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 07 '11 at 16:07
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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 07 '11 at 16:12
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are these "elements" numbers on a real number line? – picakhu Apr 07 '11 at 16:23
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Yes, they are natural numbers. – Undercover Mathematician Apr 07 '11 at 16:25
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typically analysis is done the other way around, where you know the distribution. This is an interesting question! – picakhu Apr 07 '11 at 16:29
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Can you sample it for 1 time? Or you can have a lot of independent samples from this data set? – SBF Apr 07 '11 at 16:31
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I'm at liberty to make as many samples of size < 10000 as I like. Although I haven't proven it, I suspect that my samples are independent. – Undercover Mathematician Apr 07 '11 at 16:34
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Yes - I do not know if you can prove it, but let us make such an assumption. – SBF Apr 07 '11 at 16:38
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@Undercover You will get helpful answers by migrating this question to the stats site. – whuber Apr 07 '11 at 20:09
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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.
Ralph Winters
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