Discrete signed mixtures of exponentials

In this paper the authors consider the problem of recovering the parameters in a mixture of exponential functions, where the weights may be of different sign. Both the case where the resulting mixture is completely known and the case where it has to be estimated from a finite number of noisy data are considered. In the first case an exact inversion formula can be derived. The recovery is derived by exploiting the resemblance of the mixture to a convolution on the multiplicative group of the positive numbers. These mixtures are the derivatives of the generalized hyperexponential distribution functions that have well-known applications in stochastic modeling.