Mod-discrete expansions

DOI10.1007/s00440-013-0498-8zbMath1416.62131arXiv0912.1886OpenAlexW1989760896MaRDI QIDQ2447301

Ashkan Nikeghbali, Andrew David Barbour, Emmanuel Kowalski

Publication date: 25 April 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1886

zbMATH Keywords

characteristic functionsmod-Poisson convergenceErdős-Kac theoremPoisson-Charlier expansions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Combinatorial probability (60C05) Approximations to statistical distributions (nonasymptotic) (62E17) Distribution functions associated with additive and positive multiplicative functions (11N60)

Related Items (9)

The method of cumulants for the normal approximation ⋮ On closeness of two discrete weighted sums ⋮ Mod-\(\phi\) convergence: approximation of discrete measures and harmonic analysis on the torus ⋮ The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles ⋮ Mod-\( \phi\) convergence of Stirling distributions and limit theorems for zeros of their generating functions ⋮ \(r\)-Lah distribution: properties, limit theorems and an application to compressed sensing ⋮ Mod-ϕ Convergence, II: Estimates on the Speed of Convergence ⋮ Unnamed Item ⋮ Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks

Cites Work

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• Total variation asymptotics for sums of independent integer random variables
• Mod-Poisson Convergence in Probability and Number Theory
• On a theorem of Erdös-Kac
• Approximation of Binomial Distributions by Infinitely Divisible Ones
• Concentration Inequalities and Martingale Inequalities: A Survey
• Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations
• Asymptotics of poisson approximation to random discrete distributions: an analytic approach

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