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MathGroup Archive 2007

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Re: Re: fit a BinomialDistribution to exptl data?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80756] Re: [mg80727] Re: fit a BinomialDistribution to exptl data?
  • From: DrMajorBob <drmajorbob at bigfoot.com>
  • Date: Thu, 30 Aug 2007 23:51:26 -0400 (EDT)
  • References: <11420600.1188458042685.JavaMail.root@m35>
  • Reply-to: drmajorbob at bigfoot.com

> It is very instructive to see how the results vary from sample to sample.

Yes, results vary wildly (for all the methods). In just a few trials of 

200 draws from BinomialDistribution[20, 0.2], I got n anywhere from 13 to  
96.

In more extensive testing (300 trials), the simple moment estimator  
(setting theoretical mean and variance equal to the sample mean and  
variance, then solving for n and p) returned n from -1447 to +521, and the  
other methods were not much better. Darren Glosemeyer's FindFit solver  
failed to converge on one sample, returning n greater than 4000. And so 
forth.

Statistics is more art than science.

Bobby

On Thu, 30 Aug 2007 01:34:27 -0500, P_ter <peter_van_summeren at yahoo.co.uk>  
wrote:

> This fitting with Mathematica is quite impressive for me. But it is not  
> enough just to fit.
> I did in R with the package gamlss {n,p=.2} experiment with one sample.  
> The results were nearly the same (correction for sample size).
> I give some {n,p} results from Ray's program:
> {3.88, 3.25186},{23.9666, 0.161892},{22, 0.176364}
> {3.965, 2.99877},{16.2707, 0.24369},{16, 0.247813}
> {3.775, 3.16018},{23.1784, 0.162867},{21, 0.179762}
> It is very instructive to see how the results vary from sample to  
> sample. And this is for fitting!
> It could be a very nice demonstration for findFit: to see the difference  
> between the theoretical distribution, the sample and the found  
> distribution.
> Very impressive what one can do with a few lines of code!
> with friendly greetings,
> P_ter
>
>



-- 

DrMajorBob at bigfoot.com


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