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. In any statistical function, you can use the optional parameter «w» to specify unequal weights for its samples. This lets you estimate conditional statistics. For example:

Mean(X, w: X > 0)

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 weights, 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

• Mean()
• SampleWeighting
• Importance weights
• Statistical Functions and Importance Weighting

Statistical functionsWeighted statistics and w parameterImportance analysis