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Advances in Pure and Applied Mathematics

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A probabilistic counterpart of the Askey scheme for continuous polynomials

1Department of Mathematics, University of Evry, LPMA, 91037 Evry cedex, France

Citation Information: Advances in Pure and Applied Mathematics. Volume 3, Issue 1, Pages 85–111, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.014, January 2012

Publication History

Received:
2011-08-03
Revised:
2011-09-20
Published Online:
2012-01-19

Abstract.

Random variables corresponding to weight functions of the Askey scheme for continuous polynomials are introduced. Beside normal, Beta and Gamma distributions four new families of real random variables corresponding to Wilson, continuous dual Hahn, continuous Hahn and Meixner–Pollaczek polynomials are discussed. Formulas for the moments and asymptotic behavior of the tails of the distributions are provided.

Keywords.: Askey scheme; orthogonal polynomials; parametric model

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