Jones, M. C.
PDF (Accepted Manuscript)
- Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
|Google Scholar:||Look up in Google Scholar|
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|
|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
Mathematics, Computing and Technology
|Depositing User:||Sarah Frain|
|Date Deposited:||18 Aug 2010 11:55|
|Last Modified:||25 Feb 2016 13:46|
|Share this page:|
Download history for this item
These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.