shotGroups (version 0.2-2)

getCEP: Circular error probable (CEP)

Description

Gives the Rayleigh and the modified RAND R-234 estimate for the circular error probable. CEP is defined as the radius of the circle to contain a certain fraction of points of impact.

Usage

getCEP(xy, dstTarget = 25, conversion = 'm2cm')

Arguments

xy

a numerical (n x 2)-matrix with the (x,y)-coordinates of n points (1 row of coordinates per point).

dstTarget

a numerical value with the distance to the target in MOA calculation. See getMOA.

conversion

how to convert the measurement unit for distance to target to that of the (x,y)-coordinates in MOA calculation. See getMOA.

Value

• A list with the CEP estimates.
• RAND
  a numerical matrix with the modified RAND R-234 estimate for the CEP at levels 50%, 90%, and 95% (in original measurement units and MOA).
• Rayleigh
  a numerical matrix with the Rayleigh estimate for the CEP at levels 50%, 90%, and 95% (in original measurement units and MOA).
• ellShape
  a numerical vector with the aspect ratio and the flattening of the error ellipse.

Details

The 50%-CEP estimate based on the Rayleigh distribution is a constant fraction of the mean distance to center. The modified RAND R-234 estimate for the 50%-CEP is a weighted sum of the square root of the eigenvalues of the covariance matrix of (x,y)-coordinates. These are the standard deviations of the two principal components of the data. For zero correlation and equal variances of x- and y-coordinates, the RAND estimate is very similar to the radius of the parametric 50%-confidence ellipse under the assumption of bivariate normality. The estimates for 90% and 95% are based on table 3 in the reference given below.

References

McMillan, C. and McMillan, P. 2008. Characterizing rifle performance using circular error probable measured via a flatbed scanner. http://statshooting.com/

See Also

getConfEll

Examples

xy   <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
(cep <- getCEP(xy, dstTarget=25, conversion='m2cm'))

# plot points, center and circles indicating 90\%-CEP estimates
ctr <- colMeans(xy)             # center point
plot(xy, pch=16, asp=1)
drawCircle(ctr[1], ctr[2], cep$RAND["unit", "50%"], fg='blue')
drawCircle(ctr[1], ctr[2], cep$RAND["unit", "90%"], fg='green3')
points(ctr[1], ctr[2], pch=4, col="red", cex=2)
legend(x="bottomleft", legend=c("RAND 50", "RAND 90", "center"),
       col=c("blue", "green3", "red"), lwd=c(2, 2, 2),
       lty=c(1, 1, NA), pch=c(NA, NA, 4), bg="white")