HDRs with confidence intervals

Calculates Highest Density Regions with confidence intervals.

Usage

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

Arguments

x: 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:

hdr: Highest density regions
hdr.lo: Highest density regions corresponding to lower confidence limit.
hdr.hi: Highest density regions corresponding to upper confidence limit.
falpha: Values of \(f_\alpha\) corresponding to HDRs.
falpha.ci: Values 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.

Author

Rob J Hyndman

Examples

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(n=200)"))
}