Re: Geiger, not binomial ?

["John S. Denker" <jsd@MONMOUTH.COM>]

At 10:15 AM 3/27/00 -0500, Michael Edmiston wrote:
> ... I had forgotten all these details.  That
> realization prompted me to blow the dust off my copy of "Data Reduction and
> Error Analysis for the Physical Sciences" by Philip R. Bevington.  This 1969
> book has been mentioned on this list before (I think).  It remains one of my
> most trusted sources, even though it is not exactly easy reading.

Be careful, there....

I would have said nearly the opposite about Bevington.  I find it to be
relatively accessible, but full of bugs.  The programs that Bevington presents
  a) Use an unsophisticated approach to the problem, and
  b) Are full of amateurish bugs, e.g. endless loops.

Much better programs are available from e.g. the _Numerical Recipes_ book.


> I
> suppose it is good, once in a while, for professors to study a book with the
> same attention and care we insist our students should apply when studying
> their textbooks.

Yes indeed.

> (1) Concerning whether the Geiger counter distribution is binomial or
> Poisson.
>
> It is both.  The Poisson distribution is simply an approximation to the
> binomial distribution.

Indeed the PD is a limiting case of the BD.

> If the Poisson distribution is just an approximation to the binomial
> distribution, why bother with the Poisson distribution... why not just use
> the binomial distribution?
>
> (1a) Because the binomial distribution cannot be evaluated exactly for
> situations involving large n because the binomial distribution requires the
> evaluation of n!.

Actually there's a better reason: for large N (the total number of atoms)
and small p (probability of decay per atom, over relevant timescales), then
only the product of pN matters, so eliminating p and N in favor of pN
actually captures a valuable concept.

> (1b) Sometimes, approximation methods lead to some insight that might be
> more difficult to notice if the approximation were not performed.

Right.

> (2) What insights might be included in (1b)?

See my comment under (1a).