A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data

  • Helton Saulo
  • Víctor Leiva
  • Flavio A. Ziegelmann
  • Carolina Marchant
Original Paper


In this paper, we introduce a new nonparametric kernel method for estimating asymmetric densities based on generalized skew-Birnbaum–Saunders distributions. Kernels based on these distributions have the advantage of providing flexibility in the asymmetry and kurtosis levels. In addition, the generalized skew-Birnbaum–Saunders kernel density estimators are boundary bias free and achieve the optimal rate of convergence for the mean integrated squared error of the nonnegative asymmetric kernel estimators. We carry out a data analysis consisting of two parts. First, we conduct a Monte Carlo simulation study for evaluating the performance of the proposed method. Second, we use this method for estimating the density of three real air pollutant concentration data sets. These numerical results favor the proposed nonparametric estimators.


Air pollutant data Kernel estimator Kurtosis Monte Carlo methods Statistical software 



The authors wish to thank the Editor-in-Chief, Prof. George Christakos, an anonymous Associate Editor, and two anonymous referees for their comments on an earlier version of this manuscript, which resulted in this improved version. H. Saulo gratefully acknowledges financial support from CAPES. The research of V. Leiva was partially supported by grants FONDECYT 1090265 and 1120879 from the Chilean government.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Helton Saulo
    • 1
  • Víctor Leiva
    • 2
  • Flavio A. Ziegelmann
    • 3
  • Carolina Marchant
    • 2
  1. 1.Departamento de EconomiaUniversidade Federal do Rio Grande do Sul Porto AlegreBrazil
  2. 2.Departamento de EstadísticaUniversidad de ValparaísoValparaisoChile
  3. 3.Departamento de Estatística, PPGE and PPGAUniversidade Federal do Rio Grande do Sul Porto AlegreBrazil

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