Poisson Distribution Help

  • #1
I have been analyzing some data at work, and I have measured the occurrence rates of some event. How do I give a one sigma confidence interval to go along with it, assuming it is a Poisson event? For example, I found that something occurs 20 out of 10 000 times, something else occurs 43 out of 10 000 times, etc. How do I calculate one sigma error bars for these values? I know that for large number of events the uncertainty goes to root N, but what about for smaller numbers like, say, a rate of 5 in a 1000.
 

Answers and Replies

  • #2
DrDu
Science Advisor
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Using a sigma confidence interval you are implicitly assuming an asymptotic normal distribution. Or do you want e.g. a 64% error interval?
In the first case, if x is the parameter of the Poisson distribution, then it's variance is x, too. The estimate of x is n, the number of events observed. Then possible 1 sigma confidence intervals are
n+-sqrt(n).
If you want better CIs, with a given significance level (rather than sigma value) p, refer to the article by Crow and Gardner:
http://www.ps.uci.edu/~markm/freq/crowgardner.ps [Broken]
 
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