Error bounds for asymptotic expansion of the scale mixtures of the normal distribution

DOI10.1007/BF02491493zbMath0638.62017MaRDI QIDQ1099523

Ryoichi Shimizu

Publication date: 1987

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

error boundsscale mixtures of normal distributionst-distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Statistical distribution theory (62E99)

Related Items (6)

Non-uniform error bounds for asymptotic expansions of scale mixtures of distributions ⋮ Expansion of scale mixtures of the gamma distribution ⋮ Error bounds for asymptotic expansions of scale mixtures of univariate and multivariate distributions ⋮ Asymptotic expansions for the standardized and Studentized estimates in the growth curve model ⋮ Polynomial expansions of density of power mixtures ⋮ Exact bounds on the closeness between the Student and standard normal distributions

Cites Work

• Approximating IMRL distributions by exponential distributions, with applications to first passage times
• An error bound for an asymptotic expansion of the distribution function of an estimate in a multivariate linear model
• Inequalities for a distribution with monotone hazard rate
• Mixtures of distributions, moment inequalities and measures of exponentiality and normality
• On moment measures of departure from the normal and exponential laws
• On measures of the distance of a mixture from its parent distribution
• Laws of Large Numbers for Identically Distributed Banach-Space Valued Random Variables

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