## Bayesian Analysis

### Flexible univariate continuous distributions

#### Abstract

Based on a constructive representation, which distinguishes between a skewing mechanism $P$ and an underlying symmetric distribution $F$, we introduce two flexible classes of distributions. They are generated by nonparametric modelling of either $P$ or $F$. We examine properties of these distributions and consider how they can help us to identify which aspects of the data are badly captured by simple symmetric distributions. Within a Bayesian framework, we investigate useful prior settings and conduct inference through MCMC methods. On the basis of simulated and real data examples, we make recommendations for the use of our models in practice. Our models perform well in the context of density estimation using the multimodal galaxy data and for regression modelling with data on the body mass index of athletes.

#### Article information

Source
Bayesian Anal., Volume 4, Number 3 (2009), 497-521.

Dates
First available in Project Euclid: 22 June 2012

https://projecteuclid.org/euclid.ba/1340369852

Digital Object Identifier
doi:10.1214/09-BA418

Mathematical Reviews number (MathSciNet)
MR2551043

Zentralblatt MATH identifier
1330.62078

#### Citation

Quintana, Fernando A.; Steel, Mark F. J.; Ferreira, José T. A. S. Flexible univariate continuous distributions. Bayesian Anal. 4 (2009), no. 3, 497--521. doi:10.1214/09-BA418. https://projecteuclid.org/euclid.ba/1340369852