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- W20415572 abstract "Summary Let F n (x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér‐von Mises statistic in the form where the z nj are the principal components of . It is shown that the z nj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their asymptotic powers are compared with those of , Anderson and Darling's statistic and Watson's against shifts of mean and variance in a normal distribution. The asymptotic significance points of the residual statistic are also given for various p. It is shown that the components analogous to z nj for are the Legendre polynomial components introduced by Neyman as the basis for his “smooth” test of goodness of fit. The relationship of the components to a Fourier series analysis of F n (x) – x is discussed. An alternative set of components derived from Pyke's modification of the sample distribution function is considered. Tests based on the components z nj are applied to data on coalmining disasters." @default.
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- W20415572 date "1972-01-01" @default.
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- W20415572 title "Components of Cramér-Von Mises Statistics. I" @default.
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- W20415572 doi "https://doi.org/10.1111/j.2517-6161.1972.tb00908.x" @default.
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