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Log-Transform Kernel Density Estimation of Income Distribution

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Abstract

Standard kernel density estimation methods are very often used in practice to estimate density function. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

Suggested Citation

  • Arthur Charpentier & Emmanuel Flachaire, 2015. "Log-Transform Kernel Density Estimation of Income Distribution," AMSE Working Papers 1506, Aix-Marseille School of Economics, France.
  • Handle: RePEc:aim:wpaimx:1506
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    1. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
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    10. Bouezmarni, Taoufik & Scaillet, Olivier, 2005. "Consistency Of Asymmetric Kernel Density Estimators And Smoothed Histograms With Application To Income Data," Econometric Theory, Cambridge University Press, vol. 21(2), pages 390-412, April.
    11. Arthur Charpentier & Abder Oulidi, 2010. "Beta kernel quantile estimators of heavy-tailed loss distributions," Post-Print halshs-00425566, HAL.
    12. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    13. Ahamada, Ibrahim & Flachaire, Emmanuel, 2010. "Non-Parametric Econometrics," OUP Catalogue, Oxford University Press, number 9780199578009.
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    Cited by:

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    3. Edwin Fourrier-Nicolai & Michel Lubrano, 2021. "Bayesian Inference for Parametric Growth Incidence Curves," Working Papers halshs-03225236, HAL.
    4. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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    More about this item

    Keywords

    nonparametric density estimation; heavy-tail; income distribution; data transformation; lognormal kernel;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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