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Entropy method for earthquake volatility

Yıl 2020, Cilt: 38 Sayı: 1, 329 - 348, 27.03.2020

Öz

In this study, we obtained the volatility of 1. and 2. degree earthquake zones on the same fault line by using entropy method. The application of entropy in earthquake can be regarded as the extension of information entropy and probability theory. The entropy theory applied to derive the most likely univariate distributions subject to specified restriction by applying the principle of maximum entropy. These findings indicate the necessity of more detailed studies for a more comprehensive understanding the nature of Earthquake.

Kaynakça

  • [1] Laidler, K.J., (1995) Thermodynamics, In The World of Physical Chemistry, Oxford University Press, New York, NY, USA, 156–240.
  • [2] Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics, 52, 479-487. https://link.springer.com/content/pdf/10.1007%2FBF01016429.pdf
  • [3] Rao, M.,Chen, Y.,Vemuri, B.C., Wang, F. (2004) Cumulative residual entropy: a new measure of information , IEEE transactions on Information Theory, 50 6, 1220-1228. DOI: 10.1109/TIT.2004.828057
  • [4] Shafee, F. (2007) Lambert function and a new non-extensive form of entropy, IMA journal of applied mathematics, 72, 6, 785-800. https://doi.org/10.1093/imamat/hxm039
  • [5] Akpinar, S., Akpinar, E. K. (2006) Wind energy analysis based on maximum entropy principle (MEP)-type distribution function, Energy Conversion and Management, 48(4),1140-1149. https://doi.org/10.1016/j.enconman.2006.10.004.
  • [6] Pincus, S. (2008) Approximate entropy as an irregularity measure for financial data, Econometric Reviews, 27, 4-6, 329-362. https://doi.org/10.1080/07474930801959750
  • [7] Ubriaco, M. R. (2009) Entropies based on fractional calculus, Physics Letters A, 373, 30, 2516-2519. https://doi.org/10.1016/j.physleta.2009.05.026
  • [8] Akpinar, S., Akpinar, E. K. (2009) Estimation of wind energy potential using finite mixture distribution models, Energy Conversion and Management, 50, 4, 877-884. https://doi.org/10.1016/j.enconman.2009.01.007
  • [9] Rompolis, L. S. (2010) Retrieving risk neutral densities from European option prices based on the principle of maximum entropy, Journal of Empirical Finance, 17, 5, 918-937. https://doi.org/10.1016/j.jempfin.2010.04.007
  • [10] Moreno, B., García-Álvarez, M. T. (2011) Analyzing the effect of Renewable Energy Sources on Electricity Prices in Spain, A Maximum Entropy Econometric Approach. https://hrcak.srce.hr/107272
  • [11] Wang, G. J., Xie, C., Han, F. (2012) Multi-scale approximate entropy analysis of foreign exchange markets efficiency, Systems Engineering Procedia, 3, 201-208. https://doi.org/10.1016/j.sepro.2011.10.030
  • [12] Moreno, B., Garcia-Alvarez, M. T. (2013) The role of renewable energy sources on electricity prices in Spain. A maximum entropy econometric model, Strojarstvo: časopis za teoriju i praksu u strojarstvu, 55, 2, 149-159 https://hrcak.srce.hr/107272
