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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

T. W. Anderson and D. A. Darling
The Annals of Mathematical Statistics
Vol. 23, No. 2 (Jun., 1952), pp. 193-212
Stable URL: http://www.jstor.org/stable/2236446
Page Count: 20
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
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Abstract

The statistical problem treated is that of testing the hypothesis that n independent, identically distributed random variables have a specified continuous distribution function F(x). If Fn(x) is the empirical cumulative distribution function and ψ(t) is some nonnegative weight function (0 ≤ t ≤ 1), we consider $n^{\frac{1}{2}} \sup_{-\infty

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