Highest Density Regions
Calculates highest density regions in one dimension
hdr( x = NULL, prob = c(50, 95, 99), den = NULL, h = hdrbw(BoxCox(x, lambda), mean(prob)), lambda = 1, nn = 5000, all.modes = FALSE )
x |
Numeric vector containing data. If |
prob |
Probability coverage required for HDRs |
den |
Density of data as list with components |
h |
Optional bandwidth for calculation of density. |
lambda |
Box-Cox transformation parameter where |
nn |
Number of random numbers used in computing f-alpha quantiles. |
all.modes |
Return all local modes or just the global mode? |
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.
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. |
Rob J Hyndman
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.
# Old faithful eruption duration times hdr(faithful$eruptions)
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