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Fibonacci numbers, Lucas numbers and integrals of certain Gaussian processes
Author(s):
Ludwig
Baringhaus
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3875-3884.
MSC (1991):
Primary 60E05;
Secondary 11B35
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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.
References:
- [1]
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1964. MR 29:4914
- [2]
- A. Araujo and E. Giné, The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York, 1980. MR 83e:60003
- [3]
- L. Baringhaus and N. Henze, A consistent test for multivariate normality based on the empirical characteristic function, Metrika 35 (1988), 339-348. MR 90f:62174
- [4]
- S. Csörg\H{o}, Multivariate empirical characteristic functions, Z. Wahrscheinlichkeitstheorie verw. Gebiete 55 (1981), 203-229. MR 82j:60026
- [5]
- D. A. Darling, The Cramér-Smirnov test in the parametric case, Ann. Statist. 26 (1955), 1-20. MR 16:729g
- [6]
- N. Dunford and J. T. Schwartz, Linear Operators, Part II, Wiley, New York, 1963. MR 32:6181
- [7]
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions. Vol. 2, McGraw-Hill, New York, 1953. MR 15:419i
- [8]
- -, Tables of Integral Transforms. Vols. 1, 2, McGraw-Hill, New York, 1954. MR 15:868a; MR 16:468c
- [9]
- A. Feuerverger and R. A. Mureika, The empirical characteristic function and its applications, Ann. Statist. 5 (1977), 88-97. MR 55:1605
- [10]
- H.-D. Keller, Einige Untersuchungen zur empirischen charakteristischen Funtion und deren Anwendungen, Dissertation, Dortmund, 1979.
- [11]
- S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Ellis Horwood, Chichester, 1989. MR 90h:11014
- [12]
- W. Whitt, Weak convergence of probability measures on the spaces
 , Ann. Math. Statist. 41 (1970), 939-944. MR 41:6259
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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