WinsorizedVariance

WinsorizedVariance[list, f] gives the variance of the elements in list after replacing the fraction f of the smallest and largest elements by the remaining extreme values.

• WinsorizedVariance[list, {f1, f2}] gives the variance when the fraction f1 of the smallest elements and the fraction f2 of the largest elements are replaced by the remaining extreme values.
• WinsorizedVariance[list] gives the 5% winsorized variance WinsorizedVariance[list, 0.05].
• WinsorizedVariance[dist, ...] gives the winsorized variance of a univariate distribution dist.

Winsorization is a robust statistical technique that reduces the influence of outliers.

Examples

WinsorizedVariance[{1, 2, 3, 4, 5, 6, 7, 8, 9, 100}]

WinsorizedVariance[{1, 2, 3, 4, 5, 6, 7, 8, 9, 100}, 0.1]

WinsorizedVariance[NormalDistribution[], 0.1]

*See the official Wolfram Language Reference for more details.