# 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

open allclose all

## Basic Examples(3)

BiweightMidvariance of a list:

 In[1]:=
 Out[1]=

BiweightMidvariance of columns of a matrix:

 In[1]:=
 Out[1]=

BiweightMidvariance of a list with scaling factor 8:

 In[1]:=
 Out[1]=