hdrconf: HDRs with confidence intervals

Description

Calculates Highest Density Regions with confidence intervals.

Usage

hdrconf(x, den, prob = 95, conf=95)

Arguments

Numeric vector containing data.

den

Density of data as list with components x and y.

prob

Probability coverage for for HDRs.

conf

Confidence for limits on HDR.

Value

hdrconf returns list containing the following components:
hdrHighest density regions
hdr.loHighest density regions corresponding to lower confidence limit.
hdr.hiHighest density regions corresponding to upper confidence limit.
falphaValues of $f_\alpha$ corresponding to HDRs.
falpha.ciValues of $f_\alpha$ corresponding to lower and upper limits.

References

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

Examples

Run this code

x <- c(rnorm(100,0,1),rnorm(100,4,1))
den <- density(x,bw=hdrbw(x,50))
trueden <- den
trueden$y <- 0.5*(exp(-0.5*(den$x*den$x)) + exp(-0.5*(den$x-4)^2))/sqrt(2*pi)
sortx <- sort(x)

par(mfcol=c(2,2))
for(conf in c(50,95))
{
    m <- hdrconf(sortx,trueden,conf=conf)
    plot(m,trueden,main=paste(conf,"% HDR from true density"))
    m <- hdrconf(sortx,den,conf=conf)
    plot(m,den,main=paste(conf,"% HDR from empirical density
(n=200)"))
}