Difference between revisions of "Extreme Spread"
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== Outlier Tests == | == Outlier Tests == | ||
− | = Theoretical <math> | + | = Theoretical <math>FOM</math> Distribution = |
− | + | Assuming that the shots are Rayleigh distributed allows us to make some theoretical estimates. | |
− | |||
{| class="wikitable" | {| class="wikitable" | ||
− | |+ Theoretical <math> | + | |+ Theoretical <math>ES</math> Distribution |
|- | |- | ||
| Parameters Needed | | Parameters Needed | ||
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|- | |- | ||
| <math>PDF(r; \sigma)</math> | | <math>PDF(r; \sigma)</math> | ||
− | | | + | | no direct evaluation, must be simulated via Monte Carlo |
|- | |- | ||
| <math>CDF(r; \sigma)</math> | | <math>CDF(r; \sigma)</math> | ||
− | | | + | | no direct evaluation, must be simulated via Monte Carlo |
|- | |- | ||
| Mode of PDF) | | Mode of PDF) | ||
− | | | + | | depends on <math>n</math>, in general |
|- | |- | ||
| Median of PDF | | Median of PDF | ||
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|- | |- | ||
| Variance | | Variance | ||
− | | | + | | no direct evaluation, must be simulated via Monte Carlo |
|- | |- | ||
| Variance Distribution | | Variance Distribution |
Revision as of 19:09, 5 June 2015
Contents
Experimental Summary
Given |
All of the (h,v) positions do not need to be known so a ragged hole will suffice. |
Assumptions |
|
Data transformation | Identify two holes, \(i, j\) which are the farthest apart. |
Experimental Measure | \(ES = \sqrt{(x_i - x_j)^2 - (y_i - y_j)^2)}\), |
Given
Assumptions
Data transformation
Experimental Measure
Outlier Tests
Theoretical \(FOM\) Distribution
Assuming that the shots are Rayleigh distributed allows us to make some theoretical estimates.
Parameters Needed | |
\(PDF(r; \sigma)\) | no direct evaluation, must be simulated via Monte Carlo |
\(CDF(r; \sigma)\) | no direct evaluation, must be simulated via Monte Carlo |
Mode of PDF) | depends on \(n\), in general |
Median of PDF | |
Mean of PDF | |
Variance | no direct evaluation, must be simulated via Monte Carlo |
Variance Distribution | |
(h,v) for all points? | Yes |
Symmetric about Mean? | No, skewed to larger values.
More symmetric as number of shots increases. |
Parameters Needed
Variance and Its distribution
CDF
Mode, Median, Mean
Outlier Tests
See Also
Dispersion Assumptions - A discussion of the different cases for shot dispersion
Diagonal - A different way of combing horizontal and vertical measurement