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Poisson Distribution Help

  1. Jul 25, 2012 #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.
  2. jcsd
  3. Jul 26, 2012 #2


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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
    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]
    Last edited by a moderator: May 6, 2017
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