Robust Descriptive Statistics

Descriptive statistics with consistent performance against data from different distributions are considered robust, as they are less affected by outliers. These estimators are generally defined via order statistics or optimizing certain objective functions of data.

The Wolfram Language provides a variety of robust estimators for different applications, including location, dispersion and shape characterization. They are useful in outlier detection and parametric estimation.

Robust Location Measures

Median  ▪  Commonest  ▪  TrimmedMean  ▪  WinsorizedMean  ▪  SpatialMedian  ▪  CentralFeature  ▪  BiweightLocation

Robust Dispersion Measures

TrimmedVariance  ▪  WinsorizedVariance  ▪  MedianDeviation  ▪  InterquartileRange  ▪  QuartileDeviation   ▪  QnDispersion   ▪  SnDispersion   ▪  BiweightMidvariance

Robust Shape Measures

QuartileSkewness  ▪  EstimatedDistribution  ▪  FindDistributionParameters

Order Statistics

Min  ▪  Max  ▪  MinMax  ▪  Sort  ▪  Ordering  ▪  RankedMin  ▪  RankedMax  ▪  Quantile  ▪  Quartiles  ▪  TakeLargest  ▪  TakeSmallest

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