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Modelling income data using two extensions of the exponential distribution

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  • Calderín-Ojeda, Enrique
  • Azpitarte, Francisco
  • Gómez-Déniz, Emilio

Abstract

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 preserve 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 distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding 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 interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT–Lognormal models to study the distribution of incomes in Australia for the period 2001–2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.

Suggested Citation

  • Calderín-Ojeda, Enrique & Azpitarte, Francisco & Gómez-Déniz, Emilio, 2016. "Modelling income data using two extensions of the exponential distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 756-766.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:756-766
    DOI: 10.1016/j.physa.2016.06.047
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    References listed on IDEAS

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    1. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
    2. Benito Frosini, 2012. "Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures," Empirical Economics, Springer, vol. 43(1), pages 175-197, August.
    3. Mark Wooden & Nicole Watson, 2007. "The HILDA Survey and its Contribution to Economic and Social Research (So Far)," The Economic Record, The Economic Society of Australia, vol. 83(261), pages 208-231, June.
    4. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    5. F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787, arXiv.org, revised Dec 2012.
    6. A. Drăgulescu & V.M. Yakovenko, 2001. "Evidence for the exponential distribution of income in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 585-589, April.
    7. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
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    Cited by:

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    2. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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