K. Aki, Some problems in statistical seismology, Journal of Seismological Society of Japan, vol.8, pp.205-227, 1956.

P. Atkinson, J. Jiskoot, R. Massari, and T. Murray, Generalized linear modelling in geomorphology, Earth Surface Processes and Landforms, pp.13-1185, 1998.
DOI : 10.1002/(SICI)1096-9837(199812)23:13<1185::AID-ESP928>3.0.CO;2-W

P. Bak and C. Tang, Earthquakes as a self-organized critical phenomenon, Journal of Geophysical Research: Solid Earth, vol.9, issue.B11, pp.15-635, 1989.
DOI : 10.1029/JB094iB11p15635

P. Bak, K. Christensen, L. Danon, and T. Scanlon, Unified Scaling Law for Earthquakes, Physical Review Letters, vol.88, issue.17, p.178501, 2002.
DOI : 10.1103/PhysRevLett.88.178501

W. H. Bakun and A. G. Lindh, The Parkfield, California, earthquake prediction experiment Science, pp.619-624, 1985.

H. Benioff, Earthquakes and rock creep, pp.31-62, 1951.

A. F. Bell, M. Naylor, M. J. Heap, and I. G. Main, Forecasting volcanic eruptions and other material failure phenomena: An evaluation of the failure forecast method, Geophysical Research Letters, vol.350, issue.6320, p.15304, 2011.
DOI : 10.1029/2011GL048155
URL : https://hal.archives-ouvertes.fr/hal-00724844

C. G. Bufe and D. M. Perkins, Evidence for a Global Seismic-Moment Release Sequence, Bulletin of the Seismological Society of America, vol.95, issue.3, pp.833-843, 2005.
DOI : 10.1785/0120040110

V. Carbone, L. Sorriso-valvo, P. Harabaglia, and I. Guerra, Unified scaling law for waiting times between seismic events, Europhysics Letters (EPL), vol.71, issue.6, pp.1036-1042, 2005.
DOI : 10.1209/epl/i2005-10185-0

A. Corral, Local distributions and rate fluctuations in a unified scaling law for earthquakes, Physical Review E, vol.68, issue.3, pp.68-035102, 2003.
DOI : 10.1103/PhysRevE.68.035102

A. Corral, Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes, Physical Review Letters, vol.92, issue.10, p.92, 2004.
DOI : 10.1103/PhysRevLett.92.108501

A. Corral, Dependence of earthquake recurrence times and independence of magnitudes on seismicity history, Tectonophysics, vol.424, issue.3-4, pp.177-193, 2006.
DOI : 10.1016/j.tecto.2006.03.035

A. Corral, Statistical Features of Earthquake Temporal Occurrence, Lecture Notes in Physics, vol.705, pp.191-221, 2007.
DOI : 10.1007/3-540-35375-5_8

A. Corral and K. Christensen, Comment on ???Earthquakes Descaled: On Waiting Time Distributions and Scaling Laws???, Physical Review Letters, vol.96, issue.10, p.96, 2006.
DOI : 10.1103/PhysRevLett.96.109801

J. Davidsen and C. Goltz, Are seismic waiting time distributions universal? Geophysics Research Letters, pp.31-21612, 2005.

P. M. Davis, D. D. Jackson, and Y. Y. Kagan, The longer it has been since the last earthquake, the longer the expected time till the next?, pp.1439-1456, 1989.

S. D. Davis and C. Frohlich, Single-link cluster analysis of earthquake aftershocks: Decay laws and regional variations, Journal of Geophysical Research: Solid Earth, vol.91, issue.B4, pp.6335-6350, 1991.
DOI : 10.1029/90JB02634

B. Enescu, Z. Struzik, and K. Kiyono, On the recurrence time of earthquakes: insight from Vrancea (Romania) intermediate-depth events, Geophysical Journal International, vol.172, issue.1, pp.395-404, 2008.
DOI : 10.1111/j.1365-246X.2007.03664.x

J. K. Gardner and L. Knopoff, Is the sequence of earthquakes in Southern California , with aftershocks removed Poissonian?, pp.1363-1367, 1974.

G. K. Gilbert, Earthquake Forecasts.???I, Scientific American, vol.67, issue.1730supp, pp.121-138, 1909.
DOI : 10.1038/scientificamerican02271909-142supp

C. Godano and F. Pingue, Is the seismic moment-frequency relation universal?, Geophysical Journal International, vol.142, issue.1, pp.193-198, 2000.
DOI : 10.1046/j.1365-246x.2000.00149.x

Y. Hagiwara, Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain, Tectonophysics, vol.23, issue.3, pp.323-318, 1974.
DOI : 10.1016/0040-1951(74)90030-4

S. Hainzl, F. Scherbaum, and C. Beauval, Estimating background activity based on interevent-time distribution Bulletin of the, pp.313-320, 2006.

