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

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1440680330

Digital Object Identifier
doi:10.1214/15-EJS1060

Mathematical Reviews number (MathSciNet)
MR3391123

Zentralblatt MATH identifier
1331.62090

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

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

Citation

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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