×

High order concentrated matrix-exponential distributions. (English) Zbl 1448.60034

Summary: This paper presents matrix-exponential (ME) distributions, whose squared coefficient of variation (SCV) is very low. Currently, there is no symbolic construction available to obtain the most concentrated ME distributions, and the numerical optimization-based approaches to construct them have many pitfalls. We present a numerical optimization-based procedure which avoids numerical issues.

MSC:

60E05 Probability distributions: general theory
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)

Software:

CMA-ES
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aldous, D.; Shepp, L., The least variable phase type distribution is Erlang, Stoch. Models, 3, 467-473 (1987) · Zbl 0635.60086
[2] Asmussen, S.; Bladt, M., Matrix-Analytic Methods in Stochastic Models, Renewal theory and queueing algorithms for matrix-exponential distributions, 313-341 · Zbl 0872.60064
[3] Asmussen, S.; O’Cinneide, C. A.; Kotz, S.; Read, C., Encyclopedia of Statistical Sciences, Matrix-exponential distributions – Distributions with a rational Laplace transform, 435-440 (1997), John Wiley & Sons: John Wiley & Sons, New York
[4] Éltető, T.; Rácz, S.; Telek, M.
[5] Hansen, N., Towards a New Evolutionary Computation, The CMA evolution strategy: A comparing review, 75-102 (2006)
[6] Hansen, N., Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed, Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, 2389-2396 (2009), ACM
[7] Horváth, I.; Sáfár, O.; Telek, M.; Zámbó, B., European Workshop on Performance Engineering, Concentrated matrix exponential distributions, 18-31 (2016), Springer
[8] Horváth, I.; Talyigás, Z.; Telek, M., An optimal inverse Laplace transform method without positive and negative overshoot - An integral based interpretation, Electron. Notes Theor. Comput. Sci., 337, 87-104 (2018) · doi:10.1016/j.entcs.2018.03.035
[9] Optimization procedure for finding ME(n) with low SCV
[10] Parameters of ME(n) distributions with low SCV
[11] Rechenberg, I., Simulationsmethoden in der Medizin und Biologie, Evolutionsstrategien, 83-114 (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.