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WinsorizedVariance[list,f]

给出把最小和最大的 f（比例）元素用剩下元素的极值替换后 list 中元素的方差.

WinsorizedVariance[list,{f1,f2}]

给出把最小的 f1（比例）元素和的最大的 f2（比例）元素用剩下元素的极值替换后列表中元素的方差.

WinsorizedVariance[list]

给出经 5% 缩尾处理后的方差 WinsorizedVariance[list,0.05].

WinsorizedVariance[dist,…]

给出单变量分布 dist 经缩尾处理后的方差.

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Details and Options Details and Options
范例  
基本范例  
范围  
数据  
分布  
应用  
属性和关系  
可能存在的问题  
参见
相关指南
历史
按以下格式引用：

WinsorizedVariance

WinsorizedVariance[list,f]

给出把最小和最大的 f（比例）元素用剩下元素的极值替换后 list 中元素的方差.

WinsorizedVariance[list,{f1,f2}]

给出把最小的 f1（比例）元素和的最大的 f2（比例）元素用剩下元素的极值替换后列表中元素的方差.

WinsorizedVariance[list]

给出经 5% 缩尾处理后的方差 WinsorizedVariance[list,0.05].

WinsorizedVariance[dist,…]

给出单变量分布 dist 经缩尾处理后的方差.

更多信息

范例

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基本范例  (4)

去掉极值后的缩尾方差：

Wolfram Language code: WinsorizedVariance[{-10, 1, 1, 1, 1, 20}, 0.2]

去掉最小极值后的缩尾方差：

Wolfram Language code: WinsorizedVariance[{-10, 1, 1, 1, 1, 20}, {0.2, 0}]

日期列表的缩尾方差：

Wolfram Language code: RandomDate[6, DateGranularity -> "Month"]//Sort
Wolfram Language code: WinsorizedVariance[%]

符号分布的缩尾方差：

Wolfram Language code: WinsorizedVariance[ExponentialDistribution[λ]]

范围  (11)

数据  (10)

精确输入给出精确输出：

Wolfram Language code: WinsorizedVariance[{1, 20, 3, 4}, 2 / 5]
Wolfram Language code: WinsorizedVariance[{Sqrt[2], E, Pi, Pi ^ 2, 1, 2, 3}, 1 / 4]

近似输入给出近似输出：

Wolfram Language code: WinsorizedVariance[{5., 10., 4., 25., 2., 1.}, 0.2]
Wolfram Language code: WinsorizedVariance[N[{5, 10, 4, 25, 2, 1}, 30], 0.2]

矩阵的缩尾方差按列给出方差：

Wolfram Language code: WinsorizedVariance[RandomReal[1, {50, 2}], .1]

大型数组的缩尾方差：

Wolfram Language code: WinsorizedVariance[RandomReal[1, 10 ^ 6], 1 / 100]
Wolfram Language code: WinsorizedVariance[RandomReal[1, {10 ^ 5, 5}]]

可以像对稠密数组一样使用 SparseArray 数据：

Wolfram Language code: sp = SparseArray[{{i_, i_} :> i, {i_, j_} /; j == i + 1 :> i - 1}, {100, 10}, 1];
Wolfram Language code: WinsorizedVariance[sp]

一元 WeightedData 的 WinsorizedVariance：

Wolfram Language code: wd = WeightedData[RandomReal[100, 30], Range[30]];
Wolfram Language code: WinsorizedVariance[wd]

与未加权数据的方差相比较：

Wolfram Language code: WinsorizedVariance[wd["InputData"]]

TimeSeries 的缩尾方差：

Wolfram Language code: ts = TemporalData[TimeSeries, {{{3, 8, 4, 11, 9, 2}}, {{{1, 3, 5, 7, 8, 10}}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: WinsorizedVariance[ts, 1 / 6]//N

缩尾方差只取决于数值：

Wolfram Language code: WinsorizedVariance[ts["Values"], 1 / 6]//N

可对含有量的数据求缩尾方差：

Wolfram Language code: data = Quantity[RandomReal[1, 6], "Meters"]
Wolfram Language code: WinsorizedVariance[data]

计算日期的缩尾方差：

Wolfram Language code: dates = WolframLanguageData[All, "DateIntroduced"];
Wolfram Language code: DateHistogram[dates]
Wolfram Language code: WinsorizedVariance[dates]
Wolfram Language code: UnitConvert[%, "Years" ^ 2]

计算时间的缩尾方差：

Wolfram Language code: RandomTime[3]
Wolfram Language code: WinsorizedVariance[%]

以不同的时区规范给出的时间：

Wolfram Language code: {TimeObject[{12}, TimeZone -> 0], TimeObject[{12}, TimeZone -> 2], TimeObject[{12}, TimeZone -> "Asia/Tokyo"]}
Wolfram Language code: WinsorizedVariance[%]

分布  (1)

单变量分布的缩尾方差：

Wolfram Language code: WinsorizedVariance[BinomialDistribution[10, 1 / 2]]
Wolfram Language code: WinsorizedVariance[NormalDistribution[μ, σ]]//FullSimplify
Wolfram Language code: WinsorizedVariance[WeibullDistribution[1, β]]

应用  (2)

在异常值出现的情况下，计算位置的稳健估计值：

Wolfram Language code: WinsorizedVariance[{1, 5, 2, 6, 10, 10 ^ 5, 5, 4, -200, 5}, .1]//N

