Regency B
Physically Plausible PDFs for Intervals Between Geyser Eruptions (303960)
*Gordon R Bower, Excelsior Statistics and Optimization
Keywords: semiphysical models, natural processes, model fitting
Many of Yellowstone National Park's geysers exhibit a right-skewed distribution of the intervals between successive eruptions. While it is possible to model these intervals with a translated gamma or Weibull model, an alternative is to derive a family of distributions, based on a simple physical model for the recharge of the plumbing system feeding the geyser and a simple hazard function to describe how likely an eruption is to occur, given the state of the plumbing system.
The resulting distribution fits real-world data significantly better than normal, gamma, or Weibull models, and has additional explanatory power that an ad hoc model does not: when a geyser becomes less frequent, it typically also becomes more erratic and more right-skewed. Our new family of distributions mimics this behavior as the rate-of-recharge parameter is varied.
It is suggested that many real-world problems might be best approached by means of this 'semi-physical modeling', using basic facts about the dynamics of the process being modeled to inform our choice of what family of distributions to fit.