max.depth.line {lsdepth}R Documentation

Lines with maximum depth and MAD depending on the location

Description

Calculates and plots lines of scale parameters with maximum depth for given location parameters and the lines of MAD with respect to given location parameters for distributions (populations) and samples (data sets).

Usage


distribution.max.depth.line(qdist=function(x){qnorm(x,0,1)}, pdist=function(x){pnorm(x,0,1)},mu.min,mu.max,
        lengthmu=50,d.min=0.05,lengthbeta=100,iter=50,eps=0.0001)

distribution.MAD(qdist=function(x){qnorm(x)}, pdist=function(x){pnorm(x)},mu=qdist(0.5),sym=F, 
       iter=100,eps=0.00000001)

distribution.MAD.line(qdist=function(x){qnorm(x)}, pdist=function(x){pnorm(x)},mu.min,mu.max,
       lengthmu=100,sym=F, iter=100,eps=0.00000001)

sample.max.depth.line(y,mu.min,mu.max,mu.values=T,lengthmu=100,iter=100,eps=0.0000001)

sample.MAD.line(y,mu.min,mu.max,mu.values=T,lengthmu=100)

add.max.depth.MAD.lines(max.depth.line=NULL,MAD.line=NULL)

 

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.
mu location parameter from which the MAD is calculated, default is the median.
y numerical vector of observations (data set)
mu.min minimum value for the location parameters.
mu.max maximum value for the location parameters.
mu.values logical value where mu.min and mu.max are calculated from the data set if mu.values=T (default) otherwise the values must be 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 the line is.
d.min a value which is known to be smaller than the maximum depth for all used locations.
lengthbeta length of the vector for calculating the upper and lower bound for the contour for a given location parameter and depth. The larger lengthbeta the more precise are the bounds.
iter number of iterations for each location parameter.
eps precision of scale with maximum depth for a given location parameter.
sym if sym=T, then it is a symmetric distribution and mu is assumed to be the median.
max.depth.line a list given by distribution.max.depth.line or sample.max.depth.line. This list must have components mu and s.mu where each components consist of a vector of same length. If max.depth.line=NULL, (default) then the maximum depth line is not plotted.
MAD.line a list given by distribution.MAD.line or sample.MAD.line. This list must have components mu and MAD where each components consist of a vector of same length. If MAD=NULL, (default) then the maximum depth line is not plotted.

Details

distribution.max.depth.line calculates scale parameters with maximum depth for several locations parameters for distributions.

distribution.MAD calculates the median of absolute deviations from a given location parameter for distributions.

distribution.MAD.line calculates the median of absolute deviations from several location parameters for distributions.

sample.max.depth.line calculates scale parameters with maximum depth for several locations parameters for samples (data sets).

distribution.MAD.line calculates the median of absolute deviations from several location parameters for samples (data sets).

The number of used locations parameters is given by lengthmu and the location parameters are lying equispaced in the interval from mu.min to mu.max.

add.max.depth.MAD.lines adds the lines given by distribution.max.depth.line, distribution.MAD.line or sample.max.depth.line, distribution.MAD.line to an existing contour plot.

Value

Return value of distribution.max.depth.line and sample.max.depth.line is a list with the following components: mu a vector of location parameters, s.mu a vector with corresponding scale parameters with maximum depth.
Return value of distribution.MAD.line and sample.MAD.line is a list with the following components: mu a vector of location parameters, MAD a vector with corresponding MAD's.
add.max.depth.MAD.lines 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.depth.contours, sample.depth.contours, distribution.max.depth, sample.max.depth

Examples


 normal.depth.contours<-distribution.depth.contours(lengthmu=1000)
 plot.depth.contours(normal.depth.contours)
 normal.max.depth.line<-distribution.max.depth.line(mu.min=-1.5,mu.max=1.5,lengthmu=100)
 normal.MAD.line<-distribution.MAD.line(mu.min=-1.5,mu.max=1.5,lengthmu=100)
 add.max.depth.MAD.lines(normal.max.depth.line)
 add.max.depth.MAD.lines(MAD.line=normal.MAD.line)

 y<-rt(100,1)
 y.depth.contours<-sample.depth.contours(y=y,lengthmu=1000)
 plot.depth.contours(y.depth.contours)
 y.max.depth.line<-sample.max.depth.line(y=y)
 y.MAD.line<-sample.MAD.line(y=y)
 add.max.depth.MAD.lines(y.max.depth.line,y.MAD.line)

 

[Package Contents]