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Licensed Unlicensed Requires Authentication Published by De Gruyter January 19, 2012

A probabilistic counterpart of the Askey scheme for continuous polynomials

  • Jean-Renaud Pycke EMAIL logo

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.

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

© 2012 by Walter de Gruyter Berlin Boston

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