Re: st: RE: Hypergeometric Distribution

[Marcello Pagano <pagano@hsph.harvard.edu>]

The hypergeometric plays a central role in sampling when sampling from a 
finite population.  The binomial provides an approximation for large 
samples, but why rely on approximations today when they are not 
necessary? and how good is the approximation, anyway?  Possibly the 
reliance on the approximation provided by the binomial has lulled us 
into a complacency that contributed to the "evidence since 1999"?

I did research a little with -comb( )- and that works pretty well, but I 
did a very limited study.  A Stata function with all its usual 
associated robustness and accuracy would be nice, in my opinion.

m.p.

Nick Cox wrote:

> There are many answers to this, but dinner 
> supervenes. 
> If you push hard enough, and show why it is 
> needed, either StataCorp or a user 
> will write a program for this. 
> The evidence since 1999 has been that such 
> a program is not needed. 
> Nick 
> n.j.cox@durham.ac.uk 
> Marcello Pagano
>  
>   
> > Why buy Stata if you are expected to do all this for yourself?
> >     
>  
>   
> > Nick Cox wrote:
> >     
> > > Apply -ln()-, -exp()- and -cond()- as needed. 
> > > Nick 
> > > n.j.cox@durham.ac.uk 
> > > Marcello Pagano
> > >
> > >   
> > >       
> > > > Just concerned with the accuracy.
> > > >     
> > > >         
> > >   
> > >       
> > > > Nick Cox wrote:
> > > >     
> > > >         
> > >   
> > >       
> > > > > Roger's posting includes what I presume is an allusion to 
> > > > > an -egen- function _ghyper.ado that I wrote in 1999. 
> > > > > I withdrew this program as redundant some years ago, 
> > > > > given that you can use something like 
> > > > > comb(K, k) * comb(N - K, n - k) / comb(N, n)
> > > > >
> > > > > wherever you want. In context N, K, n, k may be 
> > > > > variables, scalars or placeholders for numeric
> > > > > constants, or any mixture thereof. 
> > > > > This might need a wrapper to yield zeros where 
> > > > > appropriate, or it might need care whenever 
> > > > > individual terms get very large, but otherwise
> > > > > does it raise any problems? 
> > > > > Nick 
> > > > > n.j.cox@durham.ac.uk 
> > > > > Marcello Pagano
> > > > >  
> > > > >   
> > > > >       
> > > > >           
> > > > > > I looked at --ssizebi-- but it seems to be focused on power 
> > > > > > and sample 
> > > > > > sizes.
> > > > > >     
> > > > > >         
> > > > > >             
> > > > >  
> > > > > Newson, Roger B wrote:
> > > > >
> > > > >   
> > > > >       
> > > > >           
> > > > > > > Thanks to Marcello for telling us all about this 
> > > > > > >           
> > > > > > >               
> > > > recently-published
> > > >     
> > > >         
> > > > > > > algorithm, which looks very useful. A search on
> > > > > > >
> > > > > > > findit hypergeometric
> > > > > > >
> > > > > > > in Stata finds a single reference (to a SSC package), which was
> > > > > > > distributed as long ago as 1999. This suggests that the new 
> > > > > > >       
> > > > > > >           
> > > > > > >               
> > > > > > algorithm
> > > > > >     
> > > > > >         
> > > > > >             
> > > > > > > might be a good candidate for implementation in Mata by 
> > > > > > >       
> > > > > > >           
> > > > > > >               
> > > > > > Marcello, or by
> > > > > >     
> > > > > >         
> > > > > >             
> > > > > > > anybody else with the time and inclination to do so.
> > > > > > >       
> > > > > > >           
> > > > > > >               
> > > > > Marcello Pagano
> > > > >
> > > > >   
> > > > >       
> > > > >           
> > > > > > Does anyone have or know of Stata code to calculate the 
> > > > > >         
> > > > > >             
> > > > Hypergeometric 
> > > >     
> > > >         
> > > > > > Distribution accurately?
> > > > > >
> > > > > > See Journal of Discrete Algorithms ,  Volume 5 ,  Issue 2  
> > > > > >         
> > > > > >             
> > > > (June 2007) 
> > > >     
> > > >         
> > > > > > Pages: 341-347 for an article by Berkopec, HyperQuick 
> > > > > >         
> > > > > >             
> > > > algorithm for 
> > > >     
> > > >         
> > > > > > discrete hypergeometric distribution 
> > > > > >         
> > > > > >             
> <http://portal.acm.org/citation.cfm?id=1240586&coll=GUIDE&dl=GUIDE&CFID=
>   
> >   
> >     
> > > > 27443384&CFTOKEN=80678482>.
> > > >       
> > > >         
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>   
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/