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Subject: Geiger, not binomial ?[snip]
Date: Thu, 23 Mar 2000 00:08:42 -0500
From: Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>
I have a problem with the distribution of counts from a
Geiger counter.It must be a binomial distribution but I
can not fit it with a binomial distribution.
A weak source is placed in front of a Geiger counter
from Vernier. That counter is connected to a computer
via ULI (also from Vernier) and the event counter
software (also Vernier) is used to count the number
of counts in consecutive time intervals of 0.5 seconds.
Typical counts are like 2, 0, 1, 4, 2, 1, 6, 1 etc. After
counting 30,038 times (for nearly 5 hr.) the distribution
of counts is as follows:
0 counts per 0.5 s occurred 3321 times
1 count per 0.5 s occurred 7278 times
2 occurred 7990 times
3 occurred 5994 times
4 occurred 3260 times
5 occurred 1439
6 occurred 557
7 occured 163
8 occurred 50
9 occurred 13
The general shape is always reasonable but details
are never satisfactory. Any comments? I expected
a nearly perfect fit because Geiger counters satisfy
all criteria under which the binomial distribution
should be a very good model.
Ludwik Kowalski
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Subject: Re: Geiger, not binomial ?
Date: Wed, 22 Mar 2000 23:28:14 -0800
From: Leigh Palmer <palmer@SFU.CA>
There is no reason to expect this to be a binomial distribution.
One would expect a Poisson distribution. Check that out. A Poisson
distribution would be indistinguishable from a binomial distribution
if you let the counter run for, say, ten seconds instead of a half
second. Try that.
Leigh
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Subject: Re: Geiger, not binomial ?
Date: Thu, 23 Mar 2000 00:11:35 -0800
From: "Bernard G. Cleyet & Nancy Ann Seese" <georgeann@REDSHIFT.COM>
High their!
I've analyzed your data. It's almost too good to be true. I get a
reduced Chi square of ~ 0.6 w/ dF of 9 The probability of doing worse
than this is ~80%. So I conclude your multi-channel scalar is accurate
and you aren't having any spurious counts or dead time problems. The
only problem I had with your data is that you should have had ~ 2.5
times with ten counts, 0.5 times with 11 counts, etc. instead of zero.
I used the Poisson distrib., as that is the std. one to use (the assumed
distribution with which to compare) . You have discovered why in
counting experiments the binomial distrib. is not used! To get a good
fit n must be very large and p very small, typically 1E+20 and 1E-20
!!! This is because the number of trials is the number of radioactive
nuclei and the prob. of success is very low (i.e. the decay).
bc
If you want a reference, write.
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Subject: Re: Geiger, not binomial ?
Date: Thu, 23 Mar 2000 00:47:14 -0800
From: "Bernard G. Cleyet & Nancy Ann Seese" <georgeann@REDSHIFT.COM>
P.s. I forgot to mention that if the average (counting rate) is high
i.e. ~> 50, one may use "the" Gaussian approx. A not unexpected result
as large n also affords "the" Gaussian approx. for the binomial distrib.
bc
P.s. from this one obtains the well known +/- Squrt.(counts).