Thank you, Doug. I am still missing something here. Should this simply be sum(f(x_i) * w_i) where x_i is node i and w_i is the weight at node i? So, my function f(x) = (1/(s*sqrt(2*pi))) * exp(-((qq$nodes-mu)^2/(2*s^2))) would then be multiplied only by the weights, qq$weights
Here is some reproducible code: > library(statmod) > Q <- 5 > mu <- 0; s <- 1 > qq <- gauss.quad(Q, kind = 'hermite') > sum((1/(s*sqrt(2*pi))) * exp(-((qq$nodes-mu)^2/(2*s^2))) * qq$weights) [1] 0.5775682 > sum(qq$weights) [1] 1.772454 > (1/(s*sqrt(2*pi))) * exp(-((qq$nodes-mu)^2/(2*s^2))) [1] 0.05184442 0.25198918 0.39894228 0.25198918 0.05184442 > dnorm(qq$nodes) [1] 0.05184442 0.25198918 0.39894228 0.25198918 0.05184442 > -----Original Message----- > From: dmba...@gmail.com [mailto:dmba...@gmail.com] On Behalf Of Douglas Bates > Sent: Sunday, November 14, 2010 2:28 PM > To: Doran, Harold > Cc: r-help@r-project.org > Subject: Re: [R] Integrate to 1? (gauss.quad) > > I don't know about the statmod package and the gauss.quad function but > generally the definition of Gauss-Hermite quadrature is with respect > to the function that is multiplied by exp(-x^2) in the integrand. So > your example would reduce to summing the weights. > > On Sun, Nov 14, 2010 at 11:18 AM, Doran, Harold <hdo...@air.org> wrote: > > Does anyone see why my code does not integrate to 1? > > > > library(statmod) > > > > mu <- 0 > > s <- 1 > > Q <- 5 > > qq <- gauss.quad(Q, kind='hermite') > > sum((1/(s*sqrt(2*pi))) * exp(-((qq$nodes-mu)^2/(2*s^2))) * qq$weights) > > > > ### This does what's it is supposed to > > myNorm <- function(theta) (1/(s*sqrt(2*pi))) * exp(-((theta-mu)^2/(2*s^2))) > > integrate(myNorm, -Inf, Inf) > > ______________________________________________ > > 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. > > ______________________________________________ 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.