Computational Analysis Of The Q-Function For Intermediate To Large Parameter Range

Abstract

Cantrell has developed a very efficient algorithm using ParI's method for accurately calculating the generalized Q-function Qₘ(α,β). ParI's method using floating formats with the exponent larger than However; only values of m up to about 100 could be studied using the Real*8 floating point format. An investigation into the range in >100 is made. Real*8 F-floating are run to determine the limitations of the Parl method. Results are presented in this range of m using other floating point formats and Rice's asymptotic expansion for the non-central chi-square distribution and the probability of detection for a classical multi-observation detection problem. Also, plots of number of significant figures of the Rice uniform asmptotic expansion for different iterations verses m are given. Finally, a comparison of CPU time required for the Parl method and the Rice algorithm are presented for each iteration used in the significant figure plots.