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st: Re: St.: Truncating Poisson - using ML


From   "Jamie Griffin" <Jamie.Griffin@lshtm.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: St.: Truncating Poisson - using ML
Date   Wed, 30 Aug 2006 12:45:40 +0100

You can use the incomplete gamma function. If Y~Poisson(lambda), then
prob(Y<=k)=Q(k+1, lambda), where Q is the upper incomplete gamma
function.
So in Stata code the cumulative probability prob(Y<=k) is

1-gammap(k+1, lambda)

Jamie Griffin



>>> prabhu@unc.edu 08/30/06 12:14 am >>>
Dear all,

The MLE for poisson function is L= exp(-lambda)Lambda^Y/Y!

I found the following code for poisson on a website (by David Todd) as

follows:

program define poisreg2
args lnf theta
quietly replace `lnf' = -exp(`theta') +
$ML_y1*(`theta')-lnfact($ML_y1)
end

Now, I want to truncate the distribution. The new MLE function is
L2 = L/prob(y<=ymax).
i.e. divide the likelihood function by prob(y<=ymax).
i.e subtract the log function by CDF_POISSON(lambda,ymax).

For that I need a poisson cumulative distribution function which I am 
not able to find out.

What is the command for finding a cumulative distribution function? It

should use two parameters and should be something like, f= 
poisson(lambda,ymax)

Thanks,

Prabhu

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