极值对方差的影响很大：

Wolfram Language code: Variance[{1, 5, 2, 6, 10, 10 ^ 5, 5, 4, -200, 5}]//N

求一个班的孩子们的身高的缩尾方差：

Wolfram Language code: heights = Quantity[{134, 143, 131, 140, 145, 136, 131, 136, 143, 136, 133, 145, 147, 150, 150, 146, 137, 143, 132, 142, 145, 136, 144, 135, 141}, "Centimeters"];
Wolfram Language code: ListPlot[heights, Filling -> Axis, AxesLabel -> Automatic]

5% 缩尾方差：

Wolfram Language code: wv = WinsorizedVariance[heights]//N

绘制缩尾方差作为比例参数的函数的曲线：

Wolfram Language code: winVar[f_ ? NumericQ] /; 0 ≤ f < 0.5 := WinsorizedVariance[heights, f]
Wolfram Language code: Plot[winVar[f], {f, 0, 0.49}, AxesLabel -> {f}]

相对于缩尾均值，绘制缩尾方差的平方根：

Wolfram Language code: m = WinsorizedMean[heights]; n = Length[heights]; swv = Sqrt[wv];
Wolfram Language code: ListPlot[{heights, {{0, m}, {n, m}}, {{0, m - swv}, {n, m - swv}}, {{0, m + swv}, {n, m + swv}}}, Filling -> {1 -> 0, 3 -> {4}}, Joined -> {False, True, True, True}, PlotStyle -> {Automatic, Automatic, Gray, Gray}, PlotLegends -> {"heights", "winsorized mean", "square-root-winsorized-variance bands"}, AxesLabel -> Automatic]

属性和关系  (5)

0% WinsorizedVariance 等价于 Variance:

Wolfram Language code: WinsorizedVariance[Range[10], 0]
Wolfram Language code: Variance[Range[10]]

当 f 趋于 1/2 时 WinsorizedVariance 趋于 0：

Wolfram Language code: data = RandomReal[CauchyDistribution[0, 1], 1000];
Wolfram Language code: Plot[WinsorizedVariance[data, f], {f, 0, .499}]

一个分布的 WinsorizedVariance 是它的 CensoredDistribution 的方差：

Wolfram Language code: 𝒟 = NormalDistribution[a, b];
Wolfram Language code: f1 = .2; f2 = .3;
Wolfram Language code: wv = WinsorizedVariance[𝒟, {f1, f2}]

适当界限下的 CensoredDistribution 的方差：

Wolfram Language code: cd = CensoredDistribution[Quantile[𝒟, {f1, 1 - f2}], 𝒟]
Wolfram Language code: var = Variance[cd]
Wolfram Language code: wv == var

样本的 WinsorizedVariance 给出对删失分布的方差的估计：

Wolfram Language code: 𝒟 = NormalDistribution[]; data = RandomVariate[𝒟, 10 ^ 6];
Wolfram Language code: f1 = .2; f2 = .3;
Wolfram Language code: WinsorizedVariance[data, {f1, f2}]

适当界限下的 CensoredDistribution 的方差：

Wolfram Language code: cd = CensoredDistribution[Quantile[𝒟, {f1, 1 - f2}], 𝒟]
Wolfram Language code: Variance[cd]

TrimmedVariance 会丢弃一定分位数之上的数据，然后再计算样本方差：

Wolfram Language code: len = 100; f = 1 / 10; data = RandomReal[1, len];
Wolfram Language code: data1 = Part[Sort[data], 1 + Floor[len f] ;; len - Floor[len f]];
Wolfram Language code: TrimmedVariance[data, f] == Variance[data1]

WinsorizedVariance 剪切一定分位数之上的数据，然后再计算样本方差：

Wolfram Language code: data2 = Clip[data, {RankedMin[data, 1 + Floor[len f]], RankedMax[data, 1 + Floor[len f]]}];
Wolfram Language code: WinsorizedVariance[data, f] == Variance[data2]

绘制排序后的数据与经过截断（移除元素）或剪切（较大极值被替换）处理的数据：

Wolfram Language code: d0 = Transpose[{Range[1, len], Sort@data}]; d1 = Transpose[{Range[1 + Floor[len f], len - Floor[len f]], data1}]; d2 = Transpose[{Range[1, len], Sort@data2}];
Wolfram Language code: ListPlot[{d0, d1, d2}, Filling -> {2 -> 0}, PlotLegends -> {"data", "data1", "data2"}]

可能存在的问题  (1)

WinsorizedVariance 只接受数值型数据：

Wolfram Language code: WinsorizedVariance[{a, b, c}, .1]
Wolfram Research (2017)，WinsorizedVariance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WinsorizedVariance.html （更新于 2024 年）.

文本

Wolfram Research (2017)，WinsorizedVariance，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WinsorizedVariance.html （更新于 2024 年）.

CMS

Wolfram 语言. 2017. "WinsorizedVariance." Wolfram 语言与系统参考资料中心. Wolfram Research. 最新版本 2024. https://reference.wolfram.com/language/ref/WinsorizedVariance.html.

APA

Wolfram 语言. (2017). WinsorizedVariance. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/WinsorizedVariance.html 年

BibTeX

@misc{reference.wolfram_2026_winsorizedvariance, author="Wolfram Research", title="{WinsorizedVariance}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/WinsorizedVariance.html}", note=[Accessed: 09-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_winsorizedvariance, organization={Wolfram Research}, title={WinsorizedVariance}, year={2024}, url={https://reference.wolfram.com/language/ref/WinsorizedVariance.html}, note=[Accessed: 09-August-2026]}