hdr.den: Density plot with Highest Density Regions

In hdrcde: Highest Density Regions and Conditional Density Estimation

Description

Plots univariate density with highest density regions displayed

Usage

hdr.den(
  x,
  prob = c(50, 95, 99),
  den,
  h = hdrbw(BoxCox(x, lambda), mean(prob)),
  lambda = 1,
  xlab = NULL,
  ylab = "Density",
  ylim = NULL,
  plot.lines = TRUE,
  col = 2:8,
  bgcol = "gray",
  legend = 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.
xlab	Label for x-axis.
ylab	Label for y-axis.
ylim	Limits for y-axis.
plot.lines	If TRUE, will show how the HDRs are determined using lines.
col	Colours for regions.
bgcol	Colours for the background behind the boxes. Default "gray", if NULL no box is drawn.
legend	If TRUE add a legend on the right of the boxes.
...	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.

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, hdr.boxplot

Examples

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

# Simple bimodal example
x <- c(rnorm(100,0,1), rnorm(100,5,1))
hdr.den(x)

Example output

This is hdrcde 3.3
$hdr
        [,1]     [,2]     [,3]     [,4]
99% 1.323538 2.819354 3.152597 5.282233
95% 1.500589 2.520929 3.500000 5.091820
50% 1.923764 2.024871 3.941025 4.772941

$mode
[1] 4.378855

$falpha
        1%         5%        50% 
0.06778909 0.15321941 0.36037111 

$hdr
          [,1]     [,2]     [,3]     [,4]
99% -2.0481413 7.226990       NA       NA
95% -1.5438449 2.257851 2.925022 6.711026
50% -0.5778713 1.023053 4.350023 5.630416

$mode
[1] 0.2293077

$falpha
        1%         5%        50% 
0.03890428 0.06715987 0.12715639 

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