wt_dist: Weighted descriptive statistics for a vector of numbers

Description

Compute the weighted mean and variance of a vector of numeric values. If no weights are supplied, defaults to computing the unweighted mean and the unweighted maximum-likelihood variance.

Logical scalar determining whether variance should be unbiased (TRUE) or maximum-likelihood (FALSE).

df_type

Character scalar determining whether the degrees of freedom for unbiased estimates should be based on numbers of cases ("count"; default) or sums of weights ("sum_wts").

Value

A weighted mean and variance if weights are supplied or an unweighted mean and variance if weights are not supplied.

Details

The weighted mean is computed as
$$\bar{x}_{w}=\frac{\Sigma_{i=1}^{k}x_{i}w_{i}}{\Sigma_{i=1}^{k}w_{i}}$$
where x is a numeric vector and w is a vector of weights.

The weighted variance is computed as
$$var_{w}(x)=\frac{\Sigma_{i=1}^{k}\left(x_{i}-\bar{x}_{w}\right)^{2}w_{i}}{\Sigma_{i=1}^{k}w_{i}}$$
and the unbiased weighted variance is estimated by multiplying \(var_{w}(x)\) by \(\frac{k}{k-1}\).