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

 From "Nick Cox" To 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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```