# hdr {hdrcde}

### Description

Calculates and plots highest density regions in one dimension including the HDR boxplot.

### Usage

hdr(x, prob = c(50, 95, 99), den, h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, nn=5000, all.modes=FALSE) hdr.den(x, prob = c(50, 95, 99), den, h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, xlab=NULL, ylab="Density", ...) hdr.boxplot(x, prob = c(99, 50), h=hdrbw(BoxCox(x,lambda),mean(prob)), lambda=1, boxlabels = "", col = gray((9:1)/10), main="", xlab="", ylab="", pch=1, ...)

### Arguments

- x
- Numeric vector containing data. In
`hdr`

and`hdr.den`

, if`x`

is missing then`den`

must be provided, and the HDR is computed from the given density. For`hdr.boxplot`

,`x`

can be a list containing several vectors. - 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?
- boxlabels
- Label for each box plotted.
- col
- Colours for regions of each box.
- main
- Overall title for the plot.
- xlab
- Label for x-axis.
- ylab
- Label for y-axis.
- pch
- Plotting character.
- ...
- 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. `hdr.den`

plots the density with the HDRs superimposed. `hdr.boxplot`

displays a boxplot based on HDRs.

### Values

`hdr.boxplot`

retuns nothing. `hdr`

and `hdr.den`

return 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.

### 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.boxplot.2d`

### Examples

# Old faithful eruption duration times hdr(faithful$eruptions) hdr.boxplot(faithful$eruptions) hdr.den(faithful$eruptions) # Simple bimodal example x <- c(rnorm(100,0,1), rnorm(100,5,1)) par(mfrow=c(1,2)) boxplot(x) hdr.boxplot(x) par(mfrow=c(1,1)) hdr.den(x) # Highly skewed example x <- exp(rnorm(100,0,1)) par(mfrow=c(1,2)) boxplot(x) hdr.boxplot(x,lambda=0)

Documentation reproduced from package hdrcde, version 3.1. License: GPL (>= 2)