Skewed distributions generated by the normal kernel

Saralees Nadarajah and Samuel Kotz

Statistics & Probability Letters, 2003, vol. 65, issue 3, 269-277

Abstract: Following the recent paper by Gupta et al. (Some skew-symmetric models. Random Operators Stochastic Equations 10 (2002) 133) we generate skew probability density functions (pdfs) of the form 2f(u)G([lambda]u), where f is taken to be a normal pdf while the cumulative distributive function G is taken to come from one of normal, Student's t, Cauchy, Laplace, logistic or uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the nth moment and the characteristic function are derived. We also provide graphical illustrations and quantify the range of possible values of skewness and kurtosis.

Date: 2003
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