Optimization-Free Concentrated Matrix-Exponentials
For researchers in applied probability and stochastic modeling, this work offers a theoretically grounded alternative to numerical optimization for constructing concentrated distributions.
The paper presents an explicit family of matrix-exponential distributions that surpass the Erlang variance limit for near-deterministic delays, providing the first analytical proof of such a class with closed-form parameters.
Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distributions can empirically bypass this barrier, prior low-variance constructions relied entirely on numerical optimization. We propose an explicit family of concentrated matrix-exponential densities for the unit delay, obtained by raising the trigonometric Fejér kernel to logarithmic power. With exact moments and closed-form parameters, this gives the first analytical proof of a matrix-exponential class that asymptotically surpasses the Erlang bound.