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<p>We investigate mappings whose components are bivariate normal densities from the perspective of singularity theory. Motivated by the need to understand two-component bivariate normal mixtures, we classify these mappings up to right-left equivalence and characterize them using statistical concepts. Our analysis reveals three distinct types, each with specific geometric properties, and we derive upper bounds on the number of modes in the mixture for each type.</p>

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Singularities in bivariate normal mixtures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月15日

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  • Yutaro Kabata,
  • Hirotaka Matsumoto,
  • Seiichi Uchida,
  • Masao Ueki

摘要

We investigate mappings whose components are bivariate normal densities from the perspective of singularity theory. Motivated by the need to understand two-component bivariate normal mixtures, we classify these mappings up to right-left equivalence and characterize them using statistical concepts. Our analysis reveals three distinct types, each with specific geometric properties, and we derive upper bounds on the number of modes in the mixture for each type.