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. [1] Intergovernmental Panel on Climate Change (IPCC). Climate Change 2021: The Physical Science Basis. Cambridge, UK and New York, NY, USA: Cambridge University Press, 2021. doi: 10.1017/9781009157896.

    [2] Badan Meteorologi, Klimatologi, dan Geofisika (BMKG). Data Iklim Stasiun Meteorologi Sultan Syarif Kasim II Pekanbaru. 2023. Available at: https://dataonline.bmkg.go.id (accessed as required).

    [3] Edi Aldrian and R. Dwi Susanto. “Identification of Three Dominant Rainfall Regions within Indonesia and Their Relationship to Sea Surface Temperature”. In: International Journal of Climatology 23.12 (2003), pp. 1435–1452. doi: 10.1002/joc.950.

    [4] Stuart Coles. An Introduction to Statistical Modeling of Extreme Values. London: Springer, 2001. doi: 10.1007/978-1-4471-3675-0.

    [5] Alexander J. McNeil. Extreme Value Theory for Risk Managers. Internal Report. ETH Zürich, 1999.

    [6] W. Habibulloh and A. Y. Sofro. “Prediksi Suhu Udara di Jawa Tengah Menggunakan Extreme Value Theory”. In: MATHunesa: Jurnal Ilmiah Matematika 11.3 (2023), pp. 489–495. doi: 10.26740/mathunesa.v11n3.p489-495.

    [7] Hadi Tabari. “Extreme Value Analysis Dilemma for Climate Change Impact Assessment on Global Flood and Extreme Precipitation”. In: Journal of Hydrology 593 (2021), p. 125932. doi: 10.1016/j.jhydrol.2020.125932.

    [8] D. Rypkema and S. Tuljapurkar. “Modeling Extreme Climatic Events Using the Generalized Extreme Value Distribution”. In: Handbook of Statistics. Vol. 44. Elsevier, 2021, pp. 39–71. doi: 10.1016/bs.host.2020.12.002.

    [9] Roger B. Nelsen. An Introduction to Copulas. 2nd ed. New York: Springer, 2006. doi: 10.1007/0-387-28678-0.

    [10] Harry Joe. Multivariate Models and Multivariate Dependence Concepts. Boca Raton, FL: CRC Press, 1997.

    [11] A. Oktaviarina and A. Y. Sofro. “Analysis Between Temperature and Wind Speed in East Java Using Bivariate Extreme Value Theory”. In: Journal of Physics: Conference Series 1417.1 (2019), p. 012019. doi: 10.1088/1742-6596/1417/1/012019.

    [12] A. E. Kirana and A. Y. Sofro. “Prediksi Kelembaban dan Curah Hujan Maksimum di Kabupaten Malang Menggunakan Bivariate Extreme Value Logistic”. In: MATHunesa: Jurnal Ilmiah Matematika 12.3 (2024), pp. 465–474. doi: 10.26740/mathunesa.v12n3.p465-474.

    [13] N. Smirnov. “Table for Estimating the Goodness of Fit of Empirical Distributions”. In: The Annals of Mathematical Statistics 19.2 (1948), pp. 279–281. doi: 10.1214/aoms/1177730256.

    [14] M. B. Wilk and R. Gnanadesikan. “Probability Plotting Methods for the Analysis of Data”. In: Biometrika 55.1 (1968), pp. 1–17. doi: 10.1093/biomet/55.1.1.

    [15] N. C. Dzupire, P. Ngare, and L. Odongo. “A Copula-Based Bivariate Model for Temperature and Rainfall Processes”. In: Scientific African 8 (2020), e00365. doi: 10.1016/j.sciaf.2020.e00365.

    [16] A. Y. Sofro, W. Habibulloh, and K. N. Khikmah. “Prediction of Air Temperature Using Spatial Extreme Value with Copula Approach”. In: Journal of Theory and Applications in Mathematics 8.4 (2024), pp. 1217–1232. doi: 10.31764/jtam.v8i4.25436.

    [17] M. J. Frank. “On the Simultaneous Associativity of F(x,y) and x + y − F(x,y)”. In: Aequationes Mathematicae 19.1 (1979), pp. 194–226. doi: 10.1007/BF02189866.

    [18] A. C. Favre et al. “Multivariate Hydrological Frequency Analysis Using Copulas”. In: Water Resources Research 40.1 (2004). doi: 10.1029/2003WR002456.

    [19] Hirotugu Akaike. “A New Look at the Statistical Model Identification”. In: IEEE Transactions on Automatic Control 19.6 (1974), pp. 716–723. doi: 10.1109/TAC.1974.1100705.

    [20] Kenneth P. Burnham and David R. Anderson. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. New York: Springer, 2002. doi: 10.1007/b97636.

    [21] Samuel Kotz and Saralees Nadarajah. “Extreme Value Distributions: Theory and Applications”. In: International Encyclopedia of Statistical Science. Berlin, Heidelberg: Springer, 2011. doi: 10.1007/978-3-642-04898-2.

    [22] Edward Omey, Francisco Mallor, and Eulalia Nualart. An Introduction to Statistical Modelling of Extreme Values: Application to Calculate Extreme Wind Speeds. Technical Report. KU Leuven, 2009.

    [23] Ana Ferreira and Laurens de Haan. “On the Block Maxima Method in Extreme Value Theory: PWM Estimators”. In: The Annals of Statistics 43.1 (2015), pp. 276–298. doi: 10.1214/14-AOS1280.

    [24] Christopher P. Zwonik. Assessing Trends in Future Precipitation Extremes in the Northeastern United States Using the Method of Block Maxima. Master's Thesis. 2020.

    [25] J. D. Prang. Sebaran Nilai Ekstrim Terampat dalam Fenomena Curah Hujan. Undergraduate Thesis. Institut Pertanian Bogor, 2006.

    [26] Richard Minkah. “An Application of Extreme Value Theory to the Management of a Hydroelectric Dam”. In: SpringerPlus 5.1 (2016), pp. 1–12. doi: 10.1186/s40064-016-1719-2.

    [27] Ning Li, Xiaohui Liu, Wei Xie, Jie Wu, and Peng Zhang. “The Return Period Analysis of Natural Disasters with Statistical Modeling of Bivariate Joint Probability Distribution”. In: Risk Analysis 33.1 (2013), pp. 134–145. 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,
Maulana Malik Ibrahim State Islamic University of Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
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.