The Annals of Statistics

A Modified Kolmogorov-Smirnov Test Sensitive to Tail Alternatives

David M. Mason and John H. Schuenemeyer

Full-text: Open access


It is well known that the Kolmogorov-Smirnov (K-S) test exhibits poor sensitivity to deviations from the hypothesized distribution that occur in the tails. A modified version of the K-S test is introduced that is more sensitive than the K-S test to deviations in the tails. The finite and infinite sample distribution along with the consistency properties of the proposed test are studied. Tables of critical values are provided for two versions of the test (one sensitive to heavy tail alternatives and one sensitive to light tail alternatives) and the finite sample properties of these two versions of the test are investigated.

Article information

Ann. Statist., Volume 11, Number 3 (1983), 933-946.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G10: Hypothesis testing
Secondary: 62E20: Asymptotic distribution theory

Tail alternatives Kolmogorov-Smirnov test Renyi tests weighted empirical distributions


Mason, David M.; Schuenemeyer, John H. A Modified Kolmogorov-Smirnov Test Sensitive to Tail Alternatives. Ann. Statist. 11 (1983), no. 3, 933--946. doi:10.1214/aos/1176346259.

Export citation


  • See Correction: David M. Mason, John H. Schuenemeyer. Correction: A Modified Kolmogorov-Smirnov Test Sensitive to Tail Alternatives. Ann. Statist., Volume 20, Number 1 (1992), 620--621.