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A probabilistic counterpart of the Askey scheme for continuous polynomials
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Jean-Renaud Pycke
Published/Copyright:
January 19, 2012
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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Articles in the same Issue
- Prelims
- Warfield invariants of normed unit groups in abelian group rings
- Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
- On generalized Laplace equation and nonlinear operators
- Steady state solutions to the conserved Kuramoto–Sivashinsky equation
- Variational analysis for an indefinite quasilinear problem with variable exponent
- A probabilistic counterpart of the Askey scheme for continuous polynomials
- A characterisation of the Weyl transform
Articles in the same Issue
- Prelims
- Warfield invariants of normed unit groups in abelian group rings
- Opdam's hypergeometric functions: product formula and convolution structure in dimension 1
- On generalized Laplace equation and nonlinear operators
- Steady state solutions to the conserved Kuramoto–Sivashinsky equation
- Variational analysis for an indefinite quasilinear problem with variable exponent
- A probabilistic counterpart of the Askey scheme for continuous polynomials
- A characterisation of the Weyl transform
