A \(q\)-analogue of the Stirling formula and a continuous limiting behaviour of the \(q\)-binomial distribution -- numerical calculations

DOI10.1007/S11009-011-9231-1zbMath1263.60029OpenAlexW2033426574MaRDI QIDQ1945607

Andreas George Kyriakoussis, Malvina G. Vamvakari

Publication date: 8 April 2013

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-011-9231-1

zbMATH Keywords

asymptotic formulaspointwise convergencesaddle point methodStirling formula\(q\)-binomial distribution\(q\)-factorial number of order \(n\)continuous Stieltjes-Wigert distribution

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) (q)-calculus and related topics (05A30) Computation of special functions and constants, construction of tables (65D20) Limit theorems in probability theory (60F99)

Related Items (6)

On multivariate discrete q-Distributions-A multivariate q-Cauchy’s formula ⋮ A \(q\)-random walk approximated by a \(q\)-Brownian motion ⋮ A q -binomial extension of the CRR asset pricing model ⋮ \(q\)-random walks on \(\mathbb Z^d\), \(d = 1, 2, 3\) ⋮ Heine process as a q-analog of the Poisson process—waiting and interarrival times ⋮ Continuous Stieltjes-Wigert limiting behaviour of a family of confluent \(q\)-Chu-Vandermonde distributions

Uses Software

• qseries
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Cites Work

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• Central and local limit theorems for the coefficients of polynomials of binomial type
• Central and local limit theorems applied to asymptotic enumeration
• Moments of a class of discrete \(q\)-distributions
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• Upper Bounds and Asymptotics for the q‐Binomial Coefficients
• The q-deformed binomial distribution and its asymptotic behaviour
• On Solutions of x^d = 1 In Symmetric Groups

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