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RE: st: probability mass function for a binomial distribution


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: probability mass function for a binomial distribution
Date   Sun, 29 Jun 2008 18:37:44 +0100

Readers following along should note the renaming of various functions in
this 
territory from Stata 9 to Stata 10. Stata 10 users can see -help
whatsnew9to10-. 

That is, Carlo, as he signalled, is using Stata 9. 

Stata 9's -Binomial()- is Stata 10's -binomialtail()-. 
-Binomial()- continues to work. 

Thus I think this appearance of being undocumented  is in fact a
side-effect of name change. 

Nick 
n.j.cox@durham.ac.uk 

Steven Samuels

I agree with Nick's advice to construct the functions on first  
principles whenever possible.

Interestingly, Carlo has discovered the apparently undocumented   
"survival' function  Binomial(k,n,p) equal to P(X>=k), whereas the  
documented  function binomial(k,n,p) is P(X<=k).   Here is a version  
of Carlo's  program with a correction for k= 20.

-Steve

/*---------------------------begin example-------------------------*/
drop _all
clear
set obs 21
g id=_n-1
g n=20
g k=_n-1
g p=.2
g  double  Binomial=Binomial( n, k, p)
g  double  PMF_Binomial=Binomial[_n]- Binomial[_n+1] in 1/20
replace    PMF_Binomial=Binomial[_n] in 21   //Correction

g double PMF2 = 0.2^k * 0.8^(20 - k) * comb(20, k)

list id n k p Binomial binomial PMF*
/*--------------------------end example----------------------------*/

On Jun 29, 2008, at 11:26 AM, Nick Cox wrote:

> What is available as a defined function shows up a trade-off  
> problem. It
> wouldn't be difficult to define a thousand functions, but then some
> people might complain about the complexity of the list and the
> difficulty of finding a solution.
>
> Otherwise put, I guess the answer to Carlo's question is that Stata
> users -- unlike spreadsheet users, it seems --- are paid the  
> compliment
> of knowing enough statistics to work this out from first principles:
>
> gen double bmp = p^k * (1 - p)^(20 - k) * comb(20, k)
>
> Note in passing two other details:
>
> I prefer to use -double-s here.
>
> Putting constants into variables isn't necessary:
>
> gen double bmp = 0.2^k * 0.8^(20 - k) * comb(20, k)
>
> In cases like this the advantage of a canned function over a one-line
> solution using another canned function would be pretty small.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Carlo Lazzaro
>
> I have probably found out the answer to my last Friday thread.
> I do hope this may be useful for someone else on the list.
> However, a little concern remains about the lack among Stata 9.2/SE
> commands
> of an in-built for calculating the (probably too trivial) probability
> mass
> function for a binomial distribution, which is instead available  
> within
> the
> most widespread spreadsheets.
> One more time, my grateful thought go out to Steve and Nick (in  
> order of
> appearance in my incoming e-mail folder) for pointing me out the
> importance
> of a step-by-step research in dealing with Stata troubles.
>
> ---------------------------begin example-------------------------
> set obs 21
> g id=_n-1
> g n=20
> g k=_n-1
> g p=.2
> g Binomial=Binomial( n, k, p)
> g PMF_Binomial=1- Binomial if id==20
> replace PMF_Binomial=Binomial[_n]- Binomial[_n+1] in 1/20
> --------------------------end example----------------------------
>

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