A Criterion for Extending Continuous-Mixture Identifiability Results

• URL: http://arxiv.org/abs/2503.03536v2
• Date: Mon, 16 Jun 2025 18:39:01 GMT
• Title: A Criterion for Extending Continuous-Mixture Identifiability Results
• Authors: Michael R. Powers, Jiaxin Xu,
• Abstract summary: Mixture distributions provide a versatile and widely used framework for modeling random phenomena.<n>We specify a simple criterion - generating-function accessibility - to extend previously known kernel-based identifiability results to new kernel distributions.<n>This criterion, based on functional relationships between the relevant kernels' moment-generating functions or Laplace transforms, may be applied to continuous mixtures of both discrete and continuous random variables.
• Score: 0.9208007322096533
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of random variables, we specify a simple criterion - generating-function accessibility - to extend previously known kernel-based identifiability (or unidentifiability) results to new kernel distributions. This criterion, based on functional relationships between the relevant kernels' moment-generating functions or Laplace transforms, may be applied to continuous mixtures of both discrete and continuous random variables. To illustrate the proposed approach, we present results for several specific kernels, in each case briefly noting its relevance to research in the geosciences and/or related risk analysis.

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