TY - JOUR
T1 - A nonparametric method for estimating asymmetric densities based on skewed Birnbaum-Saunders distributions applied to environmental data
AU - Saulo, Helton
AU - Leiva, Víctor
AU - Ziegelmann, Flavio A.
AU - Marchant, Carolina
N1 - Funding Information:
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.
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
KW - Air pollutant data
KW - Kernel estimator
KW - Kurtosis
KW - Monte Carlo methods
KW - Statistical software
UR - http://www.scopus.com/inward/record.url?scp=84880078293&partnerID=8YFLogxK
U2 - 10.1007/s00477-012-0684-8
DO - 10.1007/s00477-012-0684-8
M3 - Article
AN - SCOPUS:84880078293
VL - 27
SP - 1479
EP - 1491
JO - Stochastic Environmental Research and Risk Assessment
JF - Stochastic Environmental Research and Risk Assessment
SN - 1436-3240
IS - 6
ER -