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Modeling Joint Cylindrical Distributions and Related Markov Processes

In: Directional and Multivariate Statistics

Author

Listed:
  • Toshihiro Abe

    (Hosei University, Faculty of Economics)

  • Tomoaki Imoto

    (University of Shizuoka, School of Management and Information)

  • Takayuki Shiohama

    (Nanzan University, Department of Data Science)

  • Yoichi Miyata

    (Takasaki City University of Economics, Faculty of Economics)

Abstract

Joint cylindrical distributions are key probability distributions that make possible a multivariate regression analysis as well as Markov models on a cylinder. In this study, some joint cylindrical distributions are proposed, and their statistical properties together with algorithms for random number generation are investigated. For proposed joint cylindrical distributions, the marginal distributions for various combinations of linear and circular variables are obtained. These marginal distributions are applied to the Markov process on a cylinder. The maximum likelihood estimation for unknown model parameters is investigated. To illustrate the applicability of the proposed models, time series analysis using wind speed and direction data is investigated.

Suggested Citation

  • Toshihiro Abe & Tomoaki Imoto & Takayuki Shiohama & Yoichi Miyata, 2025. "Modeling Joint Cylindrical Distributions and Related Markov Processes," Springer Books, in: Somesh Kumar & Barry C. Arnold & Kunio Shimizu & Arnab Kumar Laha (ed.), Directional and Multivariate Statistics, pages 103-129, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-2004-3_6
    DOI: 10.1007/978-981-96-2004-3_6
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