Skewed distributions generated by the Student's t kernel
Copyright policy )Skewed distributions generated by the Student's t kernel
Summary: Following \textit{A. K. Gupta, F.-C. Chang} and \textit{W. J. Huang} [Some skew-symmetric models. Random Oper. Stoch. Equ. 10, No. 2, 133--140 (2002; Zbl 1118.60300)], we construct skew pdfs of the form \(2f(u)G(\lambda u)\), where \(f\) is taken to be a Student's \(t\) pdf while the cdf \(G\) is taken to come from one of the normal, Student's \(t\), Cauchy, Laplace, logistic or uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the \(n\)\,th moment and the characteristic function are derived. We also provide graphical illustrations and quantifications of the range of possible values of skewness and kurtosis.
characteristic function, Characteristic functions; other transforms, moments, Exact distribution theory in statistics, Multivariate distribution of statistics, Student's \(t\) distribution
characteristic function, Characteristic functions; other transforms, moments, Exact distribution theory in statistics, Multivariate distribution of statistics, Student's \(t\) distribution
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