Discretizing a compound distribution with application to categorical modelling

Monique Graf & Desislava Nedyalkova

Résumé 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 define a partition of the domain of definition of the random parameters, so that we can represent the expected density of the variable of interest as a finite mixture of conditional densities. We then model the mixture probabilities of the conditional densities using information on population categories, thus modifying the original overall model. We thus obtain specific models for sub-populations that stem
from the overall model. The distribution of a sub-population of interest is thus completely specified in terms of mixing probabilities. All characteristics of interest can be derived from this distribution and the comparison between sub-populations easily proceeds from the comparison of the mixing probabilities. A real example based on EU-SILC data is given. Then the methodology is investigated through simulation.
Mots-clés KEYWORDS
GB2 distribution; mixture distribution; maximum pseudo-likelihood estimation; sandwich variance estimator; income distribution; inequality and poverty indicators; EU-SILC survey
Citation Graf, M., & Nedyalkova, D. (2017). Discretizing a compound distribution with application to categorical modelling. Statistics, 51(3), 685-710.
Type Article de périodique (Anglais)
Date de publication 17-2-2017
Nom du périodique Statistics
Volume 51
Numéro 3
Pages 685-710
Liée au projet Convention Université de Neuchâtel/Office fédéral de la s...