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An Analytical Approximation for the Distribution of the Extreme Spread of a Shot Group of N Rounds
Abstract
The purpose of this paper is to propose an analytical approximation for the inverse cumulative distribution function (ICDF) of the bivariate range (commonly referred to in the ballistic community as the extreme spread (ES)) of the circular normal distribution. A proof is given to show that the relative error of this approximation is less than 1.37% for any sample size and any percentile. Monte Carlo simulations are run to verify the results of the analytical approximation. In addition, the exact ICDF for the case of three sample points is determined.
DOI
10.12783/ballistics2019/33131
10.12783/ballistics2019/33131
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