[R] How to compute a P-value for a complex mixture of chi-squared distributions in R
Terry Therneau
therneau at mayo.edu
Mon Jun 3 14:11:27 CEST 2013
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
>> >
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