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Yes it matters -- the extent varies by several factors. Applications & Impact In many contexts using stochastic process-based models, one is well-served to use time-varying models to capture the time-dependent behavior of the system. And sometimes close enough, $I(t)\approx 1$ is good enough. In healthcare, appointment-based systems often see ...


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SecretAgentMan has given some specific examples of cases where over- and underdispersion will affect outcomes. I thought it might complement that answer to generalise those examples to some general principles about when over/under-dispersion is likely to happen. A Poisson process typically represents a count of many low-probability events, each of which is ...


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