Open AccessErratum: Improved approximations of Poissonian errors for high confidence levels
Author(s) -
Ebeling Harald
Publication year - 2004
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2004.07692.x
Subject(s) - physics , gaussian , poisson distribution , confidence interval , convergence (economics) , mathematics , approximations of π , statistics , standard deviation , confidence region , statistical physics , algorithm , quantum mechanics , economics , economic growth
We present improved numerical approximations to the exact Poissonianconfidence limits for small numbers n of observed events following the approachof Gehrels (1986). Analytic descriptions of all parameters used in theapproximations are provided to allow their straightforward inclusion incomputer algorithms for processing of large data sets. Our estimates of theupper (lower) Poisson confidence limits are accurate to better than 1% forn<100 and values of S, the derived significance in units of Gaussian standarddeviations, of up to 7 (5). In view of the slow convergence of the commonlyused Gaussian approximations toward the correct Poissonian values, inparticular for higher values of S, we argue that, for n<40, Poissonianstatistics should be used in most applications, unless errors of the order of,or exceeding, 10% are acceptable.Comment: 12 pages, 8 figures, MNRAS in pres