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Abstract The problem of testing the fit of the Levy distribution with unknown scale parameter is addressed. The corresponding empirical process is analysed, and the Cramer-von Mises W2 and the Anderson-Darling's A2 statistics are used. Well known results regarding the relationship between the Levy distribution and the gamma and inverse Gaussian are exploited. Some remarks are made regarding the use of the Rao-Blackwell estimator of the distribution function in the empirical process. Keywords: Goodness of fitRao-Blackwell estimator
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