Normal Mixture Representations and Analogs of the Multiplication Theorem for Some Distributions
V. Yu. Korolev, Yu. K. Homutov · Moscow University Computational Mathematics and Cybernetics · 2026
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.