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.

Details

  • WinsorizedVariance gives a robust estimate of the variance, as more extreme values are replaced by less extreme ones.
  • The winsorizing fraction is determined by the parameters f1 and f2, which indicate the fraction f1 of the smallest elements and the fraction f2 of the largest elements to be replaced by the remaining extreme values.
  • WinsorizedVariance[list,{f1,f2}] gives the variance of Clip[list,{z1,z2}] where z1 equals RankedMin[list,1+], z2 equals RankedMax[list,1+], and n equals the length of list.
  • WinsorizedVariance[{{x1,y1,},{x2,y2,},},f] gives {WinsorizedVariance[{x1,x2,},f],WinsorizedVariance[{y1,y2,},f],}.
  • WinsorizedVariance[dist,{f1,f2}] gives Variance[CensoredDistribution[Quantile[dist,{f1,1-f2}],dist]] for a univariate distribution dist.

Examples

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Basic Examples  (3)

Winsorized variance after removing extreme values:

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Winsorized variance after removing the smallest extreme values:

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Winsorized variance of a symbolic distribution:

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Scope  (8)

Applications  (2)

Properties & Relations  (5)

Possible Issues  (1)

See Also

Variance  StandardDeviation  Covariance  Correlation  TrimmedVariance  BiweightMidvariance  QnDispersion  SnDispersion  MeanDeviation  MedianDeviation  TruncatedDistribution  WinsorizedMean

Introduced in 2017
(11.1)