hdr.den {hdrcde}

Density plot with Highest Density Regions

Description

Plots univariate density with highest density regions displayed

Usage

hdr.den(
  x,
  prob = c(50, 95, 99),
  den,
  h = hdrbw(BoxCox(x, lambda), mean(prob)),
  lambda = 1,
  xlab = NULL,
  ylab = "Density",
  ylim = NULL,
  plot.lines = TRUE,
  col = 2:8,
  bgcol = "gray",
  legend = FALSE,
  ...
)

Arguments

x

Numeric vector containing data. If x is missing then den must be provided, and the HDR is computed from the given density.

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.

xlab

Label for x-axis.

ylab

Label for y-axis.

ylim

Limits for y-axis.

plot.lines

If TRUE, will show how the HDRs are determined using lines.

col

Colours for regions.

bgcol

Colours for the background behind the boxes. Default "gray", if NULL no box is drawn.

legend

If TRUE add a legend on the right of the boxes.

...

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.

Value

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 J Hyndman

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, hdr.boxplot

Examples

# Old faithful eruption duration times
hdr.den(faithful$eruptions)

# Simple bimodal example
x <- c(rnorm(100,0,1), rnorm(100,5,1))
hdr.den(x)