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Kolmogorv-Smirnov goodness of fit test

  1. Sep 2, 2007 #1
    1. The problem statement, all variables and given/known data
    I am needing to identify whether or not my distribution follows a normal distribution. Now by eye it kind of looks like it does, but I need to perform the kolmogorov-smirnov goodness-of-fit test to verify this. Below is a picture of my dataset with a normal curve fitted to it (red line is the normal curve).

    [​IMG]


    3. The attempt at a solution
    So anyway to test this I was using the "kstest" function in Matlab. I essentially have 13 million data points and when I test this I get H=1, which means that the null hypothesis (that the distribution DOES follow a normal distribution) has been rejected. However, when I only use 1000 data points it returns the value of H=0, which means that the null hypothesis has been accepted.

    I was just wondering if anyone knew why this would be so and if you maybe had any recommendations on what I should do?

    Appreciate any advice.

    Thanks.
     
  2. jcsd
  3. Sep 2, 2007 #2

    Astronuc

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    Staff: Mentor

  4. Sep 2, 2007 #3
    Thanks for that Astronuc. That was quite interesting. What I'm doing is I'm using the Hipparcos photometry data to estimate the possible number of occultations that were observed throughout the mission. From the photon statistics theory that I've read so far I am meant to have a normal distribution (apparently the possoin distribution is approximately normal in this case), or the data should at least be comparable to a normal distribution.

    I will have to do a test to verify this, but from the looks of it my distribution has a positive kurtosis that makes it similar to the logistic distribution. So I mean this data couldn't really be classed as comparable to a normal distribution can it?
     
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