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Some discrete distributions associated with orthogonal polynomials

Published online by Cambridge University Press:  14 July 2016

Geoffrey S. Watson
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Abstract

Five distributions on the non-negative integers are given which use the orthogonal polynomials of Hermite, Legendre, Laguerre and Chebyshev.

Keywords

NEGATIVE BINOMIAL DISTRIBUTIONPOISSON DISTRIBUTION
Type
Part 4 - Applied Probability and Quantum Theory
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 167 - 171
Copyright
Copyright © Applied Probability Trust 1988 

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References

Abramowitz, M. and Stegun, I. A. (1964) Handbook of Mathematical Functions. National Bureau of Standards Applied Mathematics Series, # 55, US Government Printing Office, Washington, DC.Google Scholar
Courant, R. and Hilbert, D. (1970) Methods of Mathematical Physics. Interscience, New York.Google Scholar
Foata, D. (1978) A combinatorial proof of the Mehler Formula. J. Comb. Theory A, 24, 367–376.CrossRefGoogle Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series, and Products. Academic Press, New York.Google Scholar
Gurland, J., Chen, E. E. and Hernandez, F. M. (1983) A new discrete distribution involving Laguerre polynomials. Comm. Statist.—Theory Methods 12 1987–2004.CrossRefGoogle Scholar
Helstrom, C. W. (1976) Quantum Detection and Estimation Theory. Academic Press, New York.Google Scholar
Jain, G. C. (1983) Hermite distributions. Encyclopaedia of Statistical Sciences, Vol. 3, ed. Kotz, S. and Johnson, N. L. Wiley, New York.Google Scholar
Mckendrick, A. G. (1926) The application of mathematics to medical problems. Proc. Edin. Math. Soc. 44, 98–130.CrossRefGoogle Scholar