Re: [Phys-L] Coincidence Statistics
Co-incidence can be slippery. For infinitely narrow pulse-widths,
coincidence at any repetition rate is highly improbable.For pulse widths as
long as a time bin, two pulses might be counted as coincident even if they were
separated by nearly one bin's time span.
On Friday, November 17, 2023 at 10:39:26 AM CST, Paul Nord via Phys-l
<phys-l@mail.phys-l.org> wrote:
Brian,
ChatGPT gives good arguments. What is more remarkable, actually, is that
your google search turned up exactly the lab writeup I was looking at.
I wrote a quick python program to do a little Monte Carlo. It always gets
values near the predicted equation. In this case the 1/100 seconds we were
discussing. Curiously, in 100,000 iterations of the test, there was one
case where it saw 8 coincident values.
Number of iterations: 100000
Average number of coincidences: 1.00223
Median number of coincidences: 1.0
Min number of coincidences: 0
Max number of coincidences: 8
Number of 0 coincidences: 36851
Number of 1 coincidences: 36731
Number of 2 coincidences: 18258
Number of 3 coincidences: 6152
Number of 4 coincidences: 1609
Number of 5 coincidences: 322
Number of 6 coincidences: 66
Number of 7 coincidences: 10
Number of 8 coincidences: 1
Number of 9 coincidences: 0
Number of 10 coincidences: 0
Number of 11 coincidences: 0
Total number of coincidences: 100223
Maybe I just need to convince myself that while the time between events is
exponentially distributed, the mean value of that probability density
remains constant.
I am still questioning whether the assumption in my program is that the
timing resolution is a full bin width or half of a bin width. Perhaps
that's two different problems. If I digitize timestamps for two different
pulses, I define a bin width and truncate each pulse to the bin width.
However, if I'm using coincidence timing hardware that sets a logic gate
whenever both pulses are present it triggers an output pulse. Then it's a
question of how much overlap is required for me to detect the output pulse.
Ok, I'm convinced. Let us commence arguing about the exponential
distribution of the time between two random pulses.
Paul
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