Logistic Normal Distribution
 John Hinde
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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 ...
 Agresti A (2002) Categorical data analysis, 2nd edn. Wiley, New York
 Aitchison J (1982) The statistical analysis of compositional data (with discussion). J R Stat Soc Ser B 44:139–177
 Aitchison J (1986) The statistical analysis of compositional data. Chapman & Hall, London
 Aitchison J, Begg CB (1976) Statistical diagnosis when basic cases are not classified with certainty. Biometrika 63:1–12 CrossRef
 Aitchison J, Shen SM (1980) Logisticnormal distributions: some properties and uses. Biometrika 67:261–272 CrossRef
 McCulloch CE, Searle SR (2001) Generalized, linear and mixed models. Wiley, New York
 Williams D (1982) Extrabinomial variation in logistic linearmodels. Appl Stat 31:144–148 CrossRef
 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
 Topics
 eBook Packages
 Editors

 Miodrag Lovric ^{(620)}
 Editor Affiliations

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

 John Hinde ^{(1)}
 Author Affiliations

 1. National University of Ireland, Galway, Ireland
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