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In this paper, a distribution called quaternion inverse Gaussian distribution (QIGD) is introduced. The fundamental properties of probability density function, raw moments, moments generating function, skewness, and kurtosis are discussed. The maximum likelihood estimators of parameters in quaternion algebra are studied. Examples based on quaternion algebra and applications to quantum mechanics are illustrated.

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Perspective of Quaternion Algebra in Quantum Mechanics: Quaternion Inverse Gaussian Distribution

  • 会议论文

  • 发表日期：

    2025年

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  • Pratibha Sharma,
  • V. R. Lakshmi Gorty

摘要

In this paper, a distribution called quaternion inverse Gaussian distribution (QIGD) is introduced. The fundamental properties of probability density function, raw moments, moments generating function, skewness, and kurtosis are discussed. The maximum likelihood estimators of parameters in quaternion algebra are studied. Examples based on quaternion algebra and applications to quantum mechanics are illustrated.