depth.contours {lsdepth}R Documentation

Location-Scale Depth Contours

Description

Calculates and plots location-scale depth contours based on Student depth for distributions (populations) and samples (data sets).

Usage

   distribution.depth.contours(depth=c(0.1,0.2,0.3,0.4),qdist=function(x){qnorm(x,0,1)}, 
                   pdist=function(x){pnorm(x,0,1)},lengthmu=100,lengthbeta=100)  

  sample.depth.contours(depth=round(c(0.1,0.2,0.3,0.4)*length(y)),y,lengthmu=1000)

  plot.depth.contours(depth.cont,ratio=1,first.plot=T,mu.min=0,mu.max=0)

Arguments

depth numerical vector of depth values in (0,0.5) for distributions, integer vector of depth values within 1 and sample size for samples
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)
lengthmu length of the vector of location parameters for which upper and lower bounds of the contour are calculated. The larger lengthmu is the smoother are the contour lines.
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.
depth.cont a list given as output of distribution.depth.contours or of sample.depth.contours.
ratio ratio of the lengths of the location and scale axes.
first.plot if first.plot=T (default) a new plot is generated, if first.plot=F the plot is added to an existing plot.
mu.min minimum value of the location axis. If mu.min==mu.max (default) then the minimu and maximum value of the location axis is determined by the location vector of the first list component of depth.cont.
mu.max maximum value of the location axis. Compare mu.min.

Details

distribution.depth.contours calculates the upper and lower bounds of the depth contours of a distribution (population).

sample.depth.contours calculates the the upper and lower bounds of the depth contours of a sample (data set).

plot.depth.contours plots the contours given by distribution.depth.contours or sample.depth.contours .

Value

Return value of distribution.depth.contours and sample.depth.contours is a list. Each component of the list is list with the following components: depth provides the depth, cont.exist a logical value whether a contour for the depth exists. If it is TRUE then the list has the further components: mubound a vector of location values, lbound a vector of the lower bounds of the scale values and ubound a vector of of the upper bounds of the scale values.
plot.depth.contours has no return value.

Author(s)

Christine Müller (mueller@math.uni-oldenburg.de)

References

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

See Also

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

Examples


 cauchy.depth.contours<-distribution.depth.contours(qdist=function(x){qt(x,1)},pdist=function(x){pt(x,1)}, lengthmu=1000)
 plot.depth.contours(cauchy.depth.contours)

 y<-rt(100,1)
 y.depth.contours<-sample.depth.contours(y=y,lengthmu=1000)
 plot.depth.contours(y.depth.contours)
 

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