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st: Stirling's approximation


From   David Greenberg <dg4@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Stirling's approximation
Date   Fri, 06 Feb 2009 19:41:24 -0500

When it is inconvenient or impossible to compute a factorial directly, Stirling's approximation, which is valid for large n, may be useful:
  n! = (sqrt(2*pi*n))(n/e)^n .
   - David Greenberg, Sociology Department, New York U.

----- Original Message -----
From: Maarten buis <maartenbuis@yahoo.co.uk>
Date: Thursday, February 5, 2009 4:56 am
Subject: Re: st: large numbers in comb(n,k) function: no success
To: statalist@hsphsun2.harvard.edu


> --- On Thu, 5/2/09, Inna Becher wrote:
> > I would like to implement a comb(n,k) function. But my
> > Stata does not allow it because of large n, k-numbers.
> > N=180000 and k=2000. Is there any other way to do it? I
> > wasn't successful by using exp(lnfactorial(n)) in mata
> > as well.
> 
> The outcome of comb(180000,2000) is going to be,
> ridiculously large (> 8e+307) and it hits the limit of what 
> can be stored in double precision, so I don't think there 
> is any way of doing this. 
> 
> -- Maarten
> 
> -----------------------------------------
> Maarten L. Buis
> Department of Social Research Methodology
> Vrije Universiteit Amsterdam
> Boelelaan 1081
> 1081 HV Amsterdam
> The Netherlands
> 
> visiting address:
> Buitenveldertselaan 3 (Metropolitan), room N515
> 
> +31 20 5986715
> 
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
> 
> 
> 
> 
> 
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