Fitting Skewed Distributions to Data: Estimation and Testing Problems
Tõnu Kollo
Institute of Mathematical Statistics, University of Tartu, Tartu, Estonia

In last 15 years many new possibilities have been introduced for modelling skewed multivariate data. The seminal paper on skewed elliptical distributions appeared in 1996 (Azzalini, Dalla Valle, 1996). Parallel to skewed elliptical families copula models became in use at the same time. An overview of the copula theory on introductory level can be found in Nelsen (1999). New distribution families brought in need for parameter estimation for fitting the models. Our main interest is concentrated to multivariate skew normal, skew t and asymmetric Laplace distributions. Construction of skew normal and skew t copulas and parameter estimation for these copulas will be considered either. Comparison o different models on real data will be presented.


Azzalini, A., Dalla Valle, A. (1996). The multivariate skew normal distribution. Biometrika 83 715-726.

Nelsen, R. B. (1999). An Introduction to Copulas. Springer-Verlag, New York.

Keywords: skew normal distribution; asymmetric Laplace distribution; skew t-distribution; skew elliptical copula

Biography: I am employd by the University of Tartu, Estonia, as a Professor of Mathematical Statistics. My main reasearch area is multivariate statistics with special emphasis on distribution theory. The results have been obtained using related matrix algebra. In recent years skewed multivariate distributions have been the main objects of interest.