S. Hainzl and D. Marsan, Dependence of the Omori-Utsu law parameters on main shock magnitude: Observations and modeling, Journal of Geophysical Research, vol.110, issue.B5, p.113, 2008.
DOI : 10.1029/2007JB005492
URL : https://hal.archives-ouvertes.fr/insu-00354251

T. Hasumi, T. Akimoto, and Y. Aizawa, The Weibull -Log Weibull Distribution for Interoccurrence Times of Earthquakes Physica A, pp.491-498, 2009.

T. Hasumi, T. Akimoto, and Y. Aizawa, The Weibull -Log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge-Knopoff earthquake modelPhysica A, p.483, 2009.

C. Hasumi, T. Chen, &. Akimoto, and Y. Yaizawa, The Weibull???log Weibull transition of interoccurrence time for synthetic and natural earthquakes, Tectonophysics, vol.485, issue.1-4, p.9, 2010.
DOI : 10.1016/j.tecto.2009.11.012

M. Holschneider, G. Zöller, and S. Hainzl, Estimation of the Maximum Possible Magnitude in the Framework of a Doubly Truncated Gutenberg-Richter Model, Bulletin of the Seismological Society of America, vol.101, issue.4, pp.1649-1659, 2011.
DOI : 10.1785/0120100289

M. Huc and I. G. Main, Anomalous stress diffusion in earthquake triggering: Correlation length, time dependence, and directionality, Journal of Geophysical Research: Solid Earth, vol.105, issue.B7, p.2324, 2003.
DOI : 10.1029/2001JB001645

H. J. Jensen, Self-organized criticallity, 1998.

Y. Y. Kagan, Seismic moment distribution, Geophysical Journal International, vol.106, issue.1, pp.123-134, 1991.
DOI : 10.1111/j.1365-246X.1991.tb04606.x
URL : http://gji.oxfordjournals.org/cgi/content/short/148/3/520

Y. Y. Kagan, Seismic moment distribution revisited: I. Statistical results, Geophysical Journal International, vol.148, issue.3, pp.520-541, 2002.
DOI : 10.1046/j.1365-246x.2002.01594.x
URL : http://gji.oxfordjournals.org/cgi/content/short/148/3/520

Y. Y. Kagan, Earthquake size distribution: Power-law with exponent ?, Tectonophysics, vol.490, issue.1-2, pp.103-114, 2010.
DOI : 10.1016/j.tecto.2010.04.034

Y. Y. Kagan, Random stress and Omori's law, Geophysical Journal International, vol.186, issue.3, pp.1347-1364, 2011.
DOI : 10.1111/j.1365-246X.2011.05114.x
URL : http://arxiv.org/abs/1011.4992

Y. Y. Kagan and D. D. Jackson, Seismic Gap Hypothesis: Ten years after, Journal of Geophysical Research: Solid Earth, vol.341, issue.B13, pp.419-421, 1991.
DOI : 10.1029/91JB02210

Y. Y. Kagan and D. D. Jackson, New seismic gap hypothesis: Five years after, Journal of Geophysical Research: Solid Earth, vol.76, issue.43, pp.3943-3959, 1995.
DOI : 10.1029/94JB03014

Y. Y. Kagan and L. Knopoff, Statistical Short-Term Earthquake Prediction, Science, vol.236, issue.4808, pp.1563-1567, 1987.
DOI : 10.1126/science.236.4808.1563

Y. Y. Kagan and L. Knopoff, Random stress and earthquake statistics: time dependence, Geophysical Journal International, vol.88, issue.3, pp.723-731, 1987.
DOI : 10.1111/j.1365-246X.1987.tb01653.x

H. Kanamori, The energy release in great earthquakes, Journal of Geophysical Research, vol.82, issue.203, pp.2981-2987, 1977.
DOI : 10.1029/JB082i020p02981

R. A. Kerr, SEISMOLOGY: Parkfield Keeps Secrets After a Long-Awaited Quake, Science, vol.306, issue.5694, pp.206-207, 2004.
DOI : 10.1126/science.306.5694.206

A. Kijko, Estimation of the Maximum Earthquake Magnitude, m max, Pure and Applied Geophysics, vol.161, issue.8, pp.1-27, 2004.
DOI : 10.1007/s00024-004-2531-4

