Enriched Lognormal Models for Income Data

As an important indicator of social well-being, a comprehensive understanding of the distribution of population income for policy makers to mitigate harmful social and economic effects is essential. The lognormal distribution is often considered as the model of choice for the modelling of income data. We make use of this model in a data-enriched way to explore an income data set by incorporating a regression function within the model. This regression function serves as the component of the dependency between the response variable (income) and a covariate. A finite mixture enriched lognormal for the response variable is also considered for a particular income data set presenting bimodality or a dynamic change after a certain value. Furthermore, we present a novel extension where the data-enrichment component is incorporated into the conditional mode parameterized lognormal model. A simulation study illustrates the performance of the approach and the value added by this different perspective and implementation. The findings emphasize that this approach can successfully be considered in practice for health and socio-economic data scenarios, amongst others.