topic Fitting poisson distribution to a histogram in Statistical Procedures

Fitting poisson distribution to a histogram

JatinRai — Mon, 02 Apr 2012 00:22:37 GMT

I want to chart the poisson distribution on a histogram and subsequently to a qqplot. Proc univariate doesn't seem to support this. Any help is deeply appreciated.

Fitting poisson distribution to a histogram

SteveDenham — Mon, 02 Apr 2012 12:15:00 GMT

Do you have access to SAS/QC? If so, PROC CAPABILITY should be able to help with this problem.

Steve Denham

Fitting poisson distribution to a histogram

Rick_SAS — Mon, 02 Apr 2012 13:39:09 GMT

1) Estimate the parameter with PROC GENMOD: http://support.sas.com/kb/24/166.html

2) Use the DATA step and he tPDF function to compute the Poisson PDF (well, really the PMF=probability mass function) for the range of x values of interest.

3) The Poisson is a discrete distribution, so your data should be plotted with a bar chart. Because PROC SGPLOT doesn't enable you to overlay a bar chart and a scatter plot of (x, pdf(x)), you need to use the GTL to overlay the two plots.

4) You can create a Q-Q plot by following the steps laid out in my blog: http://blogs.sas.com/content/iml/2011/10/28/modeling-the-distribution-of-data-create-a-qq-plot/

Rick

Fitting poisson distribution to a histogram

PGStats — Mon, 02 Apr 2012 14:54:48 GMT

Great advice! There is even an easier way to do step 3 now. The VBARPARM can be combined with SERIES plots in SGPLOT (I think this is new to 9.3).

Fitting poisson distribution to a histogram

Rick_SAS — Mon, 02 Apr 2012 15:23:20 GMT

Clever! Yes, you can use PROC FREQ to tabulate the data. You'll want to scale the PERCENT variable to a proportion so that it is on the same scale as the PDF.

Fitting poisson distribution to a histogram

Rick_SAS — Wed, 04 Apr 2012 09:55:39 GMT

I explain the details of my answer and give an example (which includes PGStats's suggestion) on my blog in the article "Fitting a Poisson Distribution to Data in SAS."

The same approach should work for other discrete distributions such as negative binomial and geometric distributions.

Rick

Re: Fitting poisson distribution to a histogram

JatinRai — Thu, 12 Apr 2012 15:24:21 GMT

Unfortunately I don't have access to SAS/QC.

Re: Fitting poisson distribution to a histogram

JatinRai — Thu, 12 Apr 2012 15:25:40 GMT

Rick,

Thank you so much for the response and then subsequently backing this with your blog. I have read and shared your blogs in the past and they have always worked.

Thanks,

Jatin

Re: Fitting poisson distribution to a histogram

Rick_SAS — Thu, 12 Apr 2012 15:31:26 GMT

You are welcome. And thanks to you for the interesting idea.

For those who do not read my blog, I followed up my first post with a second: The Poissonness plot: A goodness-of-fit diagnostic

in which I present a graphical diagnostic plot that is an alternative to using a Q-Q plots.

Re: Fitting poisson distribution to a histogram

Rick_SAS — Thu, 12 Apr 2012 15:32:38 GMT

CAPABILITY and UNIVARIATE only model continuous distributions. The Poisson distribution is discrete.

Re: Fitting poisson distribution to a histogram

SteveDenham — Fri, 13 Apr 2012 11:44:19 GMT

I apologize--I gave an answer without checking the documentation. I knew CAPABILITY had several distributions, and wrongly assumed that it included the Poisson. There is nothing that is better than reading the manual, and I missed it on this one.

Steve Denham