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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Re: St.: Truncating Poisson - using ML
Date   Wed, 30 Aug 2006 12:55:05 +0100

Clearly better than my suggestion. 

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

Jamie Griffin
 
> 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)

prabhu@unc.edu 08/30/06 12:14 am >>>
 
> 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)

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