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Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions
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Rubio, Francisco J. and Steel, Mark F. J. (2015) Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions. Electronic Journal of Statistics, 9 (2). pp. 1884-1912. doi:10.1214/15-EJS1060
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Official URL: http://dx.doi.org/10.1214/15-EJS1060
Abstract
We formalise and generalise the definition of the family of univariate double two–piece distributions, obtained by using a density–based transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | H Social Sciences > HA Statistics | ||||||||
| Divisions: | Faculty of Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory | ||||||||
| Journal or Publication Title: | Electronic Journal of Statistics | ||||||||
| Publisher: | Institute of Mathematical Statistics | ||||||||
| ISSN: | 1935-7524 | ||||||||
| Official Date: | 27 August 2015 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 13 January 2016 | ||||||||
| Volume: | 9 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 1884-1912 | ||||||||
| DOI: | 10.1214/15-EJS1060 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access |
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