Statistical analysis of New Zealand volcanic occurrence data

The Poisson process is considered to provide a good fit to many volcanoes for forecasting eruptions. However, several exceptions exist, usually where the intensity is non-stationary. The nonhomogeneous Poisson model (the Weibull process) caters for a monotonically varying intensity, but often results in physically unrealistic behaviour. A model which allows for more general behaviour than the Poisson process is the Weibull renewal model. This paper considers data from two New Zealand volcanoes, Mt. Ruapehu and Mt. Ngauruhoe, and fits the Poisson and Weibull renewal models. We conclude that a simple Poisson process fits Ngauruhoe very well. The behaviour of Mt. Ruapehu is considerably more complex, although quite reasonable forecasts can still be obtained from the renewal models. An interesting feature of our analysis is that there seems to be no correlation between the observed eruption sequences of these two closely neighbouring volcanoes.