Business Analytics

An Alternative Class of Skew Distributions and Parametric Quantile Regression Models?

Nuttanan (Nate) Wichitaksorn, University of Sydney Business School

3rd Aug 2012  11:00 am - Room 489 Merewether Building (H04)

This paper proposes a method to construct a univariate skew distribution
through the mixture of two scaled normal distributions. As a result, we obtain
an alternative class of skew distributions where the skewness parameter value is defined in the ]0,1[ interval and this allows us to have an application on parametric quantile regression. By expressing a skew distribution as a scale mixture of normal, it can facilitate a flexible parameter estimation procedure via the Bayesian Markov Chain Monte Carlo methods. In addition, the proposed distribution has a closed-form probability density function and we can perform statistical inference via likelihood-based approaches such as maximum likelihood. The performance of the proposed distributions is demonstrated in two simulation studies on (i) regression models with skewed error distribution and (ii) parametric quantile regression models. In empirical studies, we analyse the U.S. market return data for skew error regression and the U.S. infant birthweight data for parametric quantile regression.