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arXiv · 2509.15502

Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution

Kyoya Uemura·Tomoyuki Obuch·Toshiyuki Tanaka
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Abstract

We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching processes at a sufficiently large generation in this asymptotic can be approximated by a compound Poisson-gamma distribution. Numerical experiments revealed that the compound Poisson-gamma models were in good agreement with the corresponding GW models for sufficiently large generations under a reasonable parameter regime. Our results can be regarded as supporting the use of the compound Poisson-gamma model as a model for cascaded multiplication processes, such as detection signals of electron multipliers and population sizes of individuals with specific biological characteristics.

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Kyoya Uemura, Tomoyuki Obuch, Toshiyuki Tanaka. 2025-09-19. Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution. https://doi.org/10.1103/w3yn-jpt5

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