The Annals of Mathematical Statistics

The Cramer-Smirnov Test in the Parametric Case

D. A. Darling

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Abstract

The "goodness of fit" problem, consisting of comparing the empirical and hypothetical cumulative distribution functions (cdf's), is treated here for the case when an auxiliary parameter is to be estimated. This extends the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2]. The characteristic function of the limiting distribution of the test function is found by consideration of a Guassian stochastic process.

Article information

Source
Ann. Math. Statist., Volume 26, Number 1 (1955), 1-20.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728589

Digital Object Identifier
doi:10.1214/aoms/1177728589

Mathematical Reviews number (MathSciNet)
MR67439

Zentralblatt MATH identifier
0064.13701

JSTOR
links.jstor.org

Citation

Darling, D. A. The Cramer-Smirnov Test in the Parametric Case. Ann. Math. Statist. 26 (1955), no. 1, 1--20. doi:10.1214/aoms/1177728589. https://projecteuclid.org/euclid.aoms/1177728589


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