# The Negative Binomial Distribution as a Renewal Model for the Recurrence of Large Earthquakes

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## Abstract

The negative binomial distribution is presented as the waiting time distribution of a cyclic Markov model. This cycle simulates the seismic cycle in a fault. As an example, this model, which can describe recurrences with aperiodicities between 0 and 0.5, is used to fit the Parkfield, California earthquake series in the San Andreas Fault. The performance of the model in the forecasting is expressed in terms of error diagrams and compared with other recurrence models from literature.

## Key words

Negative binomial distribution renewal process seismic cycle earthquake forecasting## References

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