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?
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.