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integral
2007 Jan 19
3
integrate and quadratic forms
...rically invert the characteristic function
of a quadratic form following Imhof's (1961, Biometrika 48)
procedure.
The parameters are:
lambda=c(.6,.3,.1)
h=c(2,2,2)
sigma=c(0,0,0)
q=3
I've implemented Imhof's procedure two ways that, for me,
should give the same answer:
#more legible
integral1 = function(u) {
o=(1/2)*sum(h*atan(lambda*u)+sigma^2*lambda*u/(1+lambda^2*u^2)) - q*u/2
rho=prod((1+lambda^2*u^2)^(h/4))*exp( (1/2)*sum((sigma*lambda*u)^2/(1+lambda^2*u^2)) )
integrand = sin(o)/(u*rho)
}
#same as above
integral2= function(u) {
((1/2)*sum(h*atan(lambda*u)+sigma^2*lambda*u/(1...