Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910039813390336 |
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| author | Uemura, Kyoya Obuch, Tomoyuki Tanaka, Toshiyuki |
| author_facet | Uemura, Kyoya Obuch, Tomoyuki Tanaka, Toshiyuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution Uemura, Kyoya Obuch, Tomoyuki Tanaka, Toshiyuki Probability 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. |
| title | Approximate Modeling for Supercritical Galton-Watson Branching Processes with Compound Poisson-Gamma Distribution |
| topic | Probability |
| url | https://arxiv.org/abs/2509.15502 |