Closed-form expressions for distribution of sum of exponential random variables

@article{Amari1997ClosedformEF,
title={Closed-form expressions for distribution of sum of exponential random variables},
author={S. Amari and R. Misra},
journal={IEEE Transactions on Reliability},
year={1997},
volume={46},
pages={519-522}
}

In many systems which are composed of components with exponentially distributed lifetimes, the system failure time can be expressed as a sum of exponentially distributed random variables. A previous paper mentions that there seems to be no convenient closed-form expression for all cases of this problem. This is because in one case the expression involves high-order derivatives of products of multiple functions. The authors prove a simple intuitive multi-function generalization of the Leibnitz… Expand