Estimation of the parameters of a second order Markov modulated Poisson process using change-point detection procedure

Authors

  • Sergey E. Vorobeychikov National Research Tomsk State University, 36 Lenina Avenue, Tomsk 634050, Russia
  • Yulia B. Burkatovskaya National Research Tomsk State University, 36 Lenina Avenue, Tomsk 634050, Russia , National Research Tomsk Polytechnic University, 30 Lenina Avenue, Tomsk 634050, Russia

Keywords:

Markov modulated Poisson process, MMPP, cumulative sums, method of moments, maximum likelihood method
Supporting Agencies
This work was partially carried out with the financial support of the Russian Foundation for Basic Research (grant No. 24-11-00191 in the name of S. E. Vorobeychikov).

Abstract

The problem of estimating the parameters of a second order Markov modulated Poisson process is considered. A new two-staged algorithm for their estimation is developed. In the first stage initial estimates of the intensity parameters are constructed using the method of moments and maximum likelihood method. In the second stage these estimates are used in the cumulative sums change-point detection algorithm to determine time intervals, during which the process intensity is constant; after that estimates of all parameters are constructed. The developed algorithm is compared with a well-known algorithm for finding maximum likelihood estimates (the EM algorithm). The proposed method is non-iterative, ensuring relatively low computational complexity.

Author Biographies

  • Sergey E. Vorobeychikov, National Research Tomsk State University, 36 Lenina Avenue, Tomsk 634050, Russia

    doctor of science (physics and mathematics), docent; professor at the department of system analysis and mathematical modelling, Institute of Applied Mathematics and Computer Science

  • Yulia B. Burkatovskaya, National Research Tomsk State University, 36 Lenina Avenue, Tomsk 634050, Russia, National Research Tomsk Polytechnic University, 30 Lenina Avenue, Tomsk 634050, Russia

    PhD (physics and mathematics), docent; associate professor at the department of system analysis and mathematical modelling, Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, and associate professor at the division for information technology, School of Computer Science and Robotics, National Research Tomsk Polytechnic University

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Published

2026-05-11

Issue

No. 1 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Vorobeychikov, S. and Burkatovskaya, Y. 2026. Estimation of the parameters of a second order Markov modulated Poisson process using change-point detection procedure. Journal of the Belarusian State University. Mathematics and Informatics. 1 (May 2026), 53–60.