| title: | Multivariate Skewed Distributions: Theory and Applications |
|---|---|
| reg no: | ETF5686 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.2. Applied Mathematics |
| status: | accepted |
| institution: | TU Faculty of Mathematics |
| head of project: | Tõnu Kollo |
| duration: | 01.01.2004 - 31.12.2007 |
| description: | The main task of the project is investigation and characterization of multivariate skewed distributions. The first distribution of interest is the multivariate skew normal distribution which was introduced by Azzalini and co-authors (Azzalini, Dalla Valle (1996), Azzalini, Capitanio (1999)). One of the most complicated problem has been estimation of the shape parameter of the skew normal distribution. Classical methods can give wrong estimates of the parameter. Our aim is to modify the existing estimation methods and apply the distribution in models of multivariate analysis and describe distribution of test-statistics in the models. The idea of defining skew normal distribution has been carried over to other distributions. Several results have been obtained on elliptical skewed distributions. It is possible to get the distribution with heavier tails in this case, but the parameter estimation is more complicated. Our aim is to find parameter estimates and main characteristics for different subclasses of skewed elliptical distributions. For geometric stable distributions and Laplace distributions the estimation can be based on the characteristic function. Beside parameter estimation we shall examine distributions of test-statistics for classical tests about the mean and the dispersion matrix. We are going to apply these distributions for modelling financial data. The last circle of problems is related to finding skewness and kurtosis characteristics and their properties for different classes of distributions. We are going to use the characteristics in estimation as well as in testing problems about the shape of different distributions. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Tõnu Kollo | TU Faculty of Mathematics | professor | |
| 2. | Tatjana Nahtman | TÜ MSI | teadur | |
| 3. | Anne-Mai Parring | TÜ MSI | dotsent | |
| 4. | Margus Pihlak | TÜ MSI | insener, doktorant | |
| 5. | Anne Selart | TÜ MSI | doktorant | |
| 6. | Marek Tuul | TÜ MSI | doktorant | |