[R] How to compute a P-value for a complex mixture of chi-squared distributions in R

[Tiago V. Pereira]

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