Comparison of Parameter Estimation Methods to Determine the Frequency Data Magnitude of Aftershock in Nabire, Papua

Alvian M Sroyer; Tiku Tandiangnga; Felix Reba; Ishak Semuel Beno

Alvian M Sroyer Department of Mathematics, Faculty of Mathematics and Natural Sciences, Cenderawasih University https://orcid.org/0000-0003-1194-5774
Tiku Tandiangnga Department of Mathematics, Faculty of Mathematics and Natural Sciences, Cenderawasih University
Felix Reba Department of Mathematics, Faculty of Mathematics and Natural Sciences, Cenderawasih University
Ishak Semuel Beno Department of Mathematics, Faculty of Mathematics and Natural Sciences, Cenderawasih University https://orcid.org/0000-0002-4300-2271

Keywords: Weibull, Maximum Likelihood Method (MLE), Least Squares Method (LSM), Graphical Method, Kolmogorov Smirnov, Magnitude

Abstract

Many researchers use Weibull distribution to analyze wind speed data parameters and so forth, but in this research Weibull distribution is used to analyze the frequency data magnitude of aftershock. We use different methods for estimating Weibull distribution parameters. Some methods are compared according to the mean square error (MSE) criteria to select the best method. The parameter estimation results from the data are then used to determine the mean and magnitude of the earthquake. Further data is depicted in a curve for analysis. The case study in this study uses an aftershock frequency data in Nabire district, Papua. After the test of conformity with Kolmogorov-Smirnov test, it is obtained that the data follows the Weibull distribution pattern. Further research results show that the best method among the three methods is the maximum likelihood method (MLE).

Keywords: Weibull, Maximum Likelihood Method (MLE), Least Squares Method (LSM), Graphical Method, Kolmogorov Smirnov, Magnitude

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References

Anton, L., & Gibson, G. (2008). Analysing earthquake hazard in Papua New Guinea. Earthquake Engineering in Australia, AEES2008, Ballarat Victoria, Australia, 21–23.

Bormann, P. (2002). New manual of seismological observatory practice (NMSOP-1). GeoForschungZentrum, Potsdam, 1252p.

Gaillard, J. C., Clavé, E., Vibert, O., Denain, J. C., Efendi, Y., Grancher, D., & Setiawan, R. (2008). Ethnic groups’ response to the 26 December 2004 earthquake and tsunami in Aceh, Indonesia. Natural Hazards, 47(1), 17–38.

Greenhough, J., & Main, I. G. (2008). A Poisson model for earthquake frequency uncertainties in seismic hazard analysis. Geophysical Research Letters, 35.

Hagiwara, Y. (1974). Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain. Tectonophysics, 23(3), 313–318.

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1996). Continuous univariate distributions. Journal of the Royal Statistical Society-Series A Statistics in Society, 159(2), 349.

Osarumwense, O. I., & Rose, N. C. (2014). Parameters estimation methods of the Weibull distribution: A comparative study. Elixir Statistics, 69, 23177–23184.

Rinne, H. (2008). The Weibull distribution: a handbook. Chapman and Hall/CRC.

Saleh, H., Aly, A. A. E. A., & Abdel-Hady, S. (2012). Assessment of different methods used to estimate Weibull distribution parameters for wind speed in Zafarana wind farm, Suez Gulf, Egypt. Energy, 44(1), 710–719.

Werapun, W., Tirawanichakul, Y., & Waewsak, J. (2015). Comparative study of five methods to estimate Weibull parameters for wind speed on Phangan Island, Thailand. Energy Procedia, 79, 976–981.