Inverse of the Generalized Circular Error Function

摘要

This report describes an algorithm, INGCE, to evaluate an inverse of the generalized circular error function, GCE, also known as the elliptical normal function. Given a two-dimensional normal distribution function with mean zero and standard deviations u, v with a circular target T centered at the mean; R, the radius of T, is determined for a specified probability, P, of a shot falling in T. A Fortran 77 subroutine, INVGCE, is available that is based on INGCE, which produces K (R=Ku) to eight significant digits for 10(exp -8) less than or equal to P less than or equal to 1 - 10(exp -8) and 0 less than or equal to c = v/u less than or equal to 1. A table of K versus P and c is included. The appendix contains a 22-page table that shows the tabulation of K as a function of P and c.