       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>

```> 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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