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Advances in Pure and Applied Mathematics

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1869-6090
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A probabilistic counterpart of the Askey scheme for continuous polynomials

Jean-Renaud Pycke
  • Department of Mathematics, University of Evry, LPMA, 91037 Evry cedex, France
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Published Online: 2012-01-19 | DOI: https://doi.org/10.1515/apam.2011.014

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

About the article

Received: 2011-08-03

Revised: 2011-09-20

Published Online: 2012-01-19

Published in Print: 2012-01-01


Citation Information: Advances in Pure and Applied Mathematics, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.014. Export Citation

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