Products of normal, beta and gamma random variables: Stein operators and distributional theory

DOI10.1214/16-BJPS349zbMath1393.60020arXiv1507.07696MaRDI QIDQ1654337

Robert E. Gaunt

Publication date: 8 August 2018

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.07696

zbMATH Keywords

Stein's methodnormal distributiongamma distributionMeijer \(G\)-functionbeta distributiongeneralised gamma distributionproducts of random variables distribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items

Spatial Shrinkage Via the Product Independent Gaussian Process Prior ⋮ Stein’s method and the distribution of the product of zero mean correlated normal random variables ⋮ Stein's method for functions of multivariate normal random variables ⋮ Identifying the distribution of linear combinations of gamma random variables via Stein’s method ⋮ A probabilistic proof of some integral formulas involving the Meijer \(G\)-function ⋮ Unnamed Item ⋮ Stein operators for variables form the third and fourth Wiener chaoses ⋮ A bound on the Wasserstein-2 distance between linear combinations of independent random variables ⋮ Some new Stein operators for product distributions ⋮ An algebra of Stein operators ⋮ Stein characterizations for linear combinations of gamma random variables ⋮ On algebraic Stein operators for Gaussian polynomials ⋮ New error bounds for Laplace approximationviaStein’s method

Uses Software

• DLMF

Cites Work

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• Stein's method for comparison of univariate distributions
• Generalized gamma approximation with rates for urns, walks and trees
• On the rate of convergence in the multivariate CLT
• Stein's method on Wiener chaos
• Stein's method of exchangeable pairs for the Beta distribution and generalizations
• Malliavin-Stein method for variance-gamma approximation on Wiener space
• Beta-gamma tail asymptotics
• Tail asymptotics under beta random scaling
• Stein's method for diffusion approximations
• Poisson approximation for dependent trials
• Closed form summation for classical distributions: variations on a theme of de Moivre
• Distributional transformations, orthogonal polynomials, and Stein characterizations
• Degree asymptotics with rates for preferential attachment random graphs
• Chi-square approximation by Stein's method with application to Pearson's statistic
• On Stein's method for products of normal random variables and zero bias couplings
• New rates for exponential approximation and the theorems of Rényi and Yaglom
• Variance-gamma approximation via Stein's method
• On the product and ratio of gamma and beta random variables
• The special functions and their approximations. Vol. I, II
• Large-scale behavior of the partial duplication random graph
• Uniform bounds for expressions involving modified Bessel functions
• Stein's method and the Laplace distribution
• A Stein characterisation of the generalized hyperbolic distribution
• Stein's method for the half-normal distribution with applications to limit theorems related to the simple symmetric random walk
• Stein's Method for the Beta Distribution and the Pólya-Eggenberger Urn
• The Distribution of Products of Independent Random Variables
• Exact Distribution of the Product of Independent Generalized Gamma Variables with the Same Shape Parameter
• The Distribution of Products of Beta, Gamma and Gaussian Random Variables
• Some Applications of the Mellin Transform in Statistics
• Orthogonal polynomials in Stein's method