Winsorize (Replace Extreme Values by Less Extreme Ones)

Winsorizing a vector means that a predefined quantum of the smallest and/or the largest values are replaced by less extreme values. Thereby the substitute values are the most extreme retained values.

Winsorize(x, val = quantile(x, probs = c(0.05, 0.95), na.rm = FALSE))

Arguments

x: a numeric vector to be winsorized.
val: the low border, all values being lower than this will be replaced by this value. The default is set to the 5%-quantile of x.

Value

A vector of the same length as the original data x containing the winsorized data.

Details

The winsorized vector is obtained by

$$g(x) = \left\{\begin{array}{ll} -c &\textup{for } x \le c\\ x &\textup{for } |x| < c\\ c &\textup{for } x \ge c \end{array}\right. $$

You may also want to consider standardizing (possibly robustly) the data before you perform a winsorization.

Author

Andri Signorell andri@signorell.net

Examples



library(DescTools)

## generate data
set.seed(9128)
x <- round(runif(100) * 100, 1)

(d.frm <- DescTools::Sort(data.frame(
  x, 
  default   = Winsorize(x), 
  quantile  = Winsorize(x, quantile(x, probs=c(0.1, 0.8), na.rm = FALSE)), 
  fixed_val = Winsorize(x, val=c(15, 85)),
  fixed_n   = Winsorize(x, val=c(Small(x, k=3)[3], Large(x, k=3)[1])),
  closest   = Winsorize(x, val=unlist(Closest(x, c(30, 70)))) 
)))[c(1:10, 90:100), ]
#>       x default quantile fixed_val fixed_n closest
#> 37  0.5    3.08     9.28        15     1.2    29.3
#> 81  0.7    3.08     9.28        15     1.2    29.3
#> 28  1.2    3.08     9.28        15     1.2    29.3
#> 36  2.3    3.08     9.28        15     2.3    29.3
#> 82  2.7    3.08     9.28        15     2.7    29.3
#> 43  3.1    3.10     9.28        15     3.1    29.3
#> 16  4.3    4.30     9.28        15     4.3    29.3
#> 44  6.1    6.10     9.28        15     6.1    29.3
#> 88  6.3    6.30     9.28        15     6.3    29.3
#> 59  9.1    9.10     9.28        15     9.1    29.3
#> 97 91.9   91.90    77.22        85    91.9    70.6
#> 67 92.2   92.20    77.22        85    92.2    70.6
#> 92 93.0   93.00    77.22        85    93.0    70.6
#> 84 93.5   93.50    77.22        85    93.5    70.6
#> 49 93.6   93.60    77.22        85    93.6    70.6
#> 79 95.5   95.50    77.22        85    95.5    70.6
#> 86 95.7   95.51    77.22        85    95.7    70.6
#> 75 95.9   95.51    77.22        85    95.9    70.6
#> 41 97.3   95.51    77.22        85    97.3    70.6
#> 4  98.7   95.51    77.22        85    97.3    70.6
#> 70 99.4   95.51    77.22        85    97.3    70.6

# use Large and Small, if a fix number of values should be winsorized (here k=3)

PlotLinesA(SetNames(d.frm, rownames=NULL), lwd=2, col=Pal("Tibco"), 
           main="Winsorized Vector")

z <- 0:10
# twosided (default):
Winsorize(z, val=c(2,8))
#>  [1] 2 2 2 3 4 5 6 7 8 8 8

# onesided:
# ... replace all values > 8 with 8
Winsorize(z, val=c(min(z), 8))
#>  [1] 0 1 2 3 4 5 6 7 8 8 8
# ... replace all values < 4 with 4
Winsorize(z, val=c(4, max(z)))
#>  [1]  4  4  4  4  4  5  6  7  8  9 10