R: Density plot with Highest Density Regions

hdr.den {hdrcde} | R Documentation

## 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)

[Package hdrcde version 3.4 Index]