Domains of attraction for exponential families.

DOI10.1016/S0304-4149(03)00060-7zbMath1075.60502MaRDI QIDQ2574590

August A. Balkema, Sidney I. Resnick, Claudia Klüppelberg

Publication date: 29 November 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

asymptotic normalitynormal distributiongamma distributionEsscher transformself-neglectingconvex conjugatestrong unimodality

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05) Laplace transform (44A10)

Related Items (7)

Domains of attraction to Tweedie distributions ⋮ Natural selection as coarsening ⋮ On the Asymptotic Behaviour of Superexponential Lévy Processes ⋮ On lower tail probabilities of positive random sums ⋮ Limiting fitness distributions in evolutionary dynamics ⋮ Tail asymptotics of light-tailed Weibull-like sums ⋮ Limiting saddlepoint relative errors in large deviation regions under purely Tauberian conditions

Cites Work

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• Convolution tails, product tails and domains of attraction
• A note on the tail accuracy of the univariate saddlepoint approximation
• A classification of reproducible natural exponential families in the broad sense
• Limit laws for exponential families
• Uniform saddlepoint approximations
• Densities with Gaussian Tails
• On a strong Tauberian result
• Tauberian Results for Densities with Gaussian Tails
• Tail Exactness of Multivariate Saddlepoint Approximations
• Saddlepoint Approximations in Statistics

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