L. Knopoff and Y. Y. Kagan, Analysis of the theory of extremes as applied to earthquake problems, Journal of Geophysical Research, vol.64, issue.36, pp.5647-5657, 1977.
DOI : 10.1029/JB082i036p05647

C. Langenbruch, C. Dinske, and S. A. Shapiro, Inter event times of fluid induced earthquakes suggest their Poisson nature, Geophysical Research Letters, vol.101, issue.21, p.38, 2011.
DOI : 10.1029/2011GL049474

S. Lennartz, V. Livina, A. Bunde, and S. Havlin, Long-term memory in earthquakes and the distribution of interoccurrence times, EPL (Europhysics Letters), vol.81, issue.6, p.81, 2008.
DOI : 10.1209/0295-5075/81/69001

T. Leonard, O. Papsouliotis, and I. G. Main, A Poisson model for identifying characteristic size effects in frequency data: Application to frequency-size distributions for global earthquakes, ???starquakes???, and fault lengths, Journal of Geophysical Research: Solid Earth, vol.6, issue.B7, pp.13-473, 2001.
DOI : 10.1029/2000JB900429

A. M. Lombardi and W. Marzocchi, Evidence of clustering and nonstationarity in the time distribution of large worldwide earthquakes, Journal of Geophysical Research, vol.97, issue.B4, 2007.
DOI : 10.1029/2006JB004568

C. Lomnitz, Fundamentals of earthquakes prediction, 1994.

I. Main, Apparent breaks in scaling in the earthquake cumulative frequencymagnitude distribution: fact or artifact?, pp.86-97, 2000.

M. V. Matthews, W. L. Ellsworth, and P. A. Reasenberg, A Brownian Model for Recurrent Earthquakes, Bulletin of the Seismological Society of America, vol.92, issue.6, pp.2233-2250, 2002.
DOI : 10.1785/0120010267

W. R. Mccann, S. P. Nishenko, I. R. Sykes, and J. Krause, Seismic gaps and plate tectonics: seismic potential for major boundaries. Pure and applied geophysics, pp.1082-1147, 1979.

M. S. Mega, P. Allegrini, P. Grigolini, V. Latora, L. Palatella et al., Power-Law Time Distribution of Large Earthquakes, Physical Review Letters, vol.90, issue.18, p.18, 2003.
DOI : 10.1103/PhysRevLett.90.188501

G. Molchan, Interevent time distribution in seismicity: a theoretical approach Pure and Applied Geophysics, pp.1135-1150, 2005.

G. Molchan and T. Kronrod, Seismic Interevent Time: A Spatial Scaling and Multifractality, Pure and Applied Geophysics, vol.164, issue.1, pp.75-96, 2007.
DOI : 10.1007/s00024-006-0150-y

J. Murray and P. Segall, Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release, Nature, vol.66, issue.6904, pp.287-291, 2002.
DOI : 10.1029/1999JB900383

A. Nikoloulopoulos and D. Karlis, Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics, vol.64, issue.3, pp.251-269, 2008.
DOI : 10.1002/env.869

S. P. Nishenko and L. R. Sykes, Comment on ???Seismic gap hypothesis: Ten years after??? by Y. Y. Kagan and D. D. Jackson, Journal of Geophysical Research, vol.1053, issue.B6, pp.9909-9916, 1993.
DOI : 10.1029/93JB00101

Y. Ogata, Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, Journal of the American Statistical Association, vol.28, issue.7, pp.9-27, 1988.
DOI : 10.1007/BF02481022

Y. Ogata, Space-Time Point-Process Models for Earthquake Occurrences, Annals of the Institute of Statistical Mathematics, vol.50, issue.2, pp.379-402, 1998.
DOI : 10.1023/A:1003403601725

Y. Ogata, Seismicity Analysis through Point-process Modeling: A Review, pure and applied geophysics, vol.155, issue.2-4, pp.471-507
DOI : 10.1007/s000240050275

Y. Ogata and K. Katsura, Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophysical Journal International, vol.113, issue.3, pp.727-738, 1993.
DOI : 10.1111/j.1365-246X.1993.tb04663.x

F. Omori, On aftershocks, Journal of the College of Science, vol.7, pp.111-200, 1894.

J. F. Pacheco, C. H. Scholz, and L. R. Sykes, Changes in frequency???size relationship from small to large earthquakes, Nature, vol.355, issue.6355, pp.71-73, 1992.
DOI : 10.1038/355071a0

V. Pareto, Cours d'´ economie politique, tome 2, 1896.

T. Parsons, Global Omori law decay of triggered earthquakes: Large aftershocks outside the classical aftershock zone, Journal of Geophysical Research: Solid Earth, vol.12, issue.B9, p.2199, 2002.
DOI : 10.1029/2001JB000646

