Highest Density Regions

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?

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.

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.

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.

Author

Rob J Hyndman

Examples

# Old faithful eruption duration times
hdr(faithful$eruptions)
#> $hdr
#>         [,1]     [,2]     [,3]     [,4]
#> 99% 1.323853 2.819341 3.152141 5.282053
#> 95% 1.500687 2.520831 3.499998 5.091620
#> 50% 1.923525 2.024666 3.942171 4.772235
#> 
#> $mode
#> [1] 4.377839
#> 
#> $falpha
#>         1%         5%        50% 
#> 0.06754105 0.15304896 0.36102900 
#>