Modelling income data using two extensions of the exponential distribution

In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT{Lognormal models discussed in this paper pre- serve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distribu- tions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for exclud- ing the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is in- terested in accurately describing the lower part of the distribution. We apply the EAT and the EAT{Lognormal models to study the dis- tribution of incomes in Australia for the period 2001{2012. We nd that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.