Spherical and hyperspherical median {Directional}

Fast calculation of the spherical and hyperspherical median

Description

It calculates, very fast, the (hyper-)spherical median of a sample.

Usage

mediandir(x)
mediandir_2(x)

Arguments

x

The data, a numeric matrix with unit vectors.

Details

The "mediandir" employes a fixed poit iterative algorithm stemming from the first derivative (Cabrera and Watson, 1990) to find the median direction as described by Fisher (1985) and Fisher, Lewis and Embleton (1987). In the big samples this is much much faster than "mediandir_2", since the search is based on iterations.

Value

The median direction.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

Fisher N. I. (1985). Spherical medians. Journal of the Royal Statistical Society. Series B, 47(2): 342–348.

Fisher N. I., Lewis T. and Embleton B. J. (1987). Statistical analysis of spherical data. Cambridge university press.

Cabrera J. and Watson G. S. (1990). On a spherical median related distribution. Communications in Statistics-Theory and Methods, 19(6): 1973–1986.

See Also

nsmedian, vmf.mle, kent.mle

Examples

m <- rnorm(3)
m <- m / sqrt( sum(m^2) )
x <- rvmf(100, m, 10)
mediandir(x)
mediandir_2(x)
nsmedian(x)