Bimodal extension based on the skew-normal distribution with application to pollen data
Article first published online: 11 SEP 2009
Copyright © 2009 John Wiley & Sons, Ltd.
Volume 22, Issue 1, pages 50–62, February 2011
How to Cite
Gómez, H. W., Elal-Olivero, D., Salinas, H. S. and Bolfarine, H. (2011), Bimodal extension based on the skew-normal distribution with application to pollen data. Environmetrics, 22: 50–62. doi: 10.1002/env.1026
- Issue published online: 11 SEP 2009
- Article first published online: 11 SEP 2009
- Manuscript Accepted: 19 JUL 2009
- Manuscript Received: 17 JUL 2008
- FONDECYT 1060727 | 7070074
- maximum likelihood estimation;
- singular information matrix
This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright © 2009 John Wiley & Sons, Ltd.