L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data

ABSTRACT

Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for modelling the frequency of such events. The Birnbaum–Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962–2015, is carried out. This application identifies the extreme value Birnbaum–Saunders distribution as a better model than classic extreme value distributions for describing seismic events.

KEYWORDS:

• GCMT catalogue
• Generalized extreme value distributions
• goodness-of-fit methods
• maximum likelihood and moment estimation
• Monte Carlo simulation
• R software

Acknowledgements

The authors thank the reviewers for their constructive comments on an earlier version of this manuscript which resulted in this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work was partially supported by FONDECYT 1160868 and 1131147 grants from the Chilean government.