Computer Codes for Special Case of Counting: Exact Decision Levels, Errors of the First Kind, and Probability Density Function

摘要

In the past exact computations utilizing modified Bessel functions of integral order have been discussed for decision levels in paired counting. This paper transforms the net count to an integer and assumes that the blank count is Poisson distributed with known expected value. Utilizing the Poisson probability density function, a function in C++ is written to compute the exact probability density function for the transformed net count when it is less than zero, equal to zero and greater than zero. The validity of the computation is then checked by summing probabilities over a wide range of transformed net counts and comparing to 1.0 and by computing the expected transformed net count and comparing to 0.0. A decision level is determined by summing the right tail of the probability density function and inverting from a transformed net count to a net count. Codes were written in both double precision arithmetic and long double precision arithmetic. The double precision code is found to be adequate for most applications.