[R] How to compute a P-value for a complex mixture of chi-squared distributions in R
Tiago V. Pereira
tiago.pereira at mbe.bio.br
Sat Jun 1 06:32:22 CEST 2013
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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