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The Möbius distribution on the disc

Jones, M. C. (2004). The Möbius distribution on the disc. Annals of the Institute of Statistical Mathematics, 56(4) pp. 733–742.

URL: http://www.ism.ac.jp/editsec/aism/pdf/056_4_0733.p...
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Abstract

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely offcentredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.

Item Type: Journal Article
Copyright Holders: 2004 The Institute ofStatistical Mathematics
ISSN: 1572-9052
Keywords: beta distribution; bivariate distribution; circular law; Möbius transformation; Pearson type II distribution
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22595
Depositing User: Sarah Frain
Date Deposited: 17 Aug 2010 11:59
Last Modified: 28 Jan 2014 10:01
URI: http://oro.open.ac.uk/id/eprint/22595
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