Modelling earthquake interevent times using mixtures of exponential distributions

Large earthquakes are the cause for the loss of many human lives, the destruction of whole cities and an economic catastrophe; hence, estimating probabilities of new earthquakes occurring within specific time intervals has become a matter of utmost importance. In view of that, various statistical models have been considered and different statistical methods have been implemented in existing literature for estimating model parameters. As a consequence, it has been documented that different statistical distributions used for modelling time intervals between earthquakes may provide good fits to the data. However, most of these distributions are associated with complex numerical computations for parameter estimation, regardless of the statistical method of estimation, thus making their practical use quite challenging. In the present study, a method for parameter estimation that relies upon mixtures of exponential distributions is proposed. Main appealing features of the method are that it is accurate and easy to implement, and that it is expected to outperform the widely used exponential distribution for cases where the time series in hand are non-stationary. The performance of this method is evaluated using data from the North Anatolian fault and from a catalogue in Southern California.