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 <HDoran at 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)
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