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An erupting volcano is a complex system controlled by nonlinear dynamics and hence is difficult to model numerically. Statistical methods can be applied to explain behaviour or to aid the forecasting of future activity. The majority of previous studies have considered large-scale events: large explosive or effusive eruptions, with intervening long periods of repose. This has severely limited the size of the datasets and hence the significance of statistical results. In previous cases a simple Poisson model was applied, but often more sophisticated analysis methods are necessary to model the data. In this study, several statistical techniques are used to describe the data for smaller-scale events from four volcanoes. In each case study the events are relatively frequent explosions; this means that the datasets are large and thus allow a robust statistical analysis. First, time-series analysis is used to identify the presence of clustering or trends in the data. For stationary periods, the data are modelled in a probabilistic fashion, taking the survival function for increasing repose intervals and fitting different distributions to the data. Different types of events are identified, whose repose intervals have different distributions. This implies variation in the physics of the processes involved in the causation of the events. It is shown that activity can be divided into different periods based on the statistics, which can greatly aid in the construction of a model to explain the temporal evolution of eruptive activity. Contrasts between the volcanoes are highlighted, reflecting a variation in certain characteristics of their.

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