Update and Further Discussion of Past Codes for Exact Confidence Intervals for Paired Counting Using Modified Bessel Functions of Integral Order
W. E. Potter
The relationship between the exact probability distribution for the net count for paired counting and modified Bessel functions of integral order provides a powerful technique to determine Neyman-Pearson confidence intervals. Upon taking the background count close to zero, confidence intervals for the Poisson distribution can also be readily determined. The original code for 95% confidence intervals of the form [0, xx.xx] for low-level, paired counting was extended to 100 background counts and 100 observed net counts for arbitrary confidence levels in the interval [50%, 99.9%]. Also the search for xx.xx was automated. For computer systems that do not set exponent underflow equal to zero, this code can be improved for background counts close to zero by having the C++ computer code limit the number of terms in the left tail when the background count approaches zero. Subsequently this code has been extended to confidence intervals of the form [yy.yy, xx.xx]. Utilizing long double precision arithmetic, the code described above can be further extended to 1000 background counts and 1000 observed net counts. Modified Bessel functions of integral order are computed using a power series with 1800 terms. Because of the wider range of values supported by the long double type, exponent underflow is not an important issue for this code.
This abstract was presented at the 35th Annual Midyear Meeting, "Decommissioning and Environmental Restoration", Poster Session, 2/17/2002 - 2/20/2002, held in Orlando, FL.