hdr: Highest Density Regions

In hdrcde: Highest Density Regions and Conditional Density Estimation

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)

Example output

This is hdrcde 3.3
$hdr
        [,1]     [,2]     [,3]     [,4]
99% 1.323334 2.819363 3.152903 5.282361
95% 1.500516 2.521003 3.500000 5.091957
50% 1.923864 2.025074 3.940237 4.773430

$mode
[1] 4.379548

$falpha
        1%         5%        50% 
0.06795835 0.15333680 0.35991945 

hdrcde documentation built on Jan. 18, 2021, 9:05 a.m.