An expansion in the exponent for compound binomial approximations

DOI10.1007/s10986-006-0013-3zbMath1136.62019OpenAlexW2098298292MaRDI QIDQ926640

Vydas Čekanavičius, Bero Roos

Publication date: 20 May 2008

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-006-0013-3

zbMATH Keywords

sharp constantscompound Poisson distributiontotal-variation normKolmogorov normsymmetric distributionscompound binomial distributionconcentration normshifted distributions

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Approximations to statistical distributions (nonasymptotic) (62E17)

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A Pólya Approximation to the Poisson-Binomial Law ⋮ Compound Poisson approximation ⋮ A shorter proof of Kanter's Bessel function concentration bound ⋮ Closeness of convolutions of probability measures ⋮ Compound Poisson approximations for sums of 1-dependent random variables. I ⋮ On exceedances of high levels ⋮ Signed binomial approximation of binomial mixtures via differential calculus for linear opera\-tors ⋮ Refined total variation bounds in the multivariate and compound Poisson approximation ⋮ Compound Poisson approximation to weighted sums of symmetric discrete variables ⋮ On the accuracy of Poisson approximation ⋮ Binomial approximation to the Markov binomial distribution ⋮ Compound Poisson approximation to convolutions of compound negative binomial variables ⋮ Convergence Rate Estimates in the Global CLT for Compound Mixed Poisson Distributions

Cites Work

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• Binomial approximation to the Poisson binomial distribution
• Asymptotic methods in statistical decision theory
• Precision of approximation of the generalized binomial distribution by convolutions of Poisson measures
• Asymptotic expansions for generalized Poisson measures
• On a class of approximative computation methods in the individual risk model
• Compound Poisson approximation: A user's guide
• Pseudo-Poisson approximation for Markov chains
• On smoothing properties of compound Poisson distributions
• Two-parametric compound binomial approximations.
• On Hipp's compound Poisson approximations via concentration functions
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• Binomial Approximation to the Poisson Binomial Distribution: The Krawtchouk Expansion
• An Estimate for Concentration Functions
• Approximation of Binomial Distributions by Infinitely Divisible Ones
• Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson Law
• On the Rate of Approach of the Distributions of Sums of Independent Random Variables to Accompanying Distributions
• Approximation of a Generalized Binomial Distribution
• Poisson perturbations
• Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution
• Asymptotic Expansions in the Exponent: a Compound Poisson Approach
• On the Minimal Condition of Weak Dependency in the Central Limit Theorem for Stationary Sequences
• Sharp constants in the Poisson approximation