Calculate the area of ​​a 2-dimensional ellipsoid in R

Question

So, I have data converted to a log converted to a simple table:

      x         y
1.158362492 1.322219295
1.1430148   1.267171728
1.11058971  1.252853031
1.120573931 1.260071388
1.149219113 1.278753601
1.123851641 1.276461804
1.096910013 1.222716471

I know that there are functions for building a confidence ellipse for this data, but how to calculate the area of ​​the generated shape?

thank

Answer 1

First calculate the ellipse, then determine the lengths of the main and auxiliary axes, and then calculate the area .

Here's a brainless approach.

Firstly, your data.

dat <- structure(list(x = c(1.158362492, 1.1430148, 1.11058971, 1.120573931, 
          1.149219113, 1.123851641, 1.096910013), y = c(1.322219295, 1.267171728, 
          1.252853031, 1.260071388, 1.278753601, 1.276461804, 1.222716471
          )), .Names = c("x", "y"), class = "data.frame", row.names = c(NA, 
          -7L))

Then download the package car; dataEllipsecan be used to calculate an ellipse using two-dimensional normal data approximation.

require(car)
dataEllipse(dat$x, dat$y, levels=0.5)

ellipse , dataEllipse .

me <- apply(dat, 2, mean)
v <- var(dat)
rad <- sqrt(2*qf(0.5, 2, nrow(dat)-1))
z <- ellipse(me, v, rad, segments=1001)

.

dist2center <- sqrt(rowSums((t(t(z)-me))^2))

- . , .

pi*min(dist2center)*max(dist2center)

Answer 2

mclust, mvn_plot, mean std. , .