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I am investigating if an exponential distribution is a good fit for a large sample of data (200) I have. I have already looked at a histogram but was wanting to investigate further. I was going to use the Kolmogorov-Smirnov test and consider the p-value however I heard that if using a large sample this isnt a good idea because it can lead to type I errors, is this the case? And if so any suggestions of alternative tests?

kay
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    As I commented on your SO post (in general you should wait for moderators to migrate your post rather than deleting and reposting yourself ...), the issue is not really type I errors (falsely rejecting the null hypothesis). The problem is that the null hypothesis is almost never exactly true (except perhaps in physics, sometimes), and large data sets allow you to discover that. – Ben Bolker Mar 31 '14 at 21:10
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    (1) It would be useful to have some more context for why you want to know the goodness of fit; if the data are not exponentially distributed, does that mean something important? . (2) http://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless covers a more common but very closely related topic. (3) It depends on your field, but I would consider 200 data points "medium-sized" rather than "large" ... – Ben Bolker Mar 31 '14 at 21:11
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    (4) if you are interested in non-exponentialness, would it be more informative to fit a parametric distribution (Gamma, Weibull, ...) that has the exponential as a special case? – Ben Bolker Mar 31 '14 at 21:12
  • In addition to the histogram, you could also look at a QQ plot. – binkyhorse Mar 31 '14 at 22:11
  • I don't really think this is an exact dupe of http://stats.stackexchange.com/questions/92035/how-to-guess-a-curve-distribution-from-count-data -- they're both about KS testing, and exponentials are mentioned (and both are a little bit too vague to be answered well), but the rest is quite different ... – Ben Bolker Mar 31 '14 at 23:00
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    http://meta.stackexchange.com/questions/189675/what-is-the-appropriate-action-to-take-if-you-feel-your-question-has-been-unjust/189682#189682 suggests that editing the question to make it clearer how it differs from the other question will allow the possibility of re-opening. – Ben Bolker Mar 31 '14 at 23:01
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    Not much is asked here that isn't answered at least indirectly on "Is normality testing 'essentially useless'?" as well. Different distribution, but same problem, basically. – Nick Stauner Mar 31 '14 at 23:46
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    @NickStauner: I more or less agree, but we should wait to hear back from the OP. Maybe they can provide some context about why they want to test the goodness of fit of the exponential that will make more useful/interesting answers possible ... – Ben Bolker Apr 01 '14 at 02:39

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