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

where each Y_i is an exponentially distributed random variable with rate parameter λ_i, and p_i is the probability that X will take on the form of the exponential distribution with rate λ_i. 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. While the exponential distribution is the continuous analogue of the geometric distribution, the hyperexponential distribution is not analogous to the hypergeometric distribution. The hyperexponential distribution is an example of a mixture density.