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On a class of distributions with simple exponential tails

Jones, M. C. (2008). On a class of distributions with simple exponential tails. Statistica Sinica, 18(3) pp. 1101–1110.

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A simple general construction is put forward which covers many unimodal univariate distributions with simple exponentially decaying tails (e.g. asymmetric Laplace, log F and hyperbolic distributions as well as many new models). The proposed family is a special subset of a regular exponential family, and many properties flow therefrom. Two main practical points are made in the context of maximum likelihood fitting of these distributions to data. The first of these is that three, rather than an apparent four, parameters of the distributions suffice. The second is that maximum likelihood estimation of location in the new distributions is precisely equivalent to a standard form of kernel quantile estimation, choice of kernel being equivalent to specific choice of model within the class. This leads to a maximum likelihood method for bandwidth selection in kernel quantile estimation, but its practical performance is shown to be somewhat mixed. Further distribution theoretical aspects are also pursued, particularly distributions related to the main construction as special cases, limiting cases or by simple transformation.

Item Type: Journal Article
Copyright Holders: 2008 Institute of Statistical Science, Academia Sinica
ISSN: 1017-0405
Keywords: asymmetric Laplace distribution; bandwidth selection; exponential family; hyperbolic distribution; kernel quantile estimation; log f distribution; maximum likelihood
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22527
Depositing User: Sarah Frain
Date Deposited: 18 Aug 2010 11:55
Last Modified: 06 Dec 2010 20:28
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