# BiweightLocation

BiweightLocation[list]

gives the value of the biweight location estimator of the elements in list.

BiweightLocation[list,c]

gives the value of the biweight location estimator with scaling parameter c.

# Details and Options • BiweightLocation is a robust location estimator.
• BiweightLocation is given by a weighted mean of the elements. 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 location estimator is given by , where and is Median[{x1-x*,x2-x*,,xn-x*}]. The value x* of the estimator is computed iteratively, with the initial value chosen automatically by default.
• BiweightLocation[list] is equivalent to BiweightLocation[list,6].
• BiweightLocation[{{x1,y1,},{x2,y2,},}] gives {BiweightLocation[{x1,x2,}],BiweightLocation[{y1,y2,}],}.
• BiweightLocation allows c to be any positive real number.
• The following options can be given:
•  AccuracyGoal Automatic the accuracy sought MaxIterations Automatic maximum number of iterations to use Method Automatic method to use PrecisionGoal Automatic the precision sought WorkingPrecision MachinePrecision the precision used in internal computations
• The setting Method{"InitialPoint"x0} allows for a custom initial value .

# Examples

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## Basic Examples(3)

BiweightLocation of a list:

 In:= Out= BiweightLocation of columns of a matrix:

 In:= Out= BiweightLocation of a list with scaling parameter 7:

 In:= Out= ## Neat Examples(2)

Introduced in 2017
(11.1)