Hyperexponential distribution

In probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by f X ( x ) = ∑ i = 1 n f Y i ( x ) p i , {\displaystyle f_{X}(x)=\sum _{i=1}^{n}f_{Y_{i}}(x)\;p_{i},} where each Yi is an exponentially distributed random variable with rate parameter λi, and pi is the probability that X will take on the form of the exponential distribution with rate λi. It is named the hyperexponential distribution since its coefficient of variation is greater than that of the exponential distribution, whose coefficient of variation is 1, and the hypoexponential distribution, which has a coefficient of variation smaller than one.

Source: Wikipedia — Hyperexponential distribution (CC BY-SA 4.0)