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

[Terry Therneau]

You need to be more explicit about what you are doing.
For this problem:
     y = (x1 + x2)/2
where x1 and x2 are chi-square random variables, you want to use the pchisqsum() routine 
found in the survey package.  This is not a trivial computation.

For the alternate problem where y is a random choice of either x1 or x2
     y = ifelse(z, x1, x2)
z is binomial and x1, x2 are chisq, then the suggestion by Peter Dalgaard is correct.

Which of these two are you trying to solve?

Terry Therneau


On 06/02/2013 05:00 AM, r-help-request at r-project.org wrote:
> 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
>> >