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Prior Art details previous work on the problem of estimating shooting statistics.

CEP literature focuses on the broader body of work related to characterizing Circular Error Probable, which is applicable not only to ballistics but also to fields like navigation and signal processing.

Following is a complete list of useful References and Prior Art:

Important Note on Siddiqui: Siddiqui parameterizes the Rayleigh distribution with \(\frac{\sigma}{\sqrt{2}}\). Therefore, should you endeavor to relate Siddiqui's work to that referenced here and in more modern usage, remember that \(\sigma_{modern} = \sqrt{2} \sigma_{Siddiqui}\).

Reference Data

  • File:Sigma1RangeStatistics.xls: Simulated median, 50%, 80%, and 95% quantiles, plus first four sample moments, for shot groups containing 2 to 100 shots, of: Extreme Spread, Diagonal, Figure of Merit.

BallisticSimulations.ipynb is a Jupyter notebook containing extensive illustrations and validation of the math used throughout this site.