  • [13] Lucia, U. (2013) Entropy and exergy in irreversible renewable energy systems, Renewable and Sustainable Energy Reviews, 20, 559-564. https://doi.org/10.1016/j.rser.2012.12.017
  • [14] Ormos, M., Zibriczky, D. (2014) Entropy-based financial asset pricing, PloS one, 9, 12, e115742. https://doi.org/10.1371/journal.pone.0115742
  • [15] Van Erven, T., Harremos, P. (2014) Rényi divergence and Kullback-Leibler divergence, IEEE Transactions on Information Theory, 60, 7, 3797-3820. https://10.1109/TIT.2014.2320500
  • [16] Azad, A. K., Rasul, M. G., Alam, M. M., Uddin, S. A., Mondal, S. K. (2014) Analysis of wind energy conversion system using Weibull distribution Procedia Engineering, 90,725-732 https://doi.org/10.1016/j.proeng.2014.11.803
  • [17] Niu, H., Wang, J. (2015) Quantifying complexity of financial short-term time series by composite multiscale entropy measure Communications in Nonlinear Science and Numerical Simulation, 22, 1-3, 375-382. https://doi.org/10.1016/j.cnsns.2014.08.038
  • [18] Dedu, S., Toma, A. (2015) An Integrated Risk Measure and Information Theory Approach for Modeling Financial Data and Solving Decision Making Problems, Procedia Economics and Finance, 22, 531-537. https://doi.org/10.1016/S2212-5671(15)00252-X
  • [19] Sati, M. M., Gupta, N. (2015) Some characterization results on dynamic cumulative residual Tsallis entropy, Journal of Probability and Statistics. http://dx.doi.org/10.1155/2015/694203
  • [20] Sheraz, M., Dedu, S., Preda, V. (2015) Entropy measures for assessing volatile markets. Procedia Economics and Finance, 22, 655-662. https://doi.org/10.1016/S2212-5671(15)00279-8
  • [21] Stosic, D., Stosic, D., Ludermir, T., Oliveira, W., Stosic, T., (2016) Foreign exchange rate entropy evolution during financial crises, Physica A: Statistical Mechanics and its Applications, 449,233-239. https://doi.org/10.1016/j.physa.2015.12.124
  • [22] Ram, S. K., Kulia, G., Molinas, M., (2016) On wind Turbine failure detection from measurements of phase currents: a permutation entropy approach, arXiv preprint arXiv:1601.05387. https://arxiv.org/pdf/1601.05387.pdf
  • [23] Shoaib, M., Siddiqui, I., Rehman, S., Rehman, S. U., Khan, S., Lashin, A. (2016) Comparison of wind energy generation using the maximum entropy principle and the Weibull distribution function. Energies, 9,10, 842 https://doi.org/10.3390/en9100842
  • [24] Ponta, L., Carbone, A. (2018) Information measure for financial time series: quantifying short-term market heterogeneity, Physica A: Statistical Mechanics and its Applications. https://doi.org/10.1016/j.physa.2018.06.085
  • [25] Khammar, A. H., Jahanshahi, S. M. A. (2018) On weighted cumulative residual Tsallis entropy and its dynamic version, Physica A: Statistical Mechanics and its Applications, 491, 678-692 https://doi.org/10.1016/j.physa.2017.09.079
  • [26] Main, I. G., Al‐Kindy, F. H. (2002). Entropy, energy, and proximity to criticality in global earthquake populations, Geophysical Research Letters, 29, 7, 1-25. https://doi.org/10.1029/2001GL014078
Yıl 2020, Cilt: 38 Sayı: 1, 329 - 348, 27.03.2020

