hello users of the SN package,
i thought i post here some useful help on R code on the 4 moments for the skew t sampling gives seldom good results for skewness and kurtosis, so one really needs the analytical results, it took me some time to get it from the article Azzalini, A. & Capitanio, A. (2003), Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. hope it is one day useful for someone else too. bye luc # computing analytical moments for skew t of azzalini xi=location; alpha=shape; omega=sd(X); delta=alpha/sqrt(1+alpha^2); mu=delta*sqrt(df/pi)*gamma(0.5*(df-1))/gamma(0.5*df); # the 4 first moments moment1=xi+omega*mu; moment2=xi^2 + 2*omega*mu*xi + omega^2 * df/(df-2); moment3=xi^3 + 3*omega*mu*xi^2 + 3*omega^2*df/(df-2)*xi + omega^3*mu*(3-delta^2)*df/(df-3); moment4=xi^4 + 4*omega*mu*xi^3 + 6*omega^2*df/(df-2)*xi^2 + 4*omega^3*mu*(3-delta^2)*df/(df-3)*xi+omega^4*3*df^2/((df-2)*(df-4)); # the 4 useful measures mean=moment1; var=moment2; skew=moment3/var^(3/2); kurt=moment4/var^2 - 3; ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
