Re: [patch #5583] NPAR TESTS

[John Darrington]

On Mon, Dec 18, 2006 at 11:52:27AM -0500, Jason Stover wrote:
     On Sun, Dec 17, 2006 at 01:47:29PM +0900, John Darrington wrote:
     > On Sat, Dec 16, 2006 at 10:27:01PM +0000, Jason H Stover wrote:
     >      
     >      I would use the exact result until the sample size grows enough to 
cause
     >      overflows. 
     > 
     > OK.  Any ideas how large such a sample would be ?
     
     I would have to look at this closely to decide, but after some initial
     thought, I would say: Large enough that we should just use
     gsl_cdf_binomial_[PQ] always. gsl_cdf_binomial_[PQ] use a
     gamma-function reparameterization to the binomial distribution, which
     means they don't compute the summation of the binomial mass function
     to compute the binomial CDF. 

So the complexity is independent of the sample size?  That's good.

     The problem with the exact computations
     is usually overflow due to small values of the mass function. Since
     gsl_cdf_binomial_[PQ] cicumvent this by reparamaterizing with the
     gamma function, my guess is that there is no need for an asymptotic
     approximation.
     
     I can run some tests to look for a threshold at which pspp should use 
     an approximation, but I'm certain it's going to be large enough to be
     almost, and possibly never, necessary with IEEE 754 arithmetic. Because of
     that, I'd recommend checking in the NPAR procedure with the gsl
     functions. 

That would certainly make the code and the tests simpler.

J'
     

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