Open Access
March, 1953 Distribution-free Tests of fit for Continuous Distribution Functions
Z. W. Birnbaum
Ann. Math. Statist. 24(1): 1-8 (March, 1953). DOI: 10.1214/aoms/1177729078


A class of statistics, large enough to comprise those used in all the known distribution-free tests of fit for continuous distribution functions, is characterized by a structure called "structure ($d$)." A number of statistics of this class may be constructed and used for tests of fit. To make a reasonable choice among all these statistics, it appears desirable to introduce in the space of continuous distribution functions a distance which would reflect the type of discrepancy the proposed test is intended to detect. By studying the power of various statistics with regard to this distance one may then be able to choose those with optimal properties.


Download Citation

Z. W. Birnbaum. "Distribution-free Tests of fit for Continuous Distribution Functions." Ann. Math. Statist. 24 (1) 1 - 8, March, 1953.


Published: March, 1953
First available in Project Euclid: 28 April 2007

zbMATH: 0050.14607
MathSciNet: MR52740
Digital Object Identifier: 10.1214/aoms/1177729078

Rights: Copyright © 1953 Institute of Mathematical Statistics

Vol.24 • No. 1 • March, 1953
Back to Top