Transform tails of distribution

Modify tail(s) of distribution defined by certain cutoff level using method of choice. This function is useful for doing robust analysis in presence of possible outliers.

form_tails(f, level, method = "trim", direction = "both")

Arguments

f	A pdqr-function.
level	Cutoff level. For direction "both" should be between 0 and 0.5; for "left" and "right" - between 0 and 1.
method	Modification method. One of "trim" or "winsor".
direction	Information about which tail(s) to modify. One of "both", "left", "right".

Value

A pdqr-function with transformed tail(s).

Details

Edges for left and right tails are computed as level and 1 - level quantiles respectively. The left tail is interval to the left of left edge, and right tail - to the right of right edge.

Method "trim" removes tail(s) while normalizing "center part". Method "winsor" "squashes" tails inside center of distribution in dirac-like fashion, i.e. probability of tail(s) is moved inside and becomes concentrated in 1e-8 neighborhood of nearest edge.

Direction "both" affect both tails. Directions "left" and "right" affect only left and right tail respectively.

See also

form_resupport() for changing support to some known interval.

summ_center() and summ_spread() for computing summaries of distributions.

Other form functions: form_estimate(), form_mix(), form_regrid(), form_resupport(), form_retype(), form_smooth(), form_trans()

Examples

# Type "discrete"
my_dis <- new_d(data.frame(x = 1:4, prob = (1:4) / 10), type = "discrete")
meta_x_tbl(form_tails(my_dis, level = 0.1))
#>   x  prob cumprob
#> 1 2 0.250   0.250
#> 2 3 0.375   0.625
#> 3 4 0.375   1.000
meta_x_tbl(
  form_tails(my_dis, level = 0.35, method = "winsor", direction = "left")
)
#>   x prob cumprob
#> 1 3  0.6     0.6
#> 2 4  0.4     1.0

# Type "continuous"
d_norm <- as_d(dnorm)
plot(d_norm)
lines(form_tails(d_norm, level = 0.1), col = "blue")
lines(
  form_tails(d_norm, level = 0.1, method = "winsor", direction = "right"),
  col = "green"
)

# Use `form_resupport()` and `as_q()` to remove different levels from both
# directions. Here 0.1 level tail from left is removed, and 0.05 level from
# right
new_supp <- as_q(d_norm)(c(0.1, 1 - 0.05))
form_resupport(d_norm, support = new_supp)
#> Density function of continuous type
#> Support: ~[-1.28155, 1.64485] (9236 intervals)

# Examples of robust mean
set.seed(101)
x <- rcauchy(1000)
d_x <- new_d(x, "continuous")
summ_mean(d_x)
#> [1] 0.6504152
## Trimmed mean
summ_mean(form_tails(d_x, level = 0.1, method = "trim"))
#> [1] 0.1094364
## Winsorized mean
summ_mean(form_tails(d_x, level = 0.1, method = "winsor"))
#> [1] 0.1563657