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stats::winsorize

Clamp (winsorize) extremal values

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

stats::winsorize([x1, x2, …], α)
stats::winsorize([[x11, x12, …], [x21, x22, …], …], α, i)
stats::winsorize(s, α, i)

Description

stats::winsorize([x1, x2, …], α) returns a copy of [x1, x2, …] in which all entries smaller than the α quantile have been replaced by this value and likewise for all entries larger than the 1 - α quantile.

stats::winsorize([[x11, x12, …], [x21, x22, …], …], α, i) and stats::winsorize(stats::sample([[x11, x12, …], [x21, x22, …], …]), α, i) perform the operations described above on the i-th entries of the input rows.

Measurement data often contains "outliers," sample points rather far outside the range containing the majority of the points. While expected both from theory and experience, these outliers, for small or medium-sized samples, tend to distort statistical data such as the mean value.

One of the standard methods dealing with this problem for (real) continuous scales is clamping the outliers. stats::winsorize sets all data points below or above a given quantile to these quantiles. (This operation is named after its inventor, Charles P. Winsor.)

Examples

Example 1

We create a normally distributed sample, slightly contaminated:

r := stats::normalRandom(0, 1, Seed=2):
data := [r() \$ i = 1..300, 100*r() \$ i = 1..2]:

The two extra points distort the data significantly:

plot(plot::Histogram2d(data, Cells=20))

Using either stats::winsorize or stats::cutoff removes this noise and the image shows more detail:

plot(plot::Scene2d(plot::Histogram2d
(stats::winsorize(data, 1/100), Cells=20)),
plot::Scene2d(plot::Histogram2d
(stats::cutoff(data, 1/100), Cells=20)))

With larger values of α, the difference between the two is easier to see:

plot(plot::Scene2d(plot::Histogram2d
(stats::winsorize(data, 1/20), Cells=20)),
plot::Scene2d(plot::Histogram2d
(stats::cutoff(data, 1/20), Cells=20)))

Both stats::winsorize and stats::cutoff reduce the standard deviation of the sample. This effect is considerably stronger for stats::cutoff, though. Keeping in mind that the standard deviation of our random number generator is 1, we compute that of the data in its various forms:

stats::stdev(data),
stats::stdev(stats::winsorize(data, 1/20)),
stats::stdev(stats::cutoff(data, 1/20))

Parameters

 x1, x2, x11, … The statistical data: arithmetical expressions. The data to filter on must be real-valued. s Sample of type stats::sample α Cut-off parameter: a real-valued expression . i Column index: positive integer. The nested list or the sample is winsorized on its i-th column.

Return Values

The input data with outliers being replaced by the values of quantiles.