Hyperexponential distribution
= Hyperexponential distribution
{title2=$\overline F(x)=\sum_i w_i e^{-r_ix}$}
{wiki}
A finite <mixture distribution> of <exponential distributions> with rates $r_i>0$ and nonnegative weights summing to one. Its <expected value> is $\sum_iw_i/r_i$ 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.