How to use Power Analysis to Estimate Mu for Exponential Distribution

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I am drawing samples from an exponential distribution with an unknown mu. I would like to use a power analysis to determine how large a sample needs to be to accuratly estimate mu with a given power and a small sample that has already been drawn from that distribution. Is it appropriate to use the sampsizepwr function to do this even though the tests it utilizes assumes a normal distribution of data (while the distribution we draw from is exponential, the distribution of means of samples will be normal as per the central limit theorem, right?)? If so, what is the best way to utilize this function?

Accepted Answer

Jeff Miller
Jeff Miller on 7 Jul 2019
I don't think the sampsizepwr function is appropriate here. Although the sampling distribution of the mean of exponentials is approximately normal as you say (thanks to CLT), the variance of that sampling distribution increases with the mean. I am pretty sure that sampsizepwr is only appropriate when the variance of the sampling distribution does not change with the mean.
I don't know exactly how to estimate the required sample size that you are after, but it should be possible to get pretty close by simulation. Take a guess as to mu, then simulate 1,000 samples of (say) 100 and check their means. If those means vary too widely around the true value, try samples of 150 or 200, etc.

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