Flexible Class of Skew-Symmetric Distributions


Yanyuan Ma, CRSC, North Carolina State University, Box 8205, Raleigh, NC 27695-8205, USA.
E-mail: yma@unity.ncsu.edu


Abstract.  We propose a flexible class of skew-symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills data.