Skew-symmetric distributions generated by the distribution function of the normal distribution
Version of Record online: 17 NOV 2006
Copyright © 2006 John Wiley & Sons, Ltd.
Volume 18, Issue 4, pages 395–407, June 2007
How to Cite
Gómez, H. W., Venegas, O. and Bolfarine, H. (2007), Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics, 18: 395–407. doi: 10.1002/env.817
- Issue online: 27 APR 2007
- Version of Record online: 17 NOV 2006
- Manuscript Accepted: 16 AUG 2006
- Manuscript Received: 17 JUL 2006
- FONDECYT. Grant Number: 1060727
- Fisher information;
- skew-symmetric distributions
In this paper we study a general family of skew-symmetric distributions which are generated by the cumulative distribution of the normal distribution. For some distributions, moments are computed which allows computing asymmetry and kurtosis coefficients. It is shown that the range for asymmetry and kurtosis parameters is wider than for the family of models introduced by Nadarajah and Kotz (2003). For the skew-t-normal model, we discuss approaches for obtaining maximum likelihood estimators and derive the Fisher information matrix, discussing some of its properties and special cases. We report results of an application to a real data set related to nickel concentration in soil samples. Copyright © 2006 John Wiley & Sons, Ltd.