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I have a population distribution I know is exponential, with mean $\mu_1$. I also have a sample of the population (of size $n$) that appears to be exponential with mean $\mu_2$. I have all the $n$ individual samples that make up $\mu_2$. I want to figure out if the sample is a faithful sample of the population and the confidence in that decision.

My naive guess reading this would be to try the Kolmogorov-Smirnov test, but it's not something I'm very familiar with. I also saw this question, but I think my question is a little bit more basic.

My question is: Is the Kolmogorov-Smirnov test an appropriate choice here?

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A K-S test is a fine way to judge if a sample is very nearly drawn from a specific distribution. To gain more confidence in the 'accept' decision of the KS test, it's a good idea to conduct a power analysis based on the parameters you gave in the question.

A more powerful alternative to the K-S test is the energy goodness-of-fit test of Szekely and Rizzo.

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