The theory of concentrated Langevin distributions

Geoffrey S. Watson

Journal of Multivariate Analysis, 1984, vol. 14, issue 1, 74-82

Abstract: The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp ?[mu]'x, where x and the modal vector [mu] are unit vectors in q. ? (>=0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when ?1,...,?m are known but tend to infinity, and are unknown but equal to ? which tends to infinity. The three null hypotheses are H01:[mu] = [mu]0(m=1), H02:[mu]1= ... =[mu]m, H03:[mu]i [epsilon] V, I=1,...,m In each case a sequence of alternatives is taken tending to the null hypothesis.

Keywords: Directional; data; Langevin; distribution; Fisher-von; Mises; distribution; hypothesis; tests; estimates; multivariate; Gaussian; distribution; non-central; chi-square; distribution; non-central; F; distribution (search for similar items in EconPapers)
Date: 1984
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(84)90047-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:14:y:1984:i:1:p:74-82

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().