hdr.2d {hdrcde}

Bivariate Highest Density Regions

Description

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 class '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.

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.

Value

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

Author(s)

Rob J Hyndman

References

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

See Also

hdr.boxplot

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)