Large sample theory of the Langevin distribution
type: Item
instance of: scholarly article
title: Large sample theory of the Langevin distribution
zbMATH Open document ID: 0539.62033
DOI: 10.1016/0378-3758(83)90043-5
author: Geoffrey S. Watson
published in: Journal of Statistical Planning and Inference
publication date: 1983-01-01T00:00:00Z
review text: A random vector x on a unit sphere \(S_ q\) is said to have the Langevin (or von Mises-Fisher) distribution, if the density function with respect to Lebesgue measure on \(S_ q\) is given by \(a_ q(\kappa)^{- 1}\exp(\kappa \mu^ tx)\) where \(\mu^ t\mu =\| \mu \|^ 2=1\) and \(\kappa\geq 0\). \(\mu\) is the modal vector and \(\kappa\) is a concentration parameter. In this paper estimation and testing problems for \(\mu\) and \(\kappa\) are discussed. Asymptotic non-null distributions of test statistics are given and methods of checking the goodness of fit of the Langevin distribution for large samples are demonstrated.
reviewed by: Nariaki Sugiura
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3858178
zbMATH Keywords: directional data
zbMATH Keywords: von Mises-Fisher distribution
zbMATH Keywords: noncentral chi-square distribution
zbMATH Keywords: Asymptotic non-null distributions
zbMATH Keywords: Langevin distribution
MaRDI profile type: Publication
full work available at URL: 0378-3758(83)90043-5
OpenAlex ID: W2046904806
cites work: Q5656211
cites work: Q5663240
cites work: Estimation of the concentration parameter in von Mises-Fisher distributions
cites work: More significance tests on the sphere
cites work: Three aspects of the statistics of directions
cites work: Q3321248
cites work: ON THE CONSTRUCTION OF SIGNIFICANCE TESTS ON THE CIRCLE AND THE SPHERE
Wikidata QID: Q126458372
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description: scientific article; zbMATH DE number 3858178