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Abstract <p>In the book [<CitationRef CitationID="CR1">1</CitationRef>] a theorem was presented stating that a stable law can be represented as a scale mixture of a stable law with greater characteristic exponent. This theorem was called ‘‘multiplication theorem.’’ In our communication, analogs of this theorem are presented for the families of generalized Student distributions (including the classical Student law), exponential power distributions, generalized gamma distributions (including the Weibull and gamma laws), beta distributions and quasi-exponentiated normal distributions. For the latter, a complete solution is presented for the problem of its representability as a normal scale mixure.</p>

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Normal Mixture Representations and Analogs of the Multiplication Theorem for Some Distributions

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • V. Yu. Korolev,
  • Yu. K. Homutov

摘要

Abstract

In the book [1] a theorem was presented stating that a stable law can be represented as a scale mixture of a stable law with greater characteristic exponent. This theorem was called ‘‘multiplication theorem.’’ In our communication, analogs of this theorem are presented for the families of generalized Student distributions (including the classical Student law), exponential power distributions, generalized gamma distributions (including the Weibull and gamma laws), beta distributions and quasi-exponentiated normal distributions. For the latter, a complete solution is presented for the problem of its representability as a normal scale mixure.