Bivariate Highest Density Regions

Calculates and plots highest density regions in two dimensions, including the bivariate HDR boxplot.

Usage

hdr.2d(
  x,
  y,
  prob = c(50, 95, 99),
  den = NULL,
  kde.package = c("ash", "ks"),
  h = NULL,
  xextend = 0.15,
  yextend = 0.15
)

hdr.boxplot.2d(
  x,
  y,
  prob = c(50, 99),
  kde.package = c("ash", "ks"),
  h = NULL,
  xextend = 0.15,
  yextend = 0.15,
  xlab = "",
  ylab = "",
  shadecols = "darkgray",
  pointcol = 1,
  outside.points = TRUE,
  ...
)

# S3 method for hdr2d
plot(
  x,
  shaded = TRUE,
  show.points = FALSE,
  outside.points = FALSE,
  pch = 20,
  shadecols = gray((length(x$alpha):1)/(length(x$alpha) + 1)),
  pointcol = 1,
  ...
)

Arguments

x: Numeric vector
y: Numeric vector of same length as x.
prob: Probability coverage required for HDRs
den: Bivariate density estimate (a list with elements x, y and z where x and y are grid values and z is a matrix of density values). If NULL, the density is estimated.
kde.package: Package to be used in calculating the kernel density estimate when den=NULL.
h: Pair of bandwidths passed to either ash2 or kde. If NULL, a reasonable default is used. Ignored if den is not NULL.
xextend: Proportion of range of x. The density is estimated on a grid extended by xextend beyond the range of x.
yextend: Proportion of range of y. The density is estimated on a grid extended by yextend beyond the range of y.
xlab: Label for x-axis.
ylab: Label for y-axis.
shadecols: Colors for shaded regions
pointcol: Color for outliers and mode
outside.points: If TRUE, the observations lying outside the largest HDR are shown.
...: Other arguments to be passed to plot.
shaded: If TRUE, the HDR contours are shown as shaded regions.
show.points: If TRUE, the observations are plotted over the top of the HDR contours.
pch: The plotting character used for observations.

Value

Some information about the HDRs is returned. See code for details.

Details

The density is estimated using kernel density estimation. Either ash2 or kde is used to do the calculations. Then Hyndman's (1996) density quantile algorithm is used to compute the HDRs.

hdr.2d returns an object of class hdr2d containing all the information needed to compute the HDR contours. This object can be plotted using plot.hdr2d.

hdr.boxplot.2d produces a bivariate HDR boxplot. This is a special case of applying plot.hdr2d to an object computed using hdr.2d.

References

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

Author

Rob J Hyndman

Examples

x <- c(rnorm(200,0,1),rnorm(200,4,1))
y <- c(rnorm(200,0,1),rnorm(200,4,1))
hdr.boxplot.2d(x,y)


hdrinfo <- hdr.2d(x,y)
plot(hdrinfo, pointcol="red", show.points=TRUE, pch=3)