BiweightMidvariance

BiweightMidvariance[list]

gives the value of the biweight midvariance of the elements in list.

BiweightMidvariance[list,c]

gives the value of the biweight midvariance with scaling parameter c.

Details

  • BiweightMidvariance is a robust dispersion estimator.
  • BiweightMidvariance is given by a weighted second-order central moment with Median as its center. Elements farther from the center have lower weights.
  • The width scale of the weight function is controlled by a parameter c. Larger c indicates more data values are included in the computation of the statistic, and vice versa. »
  • For the list {x1,x2,,xn}, the value of the biweight midvariance estimator is given by , where , is Median[{x1,x2,,xn}], and is MedianDeviation[{x1,x2,,xn}].
  • BiweightMidvariance[list] is equivalent to BiweightMidvariance[list,9].
  • BiweightMidvariance[{{x1,y1,},{x2,y2,},}] gives {BiweightMidvariance[{x1,x2,}],BiweightMidvariance[{y1,y2,}],}.
  • BiweightMidvariance allows c to be any positive real number.

Examples

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Basic Examples  (3)

BiweightMidvariance of a list:

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BiweightMidvariance of columns of a matrix:

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BiweightMidvariance of a list with scaling factor 8:

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Scope  (7)

Applications  (5)

Properties & Relations  (3)

Possible Issues  (1)

See Also

BiweightLocation  TrimmedVariance  WinsorizedVariance  Variance  MedianDeviation  QuartileDeviation  StandardDeviation  MeanDeviation

Introduced in 2017
(11.1)