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Modelling income data using two extensions of the exponential distribution

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journal contribution
posted on 14.01.2019 by Enrique Calderin-Ojeda, Fran Azpitarte, Emilio Gomez-Deniz
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.


This paper uses confidentialized unit record file data from the HILDA Survey. The HILDA Survey Project was initiated and is funded by the Department of Social Services (DSS) and is managed by the Melbourne Institute of Applied Economic and Social Research. This research was supported by the Australian Research Council Centre of Excellence for Children and Families over the Life Course (project number CE140100027). Enrique and Emilio are funded by the grant ECO2013-47092 (Ministerio de Econom´ıa y Competitividad, Spain). Francisco gratefully acknowledges financial support from the Ministerio de Econom´ıa y Competitividad (ECO2011-23460, ECO2013-46516-C4-2-R, ECO2014-52616-R).



  • Social Sciences


  • Communication, Media, Social and Policy Studies

Published in

Physica A: Statistical Mechanics and its Applications




756 - 766


CALDERIN-OJEDA, E., AZPITARTE, F. and GOMEZ-DENIZ, E., 2016. Modelling income data using two extensions of the exponential distribution. Physica A: Statistical Mechanics and its Applications, 461, pp. 756 - 766.


© Elsevier


AM (Accepted Manuscript)

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This paper was accepted for publication in the journal Physica A: Statistical Mechanics and its Applications and the definitive published version is available at