The absorption distribution and theq-binomial theorem

DOI10.1080/03610928108828160zbMath0467.62015OpenAlexW2031717075MaRDI QIDQ3920425

Charles F. Dunkl

Publication date: 1981

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610928108828160

zbMATH Keywords

transformationabsorption distributionq-analogues of Stirling numbers

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Combinatorial probability (60C05) Approximation by polynomials (41A10) Classical hypergeometric functions, ({}_2F_1) (33C05) Approximation by other special function classes (41A30)

Related Items

Existence conditions and properties for the generalized Euler family of distributions, A joint absorption-Mahonian process, q-Multinomial and negative q-multinomial distributions, A \(q\)-Pólya urn model and the \(q\)-Pólya and inverse \(q\)-Pólya distributions, Absorption processes: Models for \(q\)-identities, The \(q\)-Bernstein basis as a \(q\)-binomial distribution, Families of power series distributions, with particular reference to the Lerch family, Discrete \(q\)-distributions on Bernoulli trials with a geometrically varying success probability, Moments and generating functions for the absortion distribution and its negative binomial analogue, The \(q\)-cluster distribution, Moments of a class of discrete \(q\)-distributions, Characterizations involving \(U|(U+V=m)\) for certain discrete distributions, A refinement of the binomial distribution using the quantum binomial theorem

Cites Work

• An addition theorem for some q-Hahn polynomials
• Bilinear forms over a finite field, with applications to coding theory
• On the Foundations of Combinatorial Theory IV Finite Vector Spaces and Eulerian Generating Functions