Communications for Statistical Applications and Methods

  • 제31권6호
  • /
  • Pages.645-659
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  • 2024
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Charlier series approximation for nonhomogenious Poisson processes

  • Hyung-Tae Ha (Department of Applied Statistics, Gachon University)
  • 투고 : 2024.07.05
  • 심사 : 2024.08.18
  • 발행 : 2024.11.30
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초록

This study investigates the Charlier series approximation for modeling nonhomogeneous Poisson processes. It focuses on mixtures of Poisson distributions and Markov-Modulated Poisson processes to address complex temporal data patterns, such as hospital admission rates. The Charlier series approximation is constructed by expanding probability mass functions using Charlier orthogonal polynomials, which allow for adjustments to reflect higher-order moments like skewness and kurtosis. These polynomials are combined with a Poisson weight function to create flexible approximations tailored to the variability in event rates. Two artificial examples demonstrate the method's effectiveness in capturing dynamic event behaviors. A real-world application to hospital admission data further highlights its practical utility. Performance is assessed using Kullback-Leibler divergence, quantifying the improvement over simple Poisson models. The results show that the Charlier series provides enhanced data fitting and deeper insights into complex probabilistic structures.

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과제정보

This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (RS-2023-00259004) supervised by the IITP (Institute for Information and Communications Technology Planning and Evaluation).

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