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

Helton Saulo, VICTOR ELISEO LEIVA SANCHEZ, Flavio A. Ziegelmann, Carolina Marchant

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49 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1479-1491
Number of pages13
JournalStochastic Environmental Research and Risk Assessment
Volume27
Issue number6
DOIs
StatePublished - 1 Aug 2013

Keywords

  • Air pollutant data
  • Kernel estimator
  • Kurtosis
  • Monte Carlo methods
  • Statistical software

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