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I have a problem with a goodness-of-fit question.. I have this question I need to answer but I have no idea how:

Why do we need to test the goodness-of-fit of a distribution of a random phenomenon to a parametric distribution (one where the distribution is known)?

I had the observations of a random variable of a completely random phenomenon, and I tested whether it fits the gamma distribution with a chi-square test. However, I have no idea how to explain why I needed to do that...

Could anyone give me a hint, please?

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    $\begingroup$ Could it just be a compulsion you have, like some people obsessively wash their hands a lot? But seriously, give us a hint why you felt you needed to. It's either because knowing the population distribution would be interesting in itself or because a gamma distribution is an necessary assumption for some further analysis. $\endgroup$ – Scortchi - Reinstate Monica May 3 '13 at 10:38
  • $\begingroup$ No, I'm working on some homework and there is this question.. $\endgroup$ – seigna May 3 '13 at 10:49
  • $\begingroup$ What was the homework problem exactly? To do the fitting or to explain why? And what is a "completely random phenomenon"? Different random phenomena will match different distributions (e.g. rolling one die - uniform distribution) $\endgroup$ – Peter Flom - Reinstate Monica May 3 '13 at 10:51
  • $\begingroup$ The homework problem was finding the distribution of the magnitude of earthquakes. I performed a few statistical tests on distribution approximations (a goodness-of-fit for gamma) - (all of which were rejected), and then there was a question that asked why would we approximate the distribution of a random phenomenon with a known distribution. $\endgroup$ – seigna May 3 '13 at 11:11
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Hints:

(a) Sometimes the population distribution is of interest in itself - the data-generating mechanism gives insight into the phenomenon behind the data. The gamma distribution is a nice example - read up on it, paying attention to its relation with the exponential distribution.

(b) When you're modelling, carrying out hypothesis tests, or whatever, there are often distributional assumptions which while not of primary interest are necessary for the validity of parameter estimates or p-values. The gamma distribution is often used in survival/reliability analysis - check that out.

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  • $\begingroup$ Thanks, that's what I thought but I wasn't sure.. $\endgroup$ – seigna May 3 '13 at 11:16

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