(TI-59) Approximating the Circular Coverage function

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An excerpt from On Approximating the Circular Coverage Function, Professional Paper No. 211, Center for Naval Analysis, ADA054429, 1976

                             ABSTRACT

     This paper presents tables and graphs assessing the accuracy of a formula (programmable on a desk calculator) for approximating the circular coverage function of a circular-normal probability distribution. Use of this formula together with the error curves presented here enable one to calculate the circular coverage function with a maximum error on the order of 0.0002 for offsets up to 5σ and covering-circle radii up to 4.5σ.
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EVALUATION OF THE FUNCTION
     Extensive tables of this function are available … However, it is more convenient to use closed-form approximation that can be programmed on a desk calculator if the accuracy desired is not too high. …
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     The formula for P can be programmed on a TI-59 calculator using 127 steps (table 1). The approximation used for the normal distribution Q(x) is (reference 6): …
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     In conclusion, the programmable formula for the circular coverage function, together with figures 1 and 2, enables one to evaluate the function with a maximum error on the order of .0002 for 0 ≤ R' ≤ 4.5 and 0 ≤ r' ≤ 5.

                                                    TABLE 1
                    TI-59 PROGRAMS FOR CIRCULAR COVERAGE OF A
                              CIRCULAR NORMAL DISTRIBUTION  …
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