getConfEll: Confidence ellipse

Description

Gives the 2D-confidence ellipse under the assumption of bivariate normality. Also includes the ellipse based on a robust estimate for the covariance matrix of the (x,y)-coordinates.

Usage

getConfEll(xy, level = 0.5, dstTarget = 25, conversion = 'm2cm', doRob=TRUE)

Arguments

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

level

a numerical value with the coverage for the confidence ellipse.

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.

doRob

logical: should robust covariance matrix estimate also be used?

Value

A list with the confidence ellipse measures.
sizea numerical matrix with the length of the semi-major and semi-minor axis of the ellipse (in original measurement units and MOA).
sizeRoba numerical matrix with the length of the semi-major and semi-minor axis of the ellipse based on a robust estimate for the covariance matrix of (x,y)-coordinates (in original measurement units and MOA).
shapea numerical vector with the aspect ratio and the flattening of the ellipse.
shapeRoba numerical vector with the aspect ratio and the flattening of the ellipse based on a robust estimate for the covariance matrix of (x,y)-coordinates.
magFacmagnification factor used to turn the error ellipse into the confidence ellipse as determined by the F(2, n-1)-distribution.

Details

Robust estimate for the covariance matrix of (x,y)-coordinates is from covMcd using the MCD algorithm. See getCEP for estimates of the circular error probable.

Examples

Run this code

xy  <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
(ce <- getConfEll(xy, level=0.5, dstTarget=25,
                  conversion='m2cm'))

# plot points, center, parametric confidence
# ellipse, and its axes
ctr    <- colMeans(xy)            # center point
eigVec <- eigen(cov(xy))$vectors  # eigenvectors
eigScl <- eigVec %*% diag(ce$size["unit", ])

# matrix with scaled ellipse axes
xMat <- rbind(ctr[1] + eigScl[1, ], ctr[1] - eigScl[1, ])
yMat <- rbind(ctr[2] + eigScl[2, ], ctr[2] - eigScl[2, ])

plot(xy, asp=1, pch=16)
drawEllipse(ctr, cov(xy), radius=ce$magFac, fg="blue")
matlines(xMat, yMat, lty=1, col="blue")
points(ctr[1], ctr[2], pch=4, col="red", cex=2)