Error bounds for asymptotic expansion of the scale mixtures of the normal distribution
type: Item
instance of: scholarly article
title: Error bounds for asymptotic expansion of the scale mixtures of the normal distribution
zbMATH Open document ID: 0638.62017
DOI: 10.1007/BF02491493
author: Ryoichi Shimizu
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let X be a standard normal random variable and let \(\sigma\) be a positive random variable independent of X. The distribution of \(\eta =\sigma X\) is expanded around that of N(0,1) and its error bounds are obtained. Bounds are given in terms of \(E(\sigma^ 2\vee \sigma^{-2}-1)^ k\), where \(\sigma^ 2\vee \sigma^{-2}\) denotes the maximum of the two quantities \(\sigma^ 2\) and \(\sigma^{-2}\), and k is a positive integer, and of \(E(\sigma^ 2-1)^ k\), if k is even.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 62E99
zbMATH DE Number: 4041035
zbMATH Keywords: scale mixtures of normal distributions
zbMATH Keywords: t-distribution
zbMATH Keywords: error bounds
MaRDI profile type: Publication
cites work: Laws of Large Numbers for Identically Distributed Banach-Space Valued Random Variables
cites work: Approximating IMRL distributions by exponential distributions, with applications to first passage times
cites work: An error bound for an asymptotic expansion of the distribution function of an estimate in a multivariate linear model
cites work: On measures of the distance of a mixture from its parent distribution
cites work: On moment measures of departure from the normal and exponential laws
cites work: Mixtures of distributions, moment inequalities and measures of exponentiality and normality
cites work: Inequalities for a distribution with monotone hazard rate
description: scientific article; zbMATH DE number 4041035