Extreme Spread
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