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<p>We propose a new general framework for obtaining and describing circular distributions based on the concept of offsetting. In this approach, a family of circular distributions is represented by a star-shaped set with unit area in the plane, and each member of the family is obtained by specifying the particular location and orientation of the coordinate axes of this set. For instance, one may construct a family of circular distributions generated by a disc in the plane. We then provide an interpretation within this framework for many known circular models, and explore possible extensions to higher dimensions.</p>

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A General Framework for Modeling Circular Distributions through Offset Representations

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • S. Rao Jammalamadaka,
  • Tomasz J. Kozubowski

摘要

We propose a new general framework for obtaining and describing circular distributions based on the concept of offsetting. In this approach, a family of circular distributions is represented by a star-shaped set with unit area in the plane, and each member of the family is obtained by specifying the particular location and orientation of the coordinate axes of this set. For instance, one may construct a family of circular distributions generated by a disc in the plane. We then provide an interpretation within this framework for many known circular models, and explore possible extensions to higher dimensions.