Weighted statistics and w parameter

Analytica User GuideStatistics, Sensitivity, and Uncertainty AnalysisWeighted statistics and w parameter

Normally, each statistical function gives an equal weight to each sample value in its parameters. You can use the optional parameter w for any statistical function to specify unequal weights for its samples. This lets you estimate conditional statistics. For example:

Mean(X, w: X>0)

This computes the mean of X for those samples of X that are positive. In this case, the weight vector contains only zeros and ones. The expression X>0 gives a weight of 1 (True) for each sample that satisfies the relationship and 0 (False) to those that do not. By default, this method works over uncertain samples, indexed by Run. You can also use it to compute weighted statistics over other indexes. For example, if Y is an array indexed by J, you could compute:

Mean(Y, I, W: Y>0)

If you set the system variable SampleWeighting to something other than 1 (see “Importance weighting” on page 291, all statistical functions use SampleWeighting as the default weights, unless you specify parameter w with some other weighting array. So, when using importance weighting, all statistics (and uncertainty views) automatically use the correct weighting.

See Also

Statistical functionsWeighted statistics and w parameterImportance analysis