# Testing the goodness-of-fit of a random distribution to a parametric distribution

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?

• 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. – Scortchi - Reinstate Monica May 3 '13 at 10:38
• No, I'm working on some homework and there is this question.. – seigna May 3 '13 at 10:49
• 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) – Peter Flom - Reinstate Monica May 3 '13 at 10:51
• 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. – seigna May 3 '13 at 11:11