Open Access
Translator Disclaimer
June, 1974 Generalized Distribution Functions: The Linearly Ordered Case with Applications to Nonparametric Statistics
Gordon Simons
Ann. Probab. 2(3): 501-508 (June, 1974). DOI: 10.1214/aop/1176996667

Abstract

We develop a theory for distribution functions which are defined on an abstract linearly ordered space. This extends and gives additional insight into the work of J. H. B. Kemperman who was concerned with a special class of linearly ordered spaces. Attention is given to nonparametric applications. The utility of Kemperman's work on tolerance regions and of related applications to goodness of fit tests, appearing in this paper, is enhanced. In particular, it is shown that a number of standard nonparametric procedures can be extended to cover almost any kind of random sample (e.g., multivariate and most time series data) occurring in practice.

Citation

Download Citation

Gordon Simons. "Generalized Distribution Functions: The Linearly Ordered Case with Applications to Nonparametric Statistics." Ann. Probab. 2 (3) 501 - 508, June, 1974. https://doi.org/10.1214/aop/1176996667

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.60008
MathSciNet: MR356159
Digital Object Identifier: 10.1214/aop/1176996667

Subjects:
Primary: 60E05
Secondary: 06A05 , 62E10 , 62E15 , 62G10

Keywords: distribution function , linear ordering , nonparametric statistics

Rights: Copyright © 1974 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.2 • No. 3 • June, 1974
Back to Top