# [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 20:52:45 CEST 2013

```Thank you very much, Rui and Peter, for you detailed and helpful tips!

It worked like a charm! I would spend more two weeks (or more) to figure
out that by myself.

Cheers!

Tiago

> Hello,
>
> No, nothing wrong. (I feel silly for not having noticed it.) In fact not
> only it's much simpler but it's also more accurate than the use of
> accurate with the default rel.tol.
> It should be better, however, to use lower.tail = FALSE, since the op
> wants p-values.
>
> 0.5 * pchisq(x^2, 1, lower.tail = FALSE) + 0.5 * pchisq(x^2, 2,
> lower.tail = FALSE)
>
>
> Em 01-06-2013 14:57, peter dalgaard escreveu:
>>
>> On Jun 1, 2013, at 06:32 , Tiago V. Pereira wrote:
>>
>>> 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?
>>
>> Er,...
>>
>> Anything wrong with
>>
>> 0.5 * pchisq(x^2, 1) + 0.5 * pchisq(x^2, 2)
>>
>> ???
>>
>> -pd
>>
>>
>>>
>>>
>>> All the best,
>>>
>>> Tiago
>>>
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