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I have a uniformly collected sample of 10000 data points from a population of about 200000. I'd like to find out what the distribution of the population is. How can I do this rigourously?

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The question as it is posed is not clear, what do you mean by "distribution of population"? – picakhu Apr 7 '11 at 16:07
Ah, sorry stats isn't my first language, so please excuse me. The elements of the population may be, say, normally distributed, or uniformly distributed etc. I would like to asertain if there is a well known distribution that models the distribution of the points in my population. Is there a more succinct way to articulate this in statsy lingo? – Undercover Mathematician Apr 7 '11 at 16:12
are these "elements" numbers on a real number line? – picakhu Apr 7 '11 at 16:23
Yes, they are natural numbers. – Undercover Mathematician Apr 7 '11 at 16:25
typically analysis is done the other way around, where you know the distribution. This is an interesting question! – picakhu Apr 7 '11 at 16:29
up vote 2 down vote accepted

There are several tests you can perform to test the hypothesis that the sample is equal to a predefined distribution. The simplest way is to bin the data, and then compare the frequency counts to the expected counts of any distribution: (normal, uniform, poisson etc.), using chi-square. Alternatively, you can also use the more powerful Kolmogorov-Smirnov test.

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