I am given two samples and and I wish to use a pivot quantity to test the hypothesis against using a suitable pivot quantity.
I know that this means that I should find a statistics with a distribution that doesn't depend on under . Since
this means that and hence
T= is a quantity with a distribution that doesn't depend on .
My questions are
1) is the above correct
2) How do I now proceed to compute a p-value. I see how I can simulate from an exponential distribution with any given parameter and compute the test statistics, but how do I evaluate the statistics for my given sample since I don't know ?
Thanks in advance,