International Encyclopedia of Statistical Science
pp 754755
Logistic Normal Distribution
 John HindeAffiliated withNational University of Ireland
The logisticnormal distribution arises by assuming that the logit (or logistic transformation) of a proportion has a normal distribution, with an obvious extension to a vector of proportions through taking a logistic transformation of a multivariate normal distribution, see Aitchison and Shen (1980). In the univariate case, this provides a family of distributions on (0, 1) that is distinct from the beta distribution, while the multivariate version is an alternative to the Dirichlet distribution. Note that in the multivariate case there is no unique way to define the set of logits for the multinomial proportions (just as in multinomial logit models, see Agresti 2002) and different formulations may be appropriate in particular applications (Aitchison 1982). The univariate distribution has been used, often implicitly, in random effects models for binary data and the multivariate version was pioneered by Aitchison for statistical diagnosis/discrimination (Aitchison and Begg 1976), the Bay ...
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 Title
 Logistic Normal Distribution
 Reference Work Title
 International Encyclopedia of Statistical Science
 Pages
 pp 754755
 Copyright
 2011
 DOI
 10.1007/9783642048982_342
 Print ISBN
 9783642048975
 Online ISBN
 9783642048982
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Miodrag Lovric ^{(620)}
 Editor Affiliations

 620. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac
 Authors

 John Hinde ^{(1216)}
 Author Affiliations

 1216. National University of Ireland, Galway, Ireland
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