| Library: | VaR |
| See also: | VaRcgfDGF2 |
| Quantlet: | VaRcharfDG | |
| Description: | computes the characteristic function for the class of quadratic forms of Gaussian vectors. |
| Usage: | r = VaRcharfDG(t,par) | |
| Input: | ||
| t | the complex argument to the cgf | |
| par | a list defining the distribution; contains at least the following components: theta - the constant term delta - the linear term lambda - the diagonal of the quadratic term | |
| Output: | ||
| r | the value of the cgf at t | |
library("plot")
library("VaR")
library("math")
proc() = VaRcharfDGtest(par,n,xlim)
dt =(xlim[2]-xlim[1])/(n-1)
t = xlim[1] +(0:(n-1))*dt
r = VaRcharfDG(complex(t,t*0),par)
z1 = setmask(t~r.re, "line", "blue")
z2 = setmask(t~r.im, "line", "red")
plot(z1,z2)
endp
theta = 0
delta = #(0)
lambda = #(1.4142)
par = list(theta,delta,lambda)
VaRcharfDGtest(par,300,#(-40,40))
Plots the real (blue line) and the imaginary part (red line) of the characteristic function for a distribution, which is close to a chi^2 distribution with one degree of freedom.