Details

Autor(en) / Beteiligte

• Mészáros, András
• Telek, Miklós

Titel

Concentrated matrix exponential distributions with real eigenvalues

Ist Teil von

• Probability in the engineering and informational sciences, 2022-10, Vol.36 (4), p.1171-1187

Ort / Verlag

New York, USA: Cambridge University Press

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Concentrated random variables are frequently used in representing deterministic delays in stochastic models. The squared coefficient of variation ($\mathrm {SCV}$) of the most concentrated phase-type distribution of order $N$ is $1/N$. To further reduce the $\mathrm {SCV}$, concentrated matrix exponential (CME) distributions with complex eigenvalues were investigated recently. It was obtained that the $\mathrm {SCV}$ of an order $N$ CME distribution can be less than $n^{-2.1}$ for odd $N=2n+1$ orders, and the matrix exponential distribution, which exhibits such a low $\mathrm {SCV}$ has complex eigenvalues. In this paper, we consider CME distributions with real eigenvalues (CME-R). We present efficient numerical methods for identifying a CME-R distribution with smallest SCV for a given order $n$. Our investigations show that the $\mathrm {SCV}$ of the most concentrated CME-R of order $N=2n+1$ is less than $n^{-1.85}$. We also discuss how CME-R can be used for numerical inverse Laplace transformation, which is beneficial when the Laplace transform function is impossible to evaluate at complex points.