Generalised K-S confidence regions: some exact results

Abstract

One-sided confidence regions for continuous cumulative distribution function are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. Significance levels necessary for implementation are given. Some other K-S type distances useful in constructing a confidence region with nonconstant width are also included.

Keywords:

• Confidence regions for continuous cdf
• empirical cdf
• generalized K-S statistics