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Math Help - Testing if data is drawn from a Poisson distribution

  1. #1
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    Testing if data is drawn from a Poisson distribution

    Hello,

    Suppose you have a set of items, labeled x_1, x_2, ..., x_n, and you have evaluated relative frequencies, call them empirical probabilities,
    p(x_1), p(x_2), ..., p(x_n) . How could you go about testing if the data are drawn from a Poisson distribution using the \chi^{2} goodness-of-fit test?

    In general, if you would like to know which distribution data is drawn from, is there any particular method?

    Thank you!
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  2. #2
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    Quote Originally Posted by EmpSci View Post
    Hello,

    Suppose you have a set of items, labeled x_1, x_2, ..., x_n, and you have evaluated relative frequencies, call them empirical probabilities,
    p(x_1), p(x_2), ..., p(x_n) . How could you go about testing if the data are drawn from a Poisson distribution using the \chi^{2} goodness-of-fit test?

    In general, if you would like to know which distribution data is drawn from, is there any particular method?

    Thank you!
    The first thing I'd do is read how to apply the test! Have you done so? If so, where are you stuck?
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  3. #3
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    Oh, yes. I am familiar with the test procedure. The point where I am stuck is the theoretical probability evaluation, which is then subtracted from the empirical p(x_i), squared and divided by theoretical probabilities. But, my difficulty is the evaluation of theoretical probabilities. I wanted to test for Poisson, and I am stuck on how to evaluate the Poisson probabilities.

    All in all, I have n observed probabilities (I do have the absolute frequencies, as well). The first few entries have the following values:
    p(x_1)=0.503,  p(x_2)=0.25,  p(x_3) = 0.0027, p(x_4) = 0.0024, ..., p(x_n)=1.03848E-05. So, you can image, I suppose, the way this discrete distribution looks like. If not Poisson, then what other theoretical distribution would you recommend to consider?

    Thanks!
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  4. #4
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    Quote Originally Posted by EmpSci View Post
    Oh, yes. I am familiar with the test procedure. The point where I am stuck is the theoretical probability evaluation, which is then subtracted from the empirical p(x_i), squared and divided by theoretical probabilities. But, my difficulty is the evaluation of theoretical probabilities. I wanted to test for Poisson, and I am stuck on how to evaluate the Poisson probabilities.

    All in all, I have n observed probabilities (I do have the absolute frequencies, as well). The first few entries have the following values:
    p(x_1)=0.503, p(x_2)=0.25, p(x_3) = 0.0027, p(x_4) = 0.0024, ..., p(x_n)=1.03848E-05. So, you can image, I suppose, the way this discrete distribution looks like. If not Poisson, then what other theoretical distribution would you recommend to consider?

    Thanks!
    Read this: http://courses.wcupa.edu/rbove/Beren...ection12_5.pdf
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  5. #5
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    mr. fantastic,

    Do you have a similar manual on performing a goodness-of-fit test for the log-series (discrete logarithmic) distribution?

    Thank you.
    Last edited by EmpSci; April 28th 2010 at 08:35 PM. Reason: changed to log-series...
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