Difference between revisions of "Closed Form Precision"
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[[Measuring Precision]] showed how a single parameter ''σ'' characterizes the precision of a shooting system. | [[Measuring Precision]] showed how a single parameter ''σ'' characterizes the precision of a shooting system. | ||
| − | This ''σ'' is the parameter for the Rayleigh distribution with probability density function < | + | This ''σ'' is the parameter for the Rayleigh distribution with probability density function <math>\frac{x}{\sigma^2}e^{-x^2/2\sigma^2}</math>. |
Using the characteristics of the Rayleigh distribution we can immediately compute the three most useful [[Describing_Precision#Measures|precision measures]]: | Using the characteristics of the Rayleigh distribution we can immediately compute the three most useful [[Describing_Precision#Measures|precision measures]]: | ||
| − | Radial Standard Deviation < | + | Radial Standard Deviation <math>RSD = \sigma \sqrt{2}</math>. The expected sample RSD of a group of size ''n'' is |
| − | :< | + | :<math>RSD_n = \sigma \sqrt{\frac{2}{c_{G}(n)}} \approx \sigma \sqrt{2 - \frac{1}{2n} - \frac{7}{16n^2} - \frac{19}{64n^3}}</math> |
| − | Mean Radius < | + | Mean Radius <math>MR = \sigma \sqrt{\frac{\pi}{2}}</math>. The expected sample MR of a group of size ''n'' is |
| − | :< | + | :<math>MR_n = \sigma \sqrt{\frac{\pi}{2 c_{B}(n)}}\ = \sigma \sqrt{\frac{\pi (n - 1)}{2 n}}</math> |
| − | Circular Error Probable < | + | Circular Error Probable <math>CEP = \sigma \sqrt{\ln(4)}</math> |
Revision as of 12:21, 19 November 2013
Measuring Precision showed how a single parameter σ characterizes the precision of a shooting system.
This σ is the parameter for the Rayleigh distribution with probability density function \(\frac{x}{\sigma^2}e^{-x^2/2\sigma^2}\).
Using the characteristics of the Rayleigh distribution we can immediately compute the three most useful precision measures:
Radial Standard Deviation \(RSD = \sigma \sqrt{2}\). The expected sample RSD of a group of size n is \[RSD_n = \sigma \sqrt{\frac{2}{c_{G}(n)}} \approx \sigma \sqrt{2 - \frac{1}{2n} - \frac{7}{16n^2} - \frac{19}{64n^3}}\]
Mean Radius \(MR = \sigma \sqrt{\frac{\pi}{2}}\). The expected sample MR of a group of size n is \[MR_n = \sigma \sqrt{\frac{\pi}{2 c_{B}(n)}}\ = \sigma \sqrt{\frac{\pi (n - 1)}{2 n}}\]
Circular Error Probable \(CEP = \sigma \sqrt{\ln(4)}\)
