Hyperexponential distribution ($\overline{F}(x)={\sum }_i{w}_i{e}^{-r_{i}x}$)

A finite mixture distribution of exponential distributions with rates $r_i>0$ and nonnegative weights summing to one. Its expected value is ${\sum }_i{w}_i/r_i$ and its moment-generating function is ${\sum }_i{w}_i{r}_i/(r_i-t)$ on the common finite domain. The mixture chooses one component for each observation; it is not a sum of independent exponential variables.