Discretizing a compound distribution with application to categorical modelling. Part I: Methods

Many probability distributions can be represented as compound distributions. Consider some parameter vector as random. The compound distribution is the expected distribution of the variable of interest given the random parameters. Our idea is to de_ne a partition of the domain of de_nition of the random parameters, so that we can represent the expected density of the variable of interest as a _nite mixture of conditional densities. We then model the probabilities of the conditional densities using information on population categories, thus modifying the original overall model. Our examples uses the European Union Statistics on Income and Living Conditions (EU-SILC) data. For each country, we estimate a mixture model derived from the GB2 in which the probability weights are predicted with household categories. Comparisons across countries are processed using compositional data analysis tools. Our method also o_ers an indirect estimation of inequality and poverty indices.