Enhanced optimization of high order concentrated matrix-exponential distributions

Abstract

This paper presents numerical methods for finding high order concentrated matrix-exponential (ME) distributions, whose squared coefficient of variation (SCV) is very low. Due to the absence of symbolic construction to obtain the most concentrated ME distributions, non-linear optimization problems are defined to obtain high order concentrated matrix-exponential (CME) distributions . The number of parameters to optimize increases with the order in the “full” version of the optimization problem. For orders, where “full” optimization is infeasible (n > 184), a “heuristic” optimization procedure, optimizing only 3 parameters independent of the order, was proposed in [6]. In this work we present an enhanced version of this heuristic optimization procedure, optimizing only 6 parameters independent of the order, which results in CME distributions with lower SCV than the existing 3-parameter method. The SCV gain of the new procedure compared to the old one is ∗This work is partially supported by the OTKA K-123914 and the NKFIH BME NC TKP2020 projects. Annales Mathematicae et Informaticae 53 (2021) pp. 5–19 doi: https://doi.org/10.33039/ami.2021.02.001 url: https://ami.uni-eszterhazy.hu