Hazard Rate Estimation of Temporal Point Process, Case Study: Earthquake Hazard Rate in Nusatenggara Region

Hazard rate estimation is one of the important topics in forecasting earthquake occurrence. Forecasting earthquake occurrence is a part of the statistical seismology where the main subject is the point process. Generally, earthquake hazard rate is estimated based on the point process likelihood equation called the Hazard Rate Likelihood of Point Process (HRLPP). In this research, we have developed estimation method, that is hazard rate single decrement HRSD. This method was adapted from estimation method in actuarial studies. Here, one individual associated with an earthquake with inter event time is exponentially distributed. The information of epicenter and time of earthquake occurrence are used to estimate hazard rate. At the end, a case study of earthquake hazard rate will be given. Furthermore, we compare the hazard rate between HRLPP and HRSD method.

Authors:

• Sunusi N.
• Kresna A. J.
• Islamiyati A.
• Raupong

Keywords:

• Earthquake forecast
• Hazard Rate
• Likelihood point process
• Point process.

References:

[1] N.L. Bowers, N.L., H.U. Gerber, J.C. Hickman, and C.J. Nesbitt.
Actuarial Mathematics, The Society of Actuaries, 1986. p. 51-59.
[2] D.J. Daley and D. Vere-Jones. An Introduction to the Theory of
Point Processes, Springer, Berlin, 2003. p.2-19.
[3] S. Darwis, I.W. Mangku, dan N. Sunusi, Updating Seismic Renewal
Model, Far East Journal of Theoretical Statistics, 2008. 27(1), 101-
112.
[4] S. Darwis, S., Sunusi, N., Triyoso, W., dan Mangku, I. W. Single
Decrement Approach for Estimating Earthquake Hazard Rate,
Advances and Applications in Statistica, 2009. 11(2), 229-237.
[5] R. L. London, FSA, Survival Models and Their Estimation, 3rd Edition,
Actex, 1997. p.113-200.
[6] S.G. Ferraes, Probabilistic Prediction of the Next Large Earthquake in
the Michoacan Fault-segment of the Mexican Subduction Zone,
Geofisica Internacional, 2003. 42, 69-83.
[7] R. Helmers, I.W. Mangku, dan R. Zitikis. Consistent Estimation of the
Intensity Function of a Cyclic Poisson Process, Journal of Multivariat
Analysis, 2003. 84, 19-39.
[8] R. Helmers, I.W. Mangku,, dan R. Zitikis. Statistical Properties of a
Kernel-Type Estimator of the Intensity Function of a Cyclic Poisson
Process, Journal of Multivariat Analysis, 2005. 92, 1-23.
[9] Y. Ogata. Seismicity Analysis Through Point Process Modeling: A
Review, Pure and Applied Geophysics, 1999.155, 471-507.
[10] T. Rikitake. Probability of an Earthquake Occurrence as Estimated from
Crustal Strain, Tectonophysics, 1974. 23, 299-312.
[11] N. Sunusi, S. Darwis, dan W. Triyoso. Estimating Intensity of Point
Processes Models Applied to Earthquake Prediction, Mathematics
Journal University Teknologi Malaysia, 2008. 2, 405-411.
[12] N. Sunusi, S. Darwis, W. Triyoso, dan I.W. Mangku, Study of
Earthquake Forecast through Hazard Rate Analysis, International
Journal of Applied Mathematics and Statistics (IJAMAS), 2010.
17(J10), 96-103.
[13] D. Vere-Jones. Forecasting Earthquakes and Earthquakes Risk,
International Journal of Forecasting, 11, 1995. 503-538.
[14] V. Yilmaz dan H.E. Celik, A Statistical Approach for Estimating the
Probability of Occurrence of Earthquake on the Northern Anatolian
Fault Zone, International Journal of Natural and Engineering Science,
2(2), 2008. 81-86.