# WinsorizedMean

WinsorizedMean[list,f]

gives the mean of the elements in list after replacing the fraction f of the smallest and largest elements by the remaining extreme values.

WinsorizedMean[list,{f1,f2}]

gives the mean when the fraction f1 of the smallest elements and the fraction f2 of the largest elements are replaced by the remaining extreme values.

WinsorizedMean[list]

gives the 5% winsorized mean WinsorizedMean[list,0.05].

WinsorizedMean[dist,]

gives the winsorized mean of a univariate distribution dist.

# Details • WinsorizedMean gives a robust estimate of the mean, with more extreme values 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.
• WinsorizedMean[list,{f1,f2}] gives the mean of Clip[list,{z1,z2}] where z1 equals RankedMin[list,1+ ], z2 equals RankedMax[list,1+ ], and n equals the length of list.
• • WinsorizedMean[{{x1,y1,},{x2,y2,},},f] gives {WinsorizedMean[{x1,x2,},f],WinsorizedMean[{y1,y2,},f],}.
• WinsorizedMean[dist,{f1,f2}] gives Mean[CensoredDistribution[Quantile[dist,{f1,1-f2}],dist]] for a univariate distribution dist.

# Examples

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## Basic Examples(3)

Winsorized mean after removing extreme values:

 In:= Out= Winsorized mean after removing the smallest extreme values:

 In:= Out= Winsorized mean of a symbolic distribution:

 In:= Out= ## Possible Issues(1)

Introduced in 2017
(11.1)