1) I deliberately used small dt=0.5 s to obtain a skewed distribution
of discrete values. The purpose was to illustrate the Central Limit
Theorem. The illustration is perfect, I strongly recommend it.
The issue of the binomial fit is marginal in the context of CML.
2) Under chosen conditions the random variable (counts per time
interval) is discrete. The Poisson distribution is continuous. That
is why I expected the binomial to fit the data perfectly. I tried
large n (up to the point at which doubling of n makes very little
difference) but no success. Why ? Why ? Why ?
3) By the way, the data posted last night refer to sums of all seven
measurements, each measurement lasted 2500 seconds and had
approximately 7 times lower frequencies of occurrence. Each
of the seven sequences would be sufficient; I was checking the
stability of the counting system. Sorry for not making this clear.
Ludwik Kowalski
Michael Edmiston wrote:
I agree with Leigh. The distribution you want is the Poisson distribution.