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Skew‐symmetric distributions generated by the distribution function of the normal distribution
Author(s) -
Gómez Héctor W.,
Venegas Osvaldo,
Bolfarine Heleno
Publication year - 2007
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.817
Subject(s) - kurtosis , skew , mathematics , estimator , asymmetry , range (aeronautics) , distribution (mathematics) , maximum likelihood , fisher information , skew normal distribution , statistics , econometrics , statistical physics , mathematical analysis , computer science , physics , telecommunications , materials science , quantum mechanics , composite material
In this paper we study a general family of skew‐symmetric distributions which are generated by the cumulative distribution of the normal distribution. For some distributions, moments are computed which allows computing asymmetry and kurtosis coefficients. It is shown that the range for asymmetry and kurtosis parameters is wider than for the family of models introduced by Nadarajah and Kotz (2003). For the skew‐ t ‐normal model, we discuss approaches for obtaining maximum likelihood estimators and derive the Fisher information matrix, discussing some of its properties and special cases. We report results of an application to a real data set related to nickel concentration in soil samples. Copyright © 2006 John Wiley & Sons, Ltd.