R: Highest Density Regions

hdr {hdrcde} | R Documentation

## Highest Density Regions

### Description

Calculates highest density regions in one dimension

### Usage

    hdr(
      x = NULL,
      prob = c(50, 95, 99),
      den = NULL,
      h = hdrbw(BoxCox(x, lambda), mean(prob)),
      lambda = 1,
      nn = 5000,
      all.modes = 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`.
`nn` | Number of random numbers used in computing f-alpha quantiles.
`all.modes` | Return all local modes or just the global mode?

### 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.den`, `hdr.boxplot`

### Examples

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

[Package hdrcde version 3.4 Index]