Table of Highest Density Regions

Compute a table of highest density regions (HDR) for a distributional object. The HDRs are returned as a tibble with one row per interval and columns: prob (giving the probability coverage), density (the value of the density at the boundary of the HDR), For one dimensional density functions, the tibble also has columns lower (the lower ends of the intervals), and upper (the upper ends of the intervals).

Usage

hdr_table(object, prob)

Arguments

object

Distributional object such as that returned by dist_kde()

prob

Vector of probabilities giving the HDR coverage (between 0 and 1)

Value

A tibble

References

Hyndman, R J (1996) "Computing and Graphing Highest Density Regions", The American Statistician, 50(2), 120–126. https://robjhyndman.com/publications/hdr/

Hyndman, R J (2026) "That's weird: Anomaly detection using R", Section 2.5, 3.4. https://OTexts.com/weird/.

See also

gg_hdrboxplot

Author

Rob J Hyndman

Examples

# Univariate HDRs
c(dist_normal(), dist_kde(c(rnorm(100), rnorm(100, 3, 1)))) |>
  hdr_table(c(0.5, 0.95))
#> # A tibble: 5 × 5
#>    prob distribution     lower upper density
#>   <dbl> <chr>            <dbl> <dbl>   <dbl>
#> 1  0.5  N(0, 1)         -0.674 0.674  0.318 
#> 2  0.95 N(0, 1)         -1.96  1.96   0.0584
#> 3  0.5  kde[1d, h=0.65] -0.640 0.948  0.164 
#> 4  0.5  kde[1d, h=0.65]  2.23  2.99   0.164 
#> 5  0.95 kde[1d, h=0.65] -1.52  4.74   0.0607
dist_kde(oldfaithful$duration) |> hdr_table(0.95)
#> # A tibble: 2 × 5
#>    prob distribution   lower upper density
#>   <dbl> <chr>          <dbl> <dbl>   <dbl>
#> 1  0.95 kde[1d, h=5.1]  99.7  135. 0.00117
#> 2  0.95 kde[1d, h=5.1] 190    289. 0.00117
# Bivariate HDRs
dist_kde(oldfaithful[, c("duration", "waiting")]) |> hdr_table(0.90)
#> # A tibble: 1 × 3
#>   distribution                                      prob    density
#>   <chr>                                            <dbl>      <dbl>
#> 1 kde[2d, H={(41, 3.5e+02)', (3.5e+02, 2.3e+04)'}]   0.9 0.00000109