-3884
MSC (1991): Primary 60E05; Secondary 11B35
MathSciNet review: 1363410
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Abstract: We study the distributions of integrals of Gaussian processes arising as limiting distributions of test statistics proposed for treating a goodness of fit or symmetry problem. We show that the cumulants of the distributions can be expressed in terms of Fibonacci numbers and Lucas numbers.


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Additional Information

Ludwig Baringhaus
Affiliation: Institut für Mathematische Stochastik, Universität Hannover, D-30167 Hannover, Germany
Email: baringhaus@mbox.stochastik.uni-hannover.de

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03691-X
PII: S 0002-9939(96)03691-X
Keywords: Gaussian processes, Fibonacci numbers, Lucas numbers, integral equations, empirical Fourier transform, testing for normality, testing for symmetry
Received by editor(s): May 15, 1995
Communicated by: Wei-Yin Loh
Article copyright: © Copyright 1996 American Mathematical Society