st.statistics - Estimate gaussian (mixture) density from a set of weighted samples

The usual EM algorithm can be modified for weighted inputs. Following along the Wikipedia presentation, you would use these formulas instead:

$a_i = frac{sum_{j=1}^N w_j y_{i,j}}{sum_{j=1}^{N}w_j}$

and

$mu_{i} = frac{sum_{j} w_jy_{i,j}x_{j}}{sum_{j} w_jy_{i,j}}$

where $w_j ge 0$ are the weights of the data points.