Comparison of Extreme Value Logistic and Copula Approaches for Bivariate Extreme Value in Pekanbaru

Fadilla Afsari, A'yunin Sofro

Abstract


Global climate change has intensified extreme weather events in tropical regions, increasing heat-related risks in Pekanbaru City. This study aims to analyze the joint behavior of extreme maximum temperature and humidity using a multivariate extreme value framework. Daily data from 2014–2024 were processed using a seasonal block maxima approach, resulting in 24 seasonal extreme observations. The marginal distributions follow a Weibull-type Generalized Extreme Value (GEV) distribution, indicating bounded extreme values. Dependence analysis indicates a weak association, where the Joe copula converges to the independence case, while the Frank copula yields the lowest AIC value among the fitted copula models. However, the difference in AIC values is small and should be interpreted cautiously. Joint return period analysis indicates that joint exceedance of seasonal block maxima is relatively infrequent (approximately 100 years), whereas single-variable exceedances occur more frequently (approximately 5.2 years). These return period estimates are exploratory and subject to uncertainty due to the limited sample size. Overall, the results suggest a weak dependence structure between the variables, and the findings should be interpreted cautiously in the context of climate-related risk assessment.

Keywords


Bivariate extreme value theory; climate risk; heat stress; humidity; Joe copula; temperature

Full Text:

PDF

References


  1. IPCC. Climate Change 2021: The Physical Science Basis. Cambridge University Press, Cambridge, UK and New York, NY, USA, 2021. doi: 10.1017/9781009157896.
  2. Badan Meteorologi, Klimatologi, dan Geofisika. Data Iklim Stasiun Meteorologi Sultan Syarif Kasim II Pekanbaru. 2023. Available at: https://dataonline.bmkg.go.id.
  3. Aldrian, E., and Susanto, R. D. “Identification of three dominant rainfall regions within Indonesia and their relationship to sea surface temperature.” International Journal of Climatology, 23(12), 1435–1452, 2003. doi: 10.1002/joc.950.
  4. Coles, S. An Introduction to Statistical Modeling of Extreme Values. Springer London, 2001. Available at: https://link.springer.com/book/10.1007/978-1-4471-3675-0.
  5. McNeil, A. J. Extreme Value Theory for Risk Managers. 1999. Available at: https://www.sfu.ca/~rjones/econ811/readings/McNeil%201999.pdf.
  6. Habibulloh, W., and Sofro, A. Y. “Prediksi suhu udara di Jawa Tengah menggunakan extreme value theory.” MATHunesa: Jurnal Ilmiah Matematika, 11(3), 489–495, 2023. doi: 10.26740/mathunesa.v11n3.p489-495.
  7. Tabari, H. “Extreme value analysis dilemma for climate change impact assessment on global flood and extreme precipitation.” Journal of Hydrology, 593, 125932, 2021. doi: 10.1016/j.jhydrol.2020.125932.
  8. Rypkema, D., and Tuljapurkar, S. “Modeling extreme climatic events using the generalized extreme value distribution.” Handbook of Statistics, 44, 39–71, 2021. doi: 10.1016/bs.host.2020.12.002.
  9. Nelsen, R. B. An Introduction to Copulas. 2nd ed. Springer New York, 2006. Available at: https://link.springer.com/book/10.1007/0-387-28678-0.
  10. Joe, H. Multivariate Models and Multivariate Dependence Concepts. CRC Press, Boca Raton, FL, 1997.
  11. Oktaviarina, A., and Sofro, A. Y. “Analysis between temperature and wind speed in East Java using bivariate extreme value theory.” Journal of Physics: Conference Series, 1417(1), 012019, 2019. doi: 10.1088/1742-6596/1417/1/012019.
  12. Kirana, A. E., and Sofro, A. Y. “Prediksi kelembaban dan curah hujan maksimum di Kabupaten Malang menggunakan bivariate extreme value logistic.” MATHunesa: Jurnal Ilmiah Matematika, 12(3), 465–474, 2024. doi: 10.26740/mathunesa.v12n3.p465-474.
  13. Smirnov, N. “Table for estimating the goodness of fit of empirical distributions.” The Annals of Mathematical Statistics, 19(2), 279–281, 1948. doi: 10.1214/aoms/1177730256.
  14. Wilk, M. B., and Gnanadesikan, R. “Probability plotting methods for the analysis of data.” Biometrika, 55(1), 1–17, 1968. doi: 10.1093/biomet/55.1.1.
  15. Dzupire, N. C., Ngare, P., and Odongo, L. “A copula-based bivariate model for temperature and rainfall processes.” Scientific African, 8, e00365, 2020. doi: 10.1016/j.sciaf.2020.e00365.
  16. Sofro, A. Y., Habibulloh, W., and Khikmah, K. N. “Prediction of air temperature using spatial extreme value with copula approach.” Journal of Theory and Applications in Mathematics, 8(4), 1217–1232, 2024. doi: 10.31764/jtam.v8i4.25436.
  17. Frank, M. J. “On the simultaneous associativity of F(x, y) and x + y - F(x, y).” Aequationes Mathematicae, 19(1), 194–226, 1979. doi: 10.1007/BF02189866.
  18. Favre, A. C., et al. “Multivariate hydrological frequency analysis using copulas.” Water Resources Research, 40(1), 2004. doi: 10.1029/2003WR002456.
  19. Akaike, H. “A new look at the statistical model identification.” IEEE Transactions on Automatic Control, 19(6), 716–723, 1974. doi: 10.1109/TAC.1974.1100705.
  20. Burnham, K. P., and Anderson, D. R. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. Springer, New York, NY, 2002. Available at: https://link.springer.com/book/10.1007/b97636.
  21. Kotz, S., and Nadarajah, S. “Extreme Value Distributions: Theory and Applications.” In: International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg, 2011. Available at: https://link.springer.com/referencework/10.1007/978-3-642-04898-2.
  22. Omey, E., Mallor, F., and Nualart, E. An Introduction to Statistical Modelling of Extreme Values: Application to Calculate Extreme Wind Speeds. Technical Report, KU Leuven, 2009. Available at: https://lirias.kuleuven.be/retrieve/231511.
  23. Ferreira, A., and de Haan, L. “On the block maxima method in extreme value theory: PWM estimators.” The Annals of Statistics, 43(1), 276–298, 2015. doi: 10.1214/14-AOS1280.
  24. Zwonik, C. P. Assessing Trends in Future Precipitation Extremes in the Northeastern United States Using the Method of Block Maxima. Master’s thesis, 2020.
  25. Prang, J. D. Sebaran Nilai Ekstrim Terampat dalam Fenomena Curah Hujan. Undergraduate thesis, Institut Pertanian Bogor, 2006. Available at: http://repository.ipb.ac.id/handle/123456789/43133.
  26. Minkah, R. “An application of extreme value theory to the management of a hydroelectric dam.” SpringerPlus, 5(1), 1–12, 2016. doi: 10.1186/s40064-016-1719-2.
  27. Li, N., Liu, X., Xie, W., Wu, J., and Zhang, P. “The return period analysis of natural disasters with statistical modeling of bivariate joint probability distribution.” Risk Analysis, 33(1), 134–145, 2013. doi: 10.1111/j.1539-6924.2012.01838.x.




DOI: https://doi.org/10.18860/cauchy.v11i1.41081

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Fadilla Afsari, A'yunin Sofro

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.