max.depth {lsdepth}R Documentation

Maximum Depth

Description

Calculates the maximum location-scale depth and the location-scale parameter with maximum depth

Usage


  distribution.max.depth(qdist=function(x){qnorm(x,0,1)}, pdist=function(x){pnorm(x,0,1)},
           d.min=1/3,lengthbeta=100,iter=10,eps=0.001)

  sample.max.depth(y,iter=100,eps=0.0001,p.length=10)

Arguments

qdist quantile function of the distribution, default is the quantile function of the standard normal distribution.
pdist distribution function of the distribution, default is the distribution function of the standard normal distribution.
y numerical vector of observations (data set)
d.min a value which is known to be smaller than the maximum depth.
lengthbeta length of the vector for calculating the upper and lower bound for the contour for a given location parameter. The larger lengthbeta the more precise are the bounds.
iter number of iterations.
eps precision of location and scale with maximum depth.
p.length maximum number of interations in a final precision step.

Details

distribution.max.depth calculates the maximum depth and the parameter pair of location and scale with maximum depth for a distribution (population). sample.max.depth calculates the maximum depth and the maximum depth estimator for location and scale for a sample (data set).

Value

Both functions return a vector with the following components: "max.depth" is the maximum depth, a value in (0,1) for distributions and an integer smaller than the sample size for samples "mu" is the location with maximum depth, "sigma" is the scale with maximum depth.

Author(s)

Christine Müller, mueller@math.uni-oldenburg.de

References

Mizera, I. and Müller, C.H. (2003). Location-scale depth.

See Also

distribution.depth.contours, sample.depth.contours, distribution.max.depth.line, sample.max.depth.line

Examples

 
 distribution.max.depth(qdist=function(x){qt(x,1)},pdist=function(x){pt(x,1)},iter=50)

  y<-rt(100,1)
  sample.max.depth(y=y,iter=50)
  

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