Jones, M. C.
(2008).
| DOI (Digital Object Identifier) Link: | http://doi.org/10.1016/j.jkss.2008.06.002 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
Student’s t distribution arose as a normal-based sampling distribution and has huge application as such. In modern times, the t distribution has also found considerable use as a symmetric heavy-tailed distribution for empirical data modelling. In this the centenary year of Student’s introduction of the t distribution, this paper constitutes a personal–and sometimes somewhat tangential–tribute to the Student-t family of distributions, by way of an exploration of some of its close and not-so-close relations. I start with a brief reminder of the (symmetric) Student-t family, with particular focus on the t distribution on two degrees of freedom which turns out to play an important role in what follows. The “close relations” of the t distribution include a number of ‘skew-t’ distributions, of which I shall briefly introduce and comment on three. The “distant relations” of the t distribution are a further trio of four-parameter families of distributions allowing control of skewness and tailweights, with particular emphasis on members of the families with (t-like) ‘power’ density tails.
| Item Type: | Journal Article |
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| ISSN: | 1226-3192 |
| Keywords: | exponential tails; heavy-tailed distribution; order statistics; power tails; sinh–arcsinh; skew-t distribution; student |
| Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 17667 |
| Depositing User: | Colin Smith |
| Date Deposited: | 09 Jul 2009 11:21 |
| Last Modified: | 02 Aug 2016 13:30 |
| URI: | http://oro.open.ac.uk/id/eprint/17667 |
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