User:Herb

Dispersion Assumptions

MediaWiki:Sidebar

My notion of sidebar:

• Introduction
• Dispersion

   Models

• References
• Examples

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Measurements

Extreme Spread

Figure of Merit

Mean Radius

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Sighting a Weapon

Derivation of the Rayleigh Distribution Equation

Measuring Precision

Fliers vs. Outliers

--- Carnac the Magnificent

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sighting shot distribution

The Mean Radius is the average distance over all shots to the groups center.

Given	set of n shots {\( (h_1, v_1), (h_2, v_2), ..., (h_n, v_n) \)} for which all of the (h,v) positions are known
Assumptions	Origin at \((r,\theta) = (0,0)\) Rayleigh Distribution for Shots \(\sigma_h = \sigma_v\) \(\rho = 0\) \(PDF_{r_i}(r) = \frac{r}{\sigma^2}e^{-r^2/2\sigma^2}\) With conversion from Cartesian coordinates to Polar coordinates, \(\theta\) will be entirely random and independent of radius No Flyers
Data Pretreatment	Shot impact positions converted from Cartesian Coordinates (h, v) to Polar Coordinates \((r,\theta)\) Origin translated from Cartesian Coordinate (\(\bar{h}, \bar{v}\)) to Polar Coordinate \((r = 0, \theta = 0)\)
Experimental Measure	\(\bar{r_n}\) - the average radius of n shots \(\bar{r_n} = \sum_{i=1}^n r_i / n\)     where \(r_i = \sqrt{(h_i - \bar{h})^2 + (v_i - \bar{v})^2}\)
\(PDF_{r_0}(r; n, \sigma)\)	\(\frac{nr}{\sigma^2}e^{-nr^2/2\sigma^2}\)
\(CDF_{r_0}(r; n, \sigma)\)	\(1 - e^{-nr^2/2\sigma^2}\)
Mode of PDF(\(\bar{r_n}\))	\( \frac{\sigma}{\sqrt{n}}\)
Median of PDF(\(\bar{r_n}\))	\( \frac{\sigma}{\sqrt{n}}\sqrt{ln{(4)}}\)
Mean of PDF(\(\bar{r_n}\))	\( \frac{\sigma}{\sqrt{n}}\sqrt{\frac{\pi}{2}}\)
(h,v) for all points?	Yes
Symmetric about Measure?
NSPG Invariant	No
Robust	No