Abstract
Cramér-von Mises (CvM) tests for the exponential distribution are discussed, particularly when the scale parameter must be estimated from the given sample. The methods used in the paper are based on components of the statistics; this leads to a matrix formulation discretizing previous analytic techniques. Some comparisons are made between the two methods. Plots are given of the eigenfunctions which arise in the analysis. Plots are also given of asymptotic powers of the tests statistics against local Weibull and Gamma alternatives; these show the Anderson-Darling statistic to be the most powerful. The power of the best component is found, and shown to be comparable to the Likelihood Ratio statistic and greater than that of the entire statistic. Some connections with Neyman smooth tests are pointed out.
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Stephens, M.A. Asymptotic Power of CvM Statistics for Exponentiality Against Weibull and Gamma Alternatives. J Stat Theory Pract 3, 627–643 (2009). https://doi.org/10.1080/15598608.2009.10411951
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DOI: https://doi.org/10.1080/15598608.2009.10411951