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Approximation of Cumulative Distribution Functions by Bernstein Phase-Type Distributions

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Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems (QEST+FORMATS 2024)

Abstract

The inclusion of generally distributed random variables in stochastic models is often tackled by choosing a parametric family of distributions and applying fitting algorithms to find appropriate parameters. A recent paper proposed the approximation of probability density functions (PDFs) by Bernstein exponentials, which are obtained from Bernstein polynomials by a change of variable and result in a particular case of acyclic phase-type distributions. In this paper, we show that this approximation can also be applied to cumulative distribution functions (CDFs), which enjoys advantageous properties; by focusing on CDFs, we propose an approach to obtain stochastically ordered approximations.

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Acknowledgments

M. Telek was supported by the OTKA K-138208 project of the Hungarian Scientific Research Fund. E. Vicario was supported bt the RESTART project, as a part of the Italian PNNR programme.

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Correspondence to Miklós Telek .

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Horváth, A., Horváth, I., Paolieri, M., Telek, M., Vicario, E. (2024). Approximation of Cumulative Distribution Functions by Bernstein Phase-Type Distributions. In: Hillston, J., Soudjani, S., Waga, M. (eds) Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems. QEST+FORMATS 2024. Lecture Notes in Computer Science, vol 14996. Springer, Cham. https://doi.org/10.1007/978-3-031-68416-6_6

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  • DOI: https://doi.org/10.1007/978-3-031-68416-6_6

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  • Online ISBN: 978-3-031-68416-6

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