Electronic Journal of Statistics

Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions

F. J. Rubio and M. F. J. Steel

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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.

Article information

Electron. J. Statist., Volume 9, Number 2 (2015), 1884-1912.

Received: January 2015
First available in Project Euclid: 27 August 2015

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Zentralblatt MATH identifier

Primary: 62E99: None of the above, but in this section 62F15: Bayesian inference

Model comparison posterior existence prior elicitation scale mixtures of normals unimodal continuous distributions


Rubio, F. J.; Steel, M. F. J. Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions. Electron. J. Statist. 9 (2015), no. 2, 1884--1912. doi:10.1214/15-EJS1060. https://projecteuclid.org/euclid.ejs/1440680330

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