exp-weighted mean

[tpapp]

Recently I have been calculating

$$\frac{\sum_i \exp(w_i) \exp(z_i) }{\sum_i \exp(w_i)}$$

forms a lot. They usually come from parametric derivatives of logsumexp, eg

$$\log \sum_i \exp(a_i + z_i y)$$

by $y$. I wonder if it is general enough to have a place in this package.