Scholarlink

<p>Circular data arises in various fields including robotics, biology, geology and material sciences. Modelling such data requires flexible distribution families on the hypertorus. Common choices are the von Mises and the wrapped normal distributions. In this work we investigate the <i>inverse stereographic normal distribution</i> as an alternative distribution family both from a theoretical and applied perspective. We first generalize unimodality results to arbitrary dimensions by proving that the inverse stereographic normal distribution is unimodal if and only if all eigenvalues of the covariance matrix are less than or equal to 0.5. We then analyze the flexibility by fitting mixtures of shifted inverse stereographic normal distributions via gradient descent to several examples of toroidal data.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An analysis of the modality and flexibility of the inverse stereographic normal distribution

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月13日

查看全文
  • Florian B. Hinz,
  • Amr H. Mahmoud,
  • Markus A. Lill

摘要

Circular data arises in various fields including robotics, biology, geology and material sciences. Modelling such data requires flexible distribution families on the hypertorus. Common choices are the von Mises and the wrapped normal distributions. In this work we investigate the inverse stereographic normal distribution as an alternative distribution family both from a theoretical and applied perspective. We first generalize unimodality results to arbitrary dimensions by proving that the inverse stereographic normal distribution is unimodal if and only if all eigenvalues of the covariance matrix are less than or equal to 0.5. We then analyze the flexibility by fitting mixtures of shifted inverse stereographic normal distributions via gradient descent to several examples of toroidal data.