Oh wise ones --(adsbygoogle = window.adsbygoogle || []).push({});

I have a Poisson process (think clicks in a Geiger counter) for which I have a fixed but short time window, sufficient to get a smallish (10-50) number of events.

I do NOT have the average arrival rate; that's what I want to estimate.

Is my estimate any better if I measure the distribution of interarrival times than if I just take the average (number of events detected divided by the width of the time window)? Can someone with more math horsepower than I have tell me if so, and (for extra credit) by how much?

I know I have quantization issues with the simple average because the arrival times are independent of my window start/stop times. I know the interarrival times are independent of each other, but they are of course not independent of the total in the window. Can any of you tell me if there's extra info hiding in there if I can get the interval distribution?

Thanks from a poor dumb engineer who only flunked two courses in college -- both math. :)

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# Can I get additional info from interarrival times?

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