BiweightLocation of a list:

BiweightLocation of columns of a matrix:

BiweightLocation of a list with scaling parameter 7:

BiweightLocation of a list of dates:

Same inputs with different precisions:

Biweight location with different scaling parameters:

Biweight location for a matrix gives columnwise estimate:

Biweight location of a large array:

Find a biweight location of a TimeSeries:

The biweight location depends only on the values:

Biweight location works with data involving quantities:

Compute biweight location of dates:

Compute biweight location of times:

List of times with different time zone specifications:

Obtain a robust estimate of location when outliers are present:

Extreme values have a large influence on the Mean:

Consider data from a Gaussian mixture distribution:

Estimate the center with Mean:

The sample mean estimator has a large spread for non-Gaussian data. The standard deviation of the estimator is:

Estimate the center with BiweightLocation:

Use bootstrapping to assess the spread of the biweight location estimator:

Simulate a trajectory with heavy-tailed measurement noise:

The underlying signal and simulated path with noise:

Smooth the trajectory using a moving BiweightLocation:

Increasing the block size gives a smoother trajectory:

Compute the biweight location of a sample:

Values outside of the interval have no effect on the statistic. Here is the value of biweight location and is the median absolute deviation with respect to . is a scaling parameter with default value equal to 6:

The shape of the weight function w(x) being used in computing biweight location:

Multiply the smallest and the largest values in the sample by 2 and compute the biweight location again:

For normally distributed samples, BiweightLocation and Mean are nearly the same:

For non-normally distributed samples such as data from CauchyDistribution, BiweightLocation gives a better estimate of the center location than Mean:

BiweightLocation approaches Mean for large values of c: