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")
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". |
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.
A pdqr-function with transformed tail(s).
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()
# 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)) meta_x_tbl( form_tails(my_dis, level = 0.35, method = "winsor", direction = "left") ) # 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) # Examples of robust mean set.seed(101) x <- rcauchy(1000) d_x <- new_d(x, "continuous") summ_mean(d_x) ## Trimmed mean summ_mean(form_tails(d_x, level = 0.1, method = "trim")) ## Winsorized mean summ_mean(form_tails(d_x, level = 0.1, method = "winsor"))
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