hdr {hdrcde}R Documentation

Highest Density Regions

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 kernel bandwidth is selected using the algorithm of Samworth and Wand (2009).

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.

Value

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.

Author(s)

Rob Hyndman

References

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

Samworth, R.J., and Wand, M.P. (2009). Asymptotics and optimal bandwidth selection for highest density region estimation. Working paper. http://www.uow.edu.au/~mwand/hdrpap.pdf.

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)

[Package hdrcde version 2.13 Index]