Highest Density Region Boxplots

Calculates and plots a univariate highest density regions boxplot.

Usage

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,
  border = 1,
  outline = TRUE,
  space = 0.25,
  ...
)

Arguments

x: Numeric vector containing data or a list containing several vectors.
prob: Probability coverage required for HDRs density.
h: Optional bandwidth for calculation of density.
lambda: Box-Cox transformation parameter where 0 <= lambda <= 1.
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.
border: Width of border of box.
outline: If not <code>TRUE</code>, the outliers are not drawn.
space: The space between each box, between 0 and 0.5.
...: Other arguments passed to plot.

Value

nothing.

Details

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.

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.

Author

Rob J Hyndman

Examples

# Old faithful eruption duration times
hdr.boxplot(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)


# Highly skewed example
x <- exp(rnorm(100,0,1))
par(mfrow=c(1,2))
boxplot(x)
hdr.boxplot(x,lambda=0)