A Modified-Form Expressions for the Hypoexponential Distribution

The Hypoexponential distribution is the distribution of the sum of m≥2 independent Exponential random variables. This distribution is used in modeling multiple exponential stages in series. This distribution can be used in many domains of application. In this paper we find a modified and simple form of the probability density function for the general case of the Hypoexponential distribution when its parameters do not have to be distinct. This modified form is found by writing the probability density function of this distribution as a linear combination of the probability density function of the known Erlang distribution. Also, this modified form generates a simple form of the cummulative distribution function, moment generating function, reliability function, hazard function, and moment of order k for the general case of the Hypoexponential distribution. Moreover, new identities are established. Finally, we consider the coefficients of this linear combination and propose an algorithm to compute them.