Thanks so much for your response. BTW, do you know any Gauss quadrature R package can deal with the arbitary PDF?
Thank you! David 2013/10/11 Spencer Graves <spencer.gra...@structuremonitoring.com> > p.s. Orthogonal polynomials can be defined for any probability > distribution on the real line, discrete, continuous, or otherwise, as > described in the Wikipedia article on "orthogonal polynomials". > > > On 10/10/2013 5:02 PM, Marino David wrote: > > Hi all, > > We know that Hermite polynomial is for > Gaussian, Laguerre polynomial for Exponential > distribution, Legendre polynomial for uniform > distribution, Jacobi polynomial for Beta distribution. Does anyone know > which kind of polynomial deals with the log-normal, > > > > * lognormal in X is normal for Z = log(X). Therefore, you'd use > Hermite polynomials in Z. > > > StudentÂ’s t, Inverse > gamma and FisherÂ’s F distribution? > > > > * If X follows an F(d1, d2) distribution, then Z = d1*x/(x1*x+d2) > follows a beta distribution. Use Jacobi polynomials on Z. > > > * If X follows a student's t(df), then X^2 follows an F(1, df) > distribution. Again, use Jacobi on the appropriate transform. > > > * If X follows an inverse gamma, then 1/X follows a gamma > distribution. > > > Does this answer the question? > > > Spencer > > Thank you in advance! > > David > > [[alternative HTML version deleted]] > > > > > ______________________________________________r-h...@r-project.org mailing > listhttps://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. > > > > [[alternative HTML version deleted]]
______________________________________________ R-help@r-project.org 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.
