Moment Matching
András Horváth, Miklós Telek · 2024
This chapter presents both moment bounds, that is, constraints that the moments must satisfy for any Phase (PH) or matrix-exponential (ME) distribution, and methods to obtain PH and ME distributions with given moments. It discusses a feature of practical importance, namely, the ability of PH distributions to capture low variability, for which the discrete phase-type and the PH cases differ significantly. The chapter considers the same feature for what concerns ME distributions and shows that ME distributions outperform PH distributions in this respect. It discusses moment matching algorithms, that is, methods that generate PH and ME distributions with given moments. Modeling real systems often involves the necessity of dealing with actions or activities whose duration has a distribution with low variability. Typical examples are deterministic timeouts in telecommunication protocols and activities that last for an (almost) deterministic period in supply chains.