T. Parsons, Earthquake recurrence on the south Hayward fault is most consistent with a time dependent, renewal process, Geophysical Research Letters, vol.101, issue.1437, p.35, 2008.
DOI : 10.1029/2008GL035887

T. Parsons and E. L. Geist, Were Global M>=8.3 Earthquake Time Intervals Random between 1900 and 2011?, Bulletin of the Seismological Society of America, vol.102, issue.4, pp.1-11, 2012.
DOI : 10.1785/0120110282

A. Ramírez-rojas, E. L. Flores-marquez, and S. Valverde-esparza, Weibull Characterization of inter-event lags of Earthquakes ocurred in the Pacific Coast of Mexico, Geophysical Research Abstracts, vol.14, p.13708, 2012.

H. F. Reid, The Mechanics of the Earthquake of The California Earthquake of, Report of the State Earthquake Investigation Commission, 1906.

D. Rhoades, A. 1996 Estimation of the Gutenberg-Richter relation allowing for individual earthquake magnitude uncertainties Tectonophysics, pp.71-83
URL : https://hal.archives-ouvertes.fr/in2p3-00990297

T. Rikitake, Probability of an earthquake occurrence as estimated from crustal strain, Tectonophysics, pp.299-312, 1974.

J. B. Rundle, P. B. Rundle, R. Shcherbakov, and D. L. Turcotte, Earthquake waiting times: Theory and comparison with results from Virtual California simulations, Geophysical Research Abstracts, vol.7, p.2477, 2005.

J. C. Savage, Empirical earthquake probabilities from observed recurrence intervals, pp.219-221, 1994.

R. Shcherbakov, G. Yakovlev, D. L. Turcotte, and J. B. Rundle, Model for the Distribution of Aftershock Interoccurrence Times, Physical Review Letters, vol.95, issue.21, pp.95-218501, 2005.
DOI : 10.1103/PhysRevLett.95.218501

S. Shlien and M. N. Toksöz, A clustering model for earthquake occurrences, pp.1765-1787, 1970.

K. Sieh, The repetition of large-earthquake ruptures., Proceedings of the National Academy of Sciences, vol.93, issue.9, pp.3764-3771, 1996.
DOI : 10.1073/pnas.93.9.3764

K. Sieh, M. Stuiver, and D. Brillinger, A more precise chronology of earthquakes produced by the San Andreas Fault in southern California, Journal of Geophysical Research, vol.19, issue.7, pp.603-623, 1989.
DOI : 10.1029/JB094iB01p00603

R. S. Stein, Characteristic or hazard?, Nature, vol.370, pp.443-444, 1995.

R. S. Stein, Earth Science: Parkfield's unfulfilled promise, Nature, vol.81, issue.6904, pp.257-258, 2002.
DOI : 10.1126/science.285.5428.718

W. Thatcher, Earthquake recurrence and risk assessment in circum-Pacific seismic gaps, Nature, vol.341, issue.6241, pp.432-434, 1989.
DOI : 10.1038/341432a0

A. Udías and J. Rice, Statistical analysis of microearthquake activity near San Andreas Geophysical Observatory, pp.809-828, 1975.

T. Utsu, Estimation of parameters for recurrence models of earthquakes, pp.53-66, 1984.

T. Utsu, Representation and analysis of the earthquake size distribution: A historical review and some new approaches, Pure and Applied Geophysics, pp.509-535, 1999.

D. Vere-jones, Stochastic models for earthquake occurrence (with discussion), Journal of Royal Statistical Society, Series B, vol.32, pp.1-62, 1970.

D. Vere-jones, Stochastic Models for Earthquake Sequences, Geophysical Journal of the Royal Astronomical Society, vol.42, issue.2, pp.811-826, 1975.
DOI : 10.1111/j.1365-246X.1975.tb05893.x

D. Vere-jones, A branching model for crack propagation, Pure and Applied Geophysics, pp.711-725, 1976.

D. Vere-jones, Statistical theories of crack propagation, Mathematical Geology, vol.7, issue.4, pp.455-481, 1977.
DOI : 10.1007/BF02100959

D. Vere-jones, R. Robinson, and W. Yang, Remarks on the accelerated moment release model: problems of model formulation, simulation and estimation, Geophysical Journal International, vol.144, issue.3, pp.517-531, 2001.
DOI : 10.1046/j.1365-246x.2001.01348.x

J. H. Wang and C. Kuo, On the frequency distribution of interoccurrence times of earthquakes, Journal of Seismology, vol.2, issue.4, pp.351-358, 1998.
DOI : 10.1023/A:1009774819512