Monique Graf

Université de Neuchâtel


Compositional analysis of a mixture distribution with application to categorical modelling (Slides)

This is joint work with Desislava Nedyalkova, Statistical Methods Unit - Federal Statistical Office - Switzerland.
In econometrics and other areas, the necessity to account for lack of symmetry in the distribution of a quantity of interest is widely recognized. There are many different approaches to the problem. One way is to modify the usual normal or Student distribution by multiplying the density by a (normalized) cumulative distribution, giving rise to a skewed normal or skewed Student distribution, see Azzalini and Genton (2008). Another way is to model the tails of the distribution separately as e.g. Van Kerm (2007). A third approach that will be utilized here, is to fit a flexible enough parametric distribution that will account for lack of symmetry. We concentrate on continuous distributions, but the method could be easily applied to discrete distributions as well.
The principle is to make first a global fit to a distribution possessing the compounding property. Then we define a natural set of L component distributions from the global fit. The global fit can be reconstructed exactly as a mixture of these components. Finally, we adjust the mixture probabilities of the components using information about subgroups. The interpretation then makes use of compositional analysis tools.
The method is applied to different categories of households, using data from the European Union Statistics on Income and Living Conditions: the EU-SILC survey (2006) and the Swiss SILC survey (2009).
This research was partly supported by the FP7-SSH-2007-217322 AMELI Research Project.