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A NEW CONFIDENCE BAND FOR CONTINUOUS CUMULATIVE DISTRIBUTION FUNCTIONS
Author(s) -
Xu Xingzhong,
Ding Xiaobo,
Zhao Shuran
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2009.00546.x
Subject(s) - mathematics , confidence and prediction bands , confidence interval , sample (material) , cumulative distribution function , distribution (mathematics) , set (abstract data type) , sample size determination , statistics , construct (python library) , algorithm , probability density function , mathematical analysis , computer science , chemistry , chromatography , programming language
Summary We consider confidence bands for continuous distribution functions. Following a review of the literature we find that previously considered confidence bands, which have exact coverage, are all step‐functions jumping only at the sample points. We find that the step‐function bands can be constructed through rectangular tolerance regions for an ordered sample from the uniform distribution R(0, 1). We then construct a set of new bands. Two criteria for assessing confidence bands are presented. One is the power criterion, and the other is the average‐width criterion that we propose. Numerical comparisons between our new bands and the old bands are carried out, and show that our new bands perform much better than the old ones.