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

[peter dalgaard]

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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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com