Anderson Darling exponential distribution I need a goodness of fit test for the exponential distribution.  I understand that Kolmogorov-Smirnov is not generally regarded as very powerful and that Anderson-Darling is regarded as superior. However I have two problems.


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*None of the literature I can find specifically talks about goodness of fit for exponential distributions.  Anderson-Darling is almost always discussed wrt the normal distribution.

*Is there an R (or python) package to do an Anderson-Darling goodness of fit for the exponential distribution? I can find them for other distributions.

*Is there  a better test (which exists in R or python)?

 A: The same considerations apply as to the distribution of the  Kolmogorov–Smirnov test statistic discussed here. The Anderson–Darling test statistic (for a given sample size) has a distribution that (1) doesn't depend on the null-hypothesis distribution when all parameters are known, & (2) depends only on the functional form of the null-hypothesis distribution when location & scale parameters are estimated. I don't know of an R implementation of the A–D test specifically for the exponential distribution with estimated rate parameter, but you could quickly make a function to calculate the test statistic by adapting the ad.test function from the nortest package: change the distribution function from  the best-fit normal, pnorm((x - mean(x))/sd(x)), to the best-fit exponential,pexp(x/mean(x)). Then get critical values for any desired significance level & sample size by simulation.
As to the "best" test, note that different tests are more powerful against different kinds of departure from the null-hypothesis distribution. If you have a quite specific alternative in mind, e.g. a Weibull distribution with shape parameter greater than one, a likelihood ratio test will be more powerful than a general-purpose goodness-of-fit test. For more vaguely specified alternatives it might be helpful to compare the power of various tests against a rogues gallery, following the approach of Stephens (1974), "EDF statistics for goodness of fit and some comparisons", JASA, 69, 347.
