# sdepth: Calculation of spherical depth In depth: Nonparametric Depth Functions for Multivariate Analysis

## Description

Computes the spherical depth of a point with respect to a multivariate data set. Supports data on the circle or on the sphere.

## Usage

 `1` ```sdepth(theta, P) ```

## Arguments

 `theta` Numerical vector whose depth is to be calculated. The coordinate system must match that of the observations. `P` The data as a vector, a matrix, a data frame or a list.

## Details

Computes the Tukey depth of `theta` with respect to the dataset `P`. For data on the circle, data must be expressed in polar coordinates as a angle in radians with values between 0 and . Data on the sphere can be expressed in Euclidean coordinates (n by 3 matrix) or in spherical coordinates (n by 2 matrix) where the first column contains θ and the second column φ. The type of coordinates is determined automatically based on the dimensions of the input.

## Value

Returns the spherical depth of multivariate point `theta` with respect to the data set `P`.

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.

`scontour` for depth graphics, `smed` for Tukey's spherical median.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## Tukey spherical depth for a dataset on the circle set.seed(2011) sdepth(pi,runif(50,min=0,max=2*pi)) ## Tukey spherical depth for data in spherical coordinates. sdepth(c(pi,pi/2),cbind(runif(50,min=0,max=2*pi),runif(50,min=0,max=pi))) ## Tukey spherical depth for data in Eudlidean coordinates. x=matrix(rnorm(150),ncol=3) x=t(apply(x,1,function(y){y/sqrt(sum(y^2))})) sdepth(x[1,],x) ```