Prior Art

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Grubbs, 1964, Statistical Measures of Accuracy for Riflemen and Missile Engineers

Statistical Measures of Accuracy for Riflemen and Missile Engineers, Frank Grubbs, 1964: Often referenced, but we haven't been able to find a manuscript. If anyone can share one please contact [[1]]!

Hogema, 2005, Shot group statistics

Jeroen Hogema provides an accessible proof of the equivalence between the symmetric bivariate normal and Rayleigh distributions. He provides extensive examples, simulations, and applications to scoring and load selection, and begins to address the problem of estimating the Rayleigh parameter.

Leslie, 1993, Is "Group Size" the Best Measure of Accuracy?

Is "Group Size" the Best Measure of Accuracy?, John "Jack" E. Leslie III, 1993. Notes:

  • Extreme Spread: Maximum distance between any two shots in group. Note that this effectively only uses two data points.
  • Figure of Merit (FOM): Average of the maximum horizontal group spread and the maximum vertical group spread. This uses only 2-4 data points depending on the group.
  • Mean Radius: Average distance to center of group for all shots.
  • Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).
  • Found military using RSD and Mean Radius as early a 1918.

His Monte Carlo analysis shows sample RSD to be most accurate predictor of accuracy, followed closely by Mean Radius. I.e., they can distinguish between loads of different inherent accuracy more accurately and using fewer shots than the other measures.

Siddiqui, 1961, Some Problems Connected With Rayleigh Distributions

Some Problems Connected With Rayleigh Distributions, M. M. Siddiqui, 1961.

Siddiqui, 1964, Statistical Inference for Rayleigh Distributions

Statistical Inference for Rayleigh Distributions, M. M. Siddiqui, 1964. Summarizes and extends Siddiqui, 1961.