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hdr {hdrcde}

Highest Density Regions
Package: 
hdrcde
Version: 
3.1

Description

Calculates and plots highest density regions in one dimension including the HDR boxplot.

Usage

hdr(x, prob = c(50, 95, 99), den, h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, 
    nn=5000, all.modes=FALSE)
hdr.den(x, prob = c(50, 95, 99), den, h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, 
    xlab=NULL, ylab="Density", ...)
hdr.boxplot(x, prob = c(99, 50), h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, 
    boxlabels = "", col = gray((9:1)/10), main="", xlab="", ylab="", pch=1, ...)

Arguments

x
Numeric vector containing data. In hdr and hdr.den, if x is missing then den must be provided, and the HDR is computed from the given density. For hdr.boxplot, x can be a list containing several vectors.
prob
Probability coverage required for HDRs
den
Density of data as list with components x and y. If omitted, the density is estimated from x using density.
h
Optional bandwidth for calculation of density.
lambda
Box-Cox transformation parameter where 0 <= lambda <= 1.
nn
Number of random numbers used in computing f-alpha quantiles.
all.modes
Return all local modes or just the global mode?
boxlabels
Label for each box plotted.
col
Colours for regions of each box.
main
Overall title for the plot.
xlab
Label for x-axis.
ylab
Label for y-axis.
pch
Plotting character.
...
Other arguments passed to plot.

Details

Either x or den must be provided. When x is provided, the density is estimated using kernel density estimation. A Box-Cox transformation is used if lambda!=1, as described in Wand, Marron and Ruppert (1991). This allows the density estimate to be non-zero only on the positive real line. The default kernel bandwidth h is selected using the algorithm of Samworth and Wand (2010).

Hyndman's (1996) density quantile algorithm is used for calculation. hdr.den plots the density with the HDRs superimposed. hdr.boxplot displays a boxplot based on HDRs.

Values

hdr.boxplot retuns nothing. hdr and hdr.den return a list of three components:

hdr
The endpoints of each interval in each HDR
mode
The estimated mode of the density.
falpha
The value of the density at the boundaries of each HDR.

References

Hyndman, R.J. (1996) Computing and graphing highest density regions. American Statistician, 50, 120-126.

Samworth, R.J. and Wand, M.P. (2010). Asymptotics and optimal bandwidth selection for highest density region estimation. The Annals of Statistics, 38, 1767-1792. Wand, M.P., Marron, J S., Ruppert, D. (1991) Transformations in density estimation. Journal of the American Statistical Association, 86, 343-353.

See Also

hdr.boxplot.2d

Examples

# Old faithful eruption duration times
hdr(faithful$eruptions)
hdr.boxplot(faithful$eruptions)
hdr.den(faithful$eruptions)
 
# Simple bimodal example
x <- c(rnorm(100,0,1), rnorm(100,5,1))
par(mfrow=c(1,2))
boxplot(x)
hdr.boxplot(x)
par(mfrow=c(1,1))
hdr.den(x)
 
# Highly skewed example
x <- exp(rnorm(100,0,1))
par(mfrow=c(1,2))
boxplot(x)
hdr.boxplot(x,lambda=0)

Author(s)

Rob J Hyndman

Documentation reproduced from package hdrcde, version 3.1. License: GPL (>= 2)