Calculate Zonoid Depth
Calculates the zonoid depth of points w.r.t. a multivariate data set.
depth.zonoid(x, data, seed = 0)
x |
Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a d-variate point. Should have the same dimension as |
data |
Matrix of data where each row contains a d-variate point, w.r.t. which the depth is to be calculated. |
seed |
the random seed. The default value |
Calculates zonoid depth (Koshevoy and Mosler, 1997; Mosler, 2002) exactly based on the algorithm of Dyckerhoff, Koshevoy and Mosler (1996), implemented in C++ (and provided) by Rainer Dyckerhoff.
Numerical vector of depths, one for each row in x; or one depth value if x is a numerical vector.
Dyckerhoff, R., Koshevoy, G., and Mosler, K. (1996). Zonoid data depth: theory and computation. In: Prat A. (ed), COMPSTAT 1996. Proceedings in computational statistics, Physica-Verlag (Heidelberg), 235–240.
Koshevoy, G. and Mosler, K. (1997). Zonoid trimming for multivariate distributions Annals of Statistics 25 1998–2017.
Mosler, K. (2002). Multivariate dispersion, central regions and depth: the lift zonoid approach Springer (New York).
depth.halfspace for calculation of the Tukey depth.
depth.Mahalanobis for calculation of Mahalanobis depth.
depth.projection for calculation of projection depth.
depth.simplicial for calculation of simplicial depth.
depth.simplicialVolume for calculation of simplicial volume depth.
depth.spatial for calculation of spatial depth.
depth.potential for calculation of data potential.
# 5-dimensional normal distribution
data <- mvrnorm(1000, rep(0, 5),
matrix(c(1, 0, 0, 0, 0,
0, 2, 0, 0, 0,
0, 0, 3, 0, 0,
0, 0, 0, 2, 0,
0, 0, 0, 0, 1),
nrow = 5))
x <- mvrnorm(10, rep(1, 5),
matrix(c(1, 0, 0, 0, 0,
0, 1, 0, 0, 0,
0, 0, 1, 0, 0,
0, 0, 0, 1, 0,
0, 0, 0, 0, 1),
nrow = 5))
depths <- depth.zonoid(x, data)
cat("Depths: ", depths, "\n")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.