User:Herb
My notion of sidebar:
- [What is precision?]
- Dispersion Assumptions
- Measuring Precision
- References
- Examples
Measurements
Derivation of the Rayleigh Distribution Equation
--- Carnac the Magnificent
sighting shot distribution
The Mean Radius is the average distance over all shots to the groups center.
Given |
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Assumptions |
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Data Pretreatment | Shot impact positions converted from Cartesian Coordinates (h, v) to Polar Coordinates \((r,\theta)\)
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Experimental Measure | \(\bar{r_n}\) - the average radius of n shots
\(\bar{r_n} = \sum_{i=1}^n r_i / n\) |
\(PDF_{r_0}(r; n, \sigma)\) | \(\frac{nr}{\sigma^2}e^{-nr^2/2\sigma^2}\) |
\(CDF_{r_0}(r; n, \sigma)\) | \(1 - e^{-nr^2/2\sigma^2}\) |
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 |