Öz

Kaynakça

  • [1] Laidler, K.J., (1995) Thermodynamics, In The World of Physical Chemistry, Oxford University Press, New York, NY, USA, 156–240.
  • [2] Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics, 52, 479-487. https://link.springer.com/content/pdf/10.1007%2FBF01016429.pdf
  • [3] Rao, M.,Chen, Y.,Vemuri, B.C., Wang, F. (2004) Cumulative residual entropy: a new measure of information , IEEE transactions on Information Theory, 50 6, 1220-1228. DOI: 10.1109/TIT.2004.828057
  • [4] Shafee, F. (2007) Lambert function and a new non-extensive form of entropy, IMA journal of applied mathematics, 72, 6, 785-800. https://doi.org/10.1093/imamat/hxm039
  • [5] Akpinar, S., Akpinar, E. K. (2006) Wind energy analysis based on maximum entropy principle (MEP)-type distribution function, Energy Conversion and Management, 48(4),1140-1149. https://doi.org/10.1016/j.enconman.2006.10.004.
  • [6] Pincus, S. (2008) Approximate entropy as an irregularity measure for financial data, Econometric Reviews, 27, 4-6, 329-362. https://doi.org/10.1080/07474930801959750
  • [7] Ubriaco, M. R. (2009) Entropies based on fractional calculus, Physics Letters A, 373, 30, 2516-2519. https://doi.org/10.1016/j.physleta.2009.05.026
  • [8] Akpinar, S., Akpinar, E. K. (2009) Estimation of wind energy potential using finite mixture distribution models, Energy Conversion and Management, 50, 4, 877-884. https://doi.org/10.1016/j.enconman.2009.01.007
  • [9] Rompolis, L. S. (2010) Retrieving risk neutral densities from European option prices based on the principle of maximum entropy, Journal of Empirical Finance, 17, 5, 918-937. https://doi.org/10.1016/j.jempfin.2010.04.007
  • [10] Moreno, B., García-Álvarez, M. T. (2011) Analyzing the effect of Renewable Energy Sources on Electricity Prices in Spain, A Maximum Entropy Econometric Approach. https://hrcak.srce.hr/107272
  • [11] Wang, G. J., Xie, C., Han, F. (2012) Multi-scale approximate entropy analysis of foreign exchange markets efficiency, Systems Engineering Procedia, 3, 201-208. https://doi.org/10.1016/j.sepro.2011.10.030
  • [12] Moreno, B., Garcia-Alvarez, M. T. (2013) The role of renewable energy sources on electricity prices in Spain. A maximum entropy econometric model, Strojarstvo: časopis za teoriju i praksu u strojarstvu, 55, 2, 149-159 https://hrcak.srce.hr/107272
  • [13] Lucia, U. (2013) Entropy and exergy in irreversible renewable energy systems, Renewable and Sustainable Energy Reviews, 20, 559-564. https://doi.org/10.1016/j.rser.2012.12.017
  • [14] Ormos, M., Zibriczky, D. (2014) Entropy-based financial asset pricing, PloS one, 9, 12, e115742. https://doi.org/10.1371/journal.pone.0115742
  • [15] Van Erven, T., Harremos, P. (2014) Rényi divergence and Kullback-Leibler divergence, IEEE Transactions on Information Theory, 60, 7, 3797-3820. https://10.1109/TIT.2014.2320500
  • [16] Azad, A. K., Rasul, M. G., Alam, M. M., Uddin, S. A., Mondal, S. K. (2014) Analysis of wind energy conversion system using Weibull distribution Procedia Engineering, 90,725-732 https://doi.org/10.1016/j.proeng.2014.11.803
  • [17] Niu, H., Wang, J. (2015) Quantifying complexity of financial short-term time series by composite multiscale entropy measure Communications in Nonlinear Science and Numerical Simulation, 22, 1-3, 375-382. https://doi.org/10.1016/j.cnsns.2014.08.038
  • [18] Dedu, S., Toma, A. (2015) An Integrated Risk Measure and Information Theory Approach for Modeling Financial Data and Solving Decision Making Problems, Procedia Economics and Finance, 22, 531-537. https://doi.org/10.1016/S2212-5671(15)00252-X
  • [19] Sati, M. M., Gupta, N. (2015) Some characterization results on dynamic cumulative residual Tsallis entropy, Journal of Probability and Statistics. http://dx.doi.org/10.1155/2015/694203
  • [20] Sheraz, M., Dedu, S., Preda, V. (2015) Entropy measures for assessing volatile markets. Procedia Economics and Finance, 22, 655-662. https://doi.org/10.1016/S2212-5671(15)00279-8
  • [21] Stosic, D., Stosic, D., Ludermir, T., Oliveira, W., Stosic, T., (2016) Foreign exchange rate entropy evolution during financial crises, Physica A: Statistical Mechanics and its Applications, 449,233-239. https://doi.org/10.1016/j.physa.2015.12.124
  • [22] Ram, S. K., Kulia, G., Molinas, M., (2016) On wind Turbine failure detection from measurements of phase currents: a permutation entropy approach, arXiv preprint arXiv:1601.05387. https://arxiv.org/pdf/1601.05387.pdf
  • [23] Shoaib, M., Siddiqui, I., Rehman, S., Rehman, S. U., Khan, S., Lashin, A. (2016) Comparison of wind energy generation using the maximum entropy principle and the Weibull distribution function. Energies, 9,10, 842 https://doi.org/10.3390/en9100842
  • [24] Ponta, L., Carbone, A. (2018) Information measure for financial time series: quantifying short-term market heterogeneity, Physica A: Statistical Mechanics and its Applications. https://doi.org/10.1016/j.physa.2018.06.085
  • [25] Khammar, A. H., Jahanshahi, S. M. A. (2018) On weighted cumulative residual Tsallis entropy and its dynamic version, Physica A: Statistical Mechanics and its Applications, 491, 678-692 https://doi.org/10.1016/j.physa.2017.09.079
  • [26] Main, I. G., Al‐Kindy, F. H. (2002). Entropy, energy, and proximity to criticality in global earthquake populations, Geophysical Research Letters, 29, 7, 1-25. https://doi.org/10.1029/2001GL014078
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Articles
Yazarlar

Ayşe Metin Karakaş Bu kişi benim 0000-0003-3552-0105

Sinan Çalık Bu kişi benim 0000-0002-4258-1662

Yayımlanma Tarihi 27 Mart 2020
Gönderilme Tarihi 7 Mayıs 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 38 Sayı: 1

Kaynak Göster

Vancouver Karakaş AM, Çalık S. Entropy method for earthquake volatility. SIGMA. 2020;38(1):329-48.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/