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9 - Systems of Frequency Distributions Using Bessel Functions and Cumulants

Published online by Cambridge University Press:  06 November 2020

Vijay P. Singh
Affiliation:
Texas A & M University
Lan Zhang
Affiliation:
Texas A & M University
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Summary

Systems of frequency distributions are derived by the use of Bessel functions and the method of expansions in terms of cumulants or moments. The resulting distributions may be useful in hydrologic, hydraulic, environmental, and water resources engineering. These methods are discussed in this chapter.

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Publisher: Cambridge University Press
Print publication year: 2020

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References

Appell, P. (1925). Sur les fonctions hypergéometriques de plusieurs variables. In Memoir. Sci. Math. Paris: Gauthier-Villars.Google Scholar
Barndorff-Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24, pp. 113.Google Scholar
Blinnikov, S., and Moessner, R. (1998). Expansions for nearly Gaussian distributions. Astronomy and Astrophysics Supplement Series 13, pp. 193205.CrossRefGoogle Scholar
Bowers, N. L. Jr. (1966). Expansion of probability density functions as a sum of gamma densities with applications in risk theory. Transactions of Society of Actuaries 18, no. 52, pp. 125147.Google Scholar
Cavalcante, C. C., Mota, J. C. M., and Romano, J. M. T. (2004) Polynomial expansion of the probability density function about Gaussian mixtures. In Machine Learning and Signal Processing, Proceedings of the 2004 14th IEEE Signal Processing Society Workshop. doi: 10.1109/MLSP.2004.1422970.Google Scholar
Johnson, N. L., Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol 1., 2nd ed. New York: John Wiley and Sons.Google Scholar
Kendall, S. M., and Stuart, A. (1977). The Advanced Theory of Statistics, Volume 1: Distribution Theory, 4th ed. New York: Macmillan Publishing Co, Inc.Google Scholar
Kolassa, J. E. (2006). Series Approximation Methods in Statistics, 3rd ed. New York: Springer Science+Business Media, Inc.Google Scholar
Mckay, A. T. (1932). A Bessel function distribution. Biometrika 24, no. ½, pp. 3944.Google Scholar
Nadarajah, S. (2008). Some product Bessel density distributions. Taiwanese Journal of Mathematics 12, no. 1, pp. 191211.Google Scholar
Suetin, P. K. (2001). Jacobi Polynomials. In Encylopedia of Mathematics, edited by Hazewinkel, M.. Springer Science+Business Media B.V./Kluwer Academic Publishers. www.encyclopediaofmath.org/index.php?title=Jacobi_polynomials&oldid=18958.Google Scholar

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