Calculating spherical medians

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Description

Computes the spherical median of a data set on the circle.

Usage

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smed(P, sort=FALSE, depths=NULL, alpha=NULL,
   method="Tukey", tracecontour=FALSE, tracepoints=FALSE)

Arguments

P

The data as a vector, a matrix, a data frame or a list.

sort

Logical; TRUE indicates that the data in P is already sorted.

depths

For Tukey's method only; An optionnal vector of the same length as P that contains the Tukey depth of each data. The calculation of the depth is then skipped and the provided values are used instead.

alpha

For Tukey's method only; alpha is an optionnal numeric value between 0 and 1 to compute the median on a trimmed region rather than on the whole dataset. The trimming keeps only those points with a depth greater than or equal to alpha. The default value of NULL computes the median from the maximum depth trimmed region (i.e. no trimming).

method

Character string which determines the depth function used. method can be "Tukey" (the default) or "Circular".

tracecontour

Only if method="Circular". Traces the plot of depth with respect to angular positions on the circle.

tracepoints

Only if method="Circular". Draws the points and their median on the circle.

Details

Calculates shperical medians for data on the circle only. The input must be a list of angles in radians between 0 and (polar coordinates). If method="Tukey", the Tukey median is returned. If method="Circular", the circular median (the point minimizing the average distance based on arccosine) is returned.

Value

A numeric value between 0 and giving the median in polar coordinate.

Author(s)

Maxime Genest.

References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783–858.

Mardia, K.V. and Jupp, E.J. (1999). Directional Statistics, Wiley.

See Also

sdepth for calculation of the depth of a point, scontour for Tukey's spherical median.

Examples

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## calculation of the Tukey spherical median for data on the circle
set.seed(2011)
smed(runif(30,min=0,max=2*pi))