Premium
A POISSON PROCESS APPROXIMATION FOR GENERALIZED K–S CONFIDENCE REG
Author(s) -
Arsham H.,
Miller D.R.
Publication year - 1985
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1985.tb01147.x
Subject(s) - confidence and prediction bands , mathematics , poisson distribution , confidence distribution , cdf based nonparametric confidence interval , cumulative distribution function , confidence interval , monotonic function , distribution (mathematics) , sample size determination , poisson regression , statistics , mathematical analysis , probability density function , population , demography , sociology
One–sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov–Smimov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This approximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modelling, and analysis of fault–tolerant systems.