, Volume 20, Issue 3, pp 2147-2164

Probability distributions of the Kolmogorov and omega-square statistics for continuous distributions with shift and scale parameters

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Abstract

The paper is devoted to the application of the statistical Kolmogorov and omega-square criteria to verification of a complex hypothesis H0 according to which the independent, identically and continuously distributed random variables X1,...,Xn have the law G[(x−θ 1)/θ 2].

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 46–74, 1979.