Create data with weights:

Compute a weighted Mean and StandardDeviation :

Create weighted univariate data:

Some weighted descriptive statistics:

Add weights to a set of multivariate values:

A set of weighted multivariate descriptive statistics:

Use a pure function to create weighted data values:

Weighted means and variances:

Visualize the impact of the various weighting schemes:

Fit nonparametric distributions to weighted data:

Fit parametric distributions to weighted data:

Compare the estimated and empirical distributions:

Extract the input data from a WeightedData object:

Compare the distributions of the unweighted and weighted data:

Obtain the weights from a WeightedData object:

Visually inspect the effect of the weights on the data values:

Compute a weighted mean from the empirical PDF :

The weighted mean can be computed directly using Mean :

Find the weighted average of an irregularly sampled TimeSeries :

Compare with the average of values:

Create weighted data involving quantities:

Some weighted descriptive statistics:

Create a weighted histogram:

Estimate confidence interval for maximum likelihood estimates of distribution parameters:

Apply fractional random weight bootstrap to estimate confidence interval, by repeating weighted estimation with weights sampled from a DirichletDistribution with unit parameters:

Generate one thousand estimates of the distribution parameters:

Visualize bootstrap estimates:

Fit joint Gaussian distribution to the bootstrapped parameters:

Descriptive statistics are based on the underlying EmpiricalDistribution :

Sample estimates are given when they differ from population estimates:

WeightedData works for TimeSeries objects:

For , the weights are proportional to :

Compare with bin‐sampled time average:

Compute integration limits: