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March, 1976 Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters
M. A. Stephens
Ann. Statist. 4(2): 357-369 (March, 1976). DOI: 10.1214/aos/1176343411


Percentage points are given for the asymptotic distributions of the goodness-of-fit statistics $W^2, U^2$ and $A^2$, for the cases where the distribution tested is (a) normal, with mean or variance, or both, unknown; (b) exponential, with scale parameter unknown. Some exact means and variances are also given. The distributions can be expressed as a sum of weighted chi-square variables; the weights are calculated, and the higher cumulants can then be found. The first four cumulants are used to approximate the distributions and give the percentage points.


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M. A. Stephens. "Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters." Ann. Statist. 4 (2) 357 - 369, March, 1976.


Published: March, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0325.62014
MathSciNet: MR397984
Digital Object Identifier: 10.1214/aos/1176343411

Primary: 62E20
Secondary: 62E15 , 62F05 , 62G30

Keywords: Asymptotic distributions , Empirical distribution function , Goodness-of-fit tests , order statistics

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 2 • March, 1976
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