Hello,
Try the following.
dmix <- function(x){
dens <- function(x, df) dchisq(x^2, df = df)*2*x
0.5*dens(x, df = 1) + 0.5*dens(x, df = 2)
}
pmix <- function(x, lower.tail = TRUE){
p <- integrate(dmix, lower = 0, upper = x)
if(lower.tail) p$value else 1 - p$value
}
quant <- 1
pmix(quant, lower.tail = FALSE)
Hope this helps,
Rui Barradas
Em 01-06-2013 05:26, Tiago V. Pereira escreveu:
Hello, R users!
I am struggling with the following problem:
I need to compute a P-value for a mixture of two chi-squared
distributions. My P-value is given by:
P = 0.5*prob(sqrt(chi2(1)) <= x) + 0.5*prob(sqrt(chi2(2)) <= x)
In words, I need to compute the p-value for 50–50 mixture of the square
root of a chi-squared random variable with 1 degree of freedom and the
square root of a chi-squared with two degrees of freedom.
Although I can quickly simulate data, the P-values I am looking for are at
the tail of the distribution, that is, alpha levels below 10^-7. Hence,
simulation is not efficient.
Are you aware of smart approach?
All the best,
Tiago
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