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I've read through some past posts about using the KS test when the distribution parameters are estimated. This one in particular was very helpful, and I implemented Greg Snow's suggestion. However, I am not clear on what to do when testing my proposed distribution against a second set of data. This is my procedure:

  1. Collect a sample of data over a given time period

  2. Determine the parameters of a hypothesized distribution from the data, and test the goodness of the fit with the KS test (modified as per Greg Snow's answer in the other post)

  3. If it passes the KS test at an acceptable confidence level, test the distribution (with the calculated parameters) against another set of data collected at a later time.

In step (3), I'm interested in how well the particular parameters values calculated in (2) work at predicting future data. That is, I'm now treating the previously calculated parameter estimates as fixed inputs. Hence, it seems to me I should be using the standard KS test with the canonical distribution for the test statistic. Is this correct?

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If you run KS test for testing normality distribution then you can rely on Central limit theorem. And you can predict normal distribution from 2. -> 3.

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    $\begingroup$ Sorry, I don't follow. It's well established that you can't use the out-of-the-box distribution for the KS statistic if your model parameters are estimated from the data you're testing, and my data is not normally distributed. Central limit theorem has nothing to do with it. $\endgroup$
    – user28597
    Jul 29, 2013 at 20:05
  • $\begingroup$ hm, Central limit theorems for dependent processes $\endgroup$
    – user1406647
    Jul 29, 2013 at 20:31

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