Cascade sizes in a branching process with Gamma distributed generations
James Burridge
TL;DR
This paper derives an exact formula for the distribution of cascade sizes in a branching process with Gamma-distributed generations, aiding the modeling of phenomena like landslides and network failures.
Contribution
It provides a novel exact expression for cascade size distribution in continuous state branching processes with Gamma-distributed generations.
Findings
Exact probability density function derived
Applicable to landslides and electrical failures
Enhances modeling accuracy for cascade phenomena
Abstract
We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of cascade processes such as landslides and electrical network failures.
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Taxonomy
TopicsInfrastructure Resilience and Vulnerability Analysis · Probabilistic and Robust Engineering Design · Evacuation and Crowd Dynamics