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Analysis of Mathematical Models and Their Application to Extreme Events

Authors: Avellino I. Mondlane, Karin Hansson, Oliver Popov

Abstract:

This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes based on these three main distributions.

Keywords: Catastrophes, extreme event, disasters, mathematical models, simulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088654

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References:


[1] D. Mooney, R. Swift, “A Course in Mathematical Modeling”. The Mathematical Association of America 1999. LCCCN 98-85688 ISBN 0-8835-712-X.
[2] E. R. David et al., “Climate Extremes: Observations, Modeling and Impacts; Review: Atmosphere Science”. 22 September 2000 Vol. 289 Science. www.sciencemag.org.
[3] W. Peter et al., Learning Lessons from Disaster Recovery: the Case of Mozambique; Disaster Risk Management Working Paper series No.12 – The World Bank, April 2005.
[4] Mondlane, A. I. Hanson, K. and Popov O. B. “Insurance as Strategy for Flood Risk Management at Limpopo River Basin – A decision making Process under Uncertainty”. Penang December 2012 Oral Presentation ICUMDM 2012. International Conference on Uncertainty Modeling and Decision Making. http://www.waset.org/proceedings.php.
[5] T.S. Ferguson, “Probability and Mathematical Statistics, a Series of Monographs and Textbooks”, Department of Mathematics, University of California, Los Angels, California, LCCCN: 66-30080. AP 1967.
[6] C.B., V. Barros, et al., “IPCC, 2012: Summary for Policymakers. In: Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change”. Cambridge University Press, Cambridge, UK, and New York, NY, USA, pp. 1-19.
[7] P.V. Desanker and C. O. Justice, “Africa and Global Change: Critical issues and suggestions for further research and integrated assessment modeling”. Vol. 17:93-103, 2001. CLIMATE RESEARCH, Clim Res. © Inter-Research 2001.
[8] K. Hiroshi, “Climate anomalies and extreme events in Africa in 2003, including heavy rains and floods that occurred during northern hemisphere summer”. African Study Monographs, Suppl.30: 165- March 2005.
[9] B. Lyon, Notes and Correspondence, “Enhanced Seasonal Rainfall in Northern Venezuela and the Extreme Events of December 1999”. International Research Institute for Climate Prediction, Columbia University, Palisades, New York. 2301 Journal of Climate Volume 16. 2003.
[10] N.A. Doherty, “Integrated Risk Management Techniques and Strategies for managing Corporate Risk”, Two Pen Plaza, New York, NY 10121-2298 ISBN: 0-07-135861-7. McGraw-Hill 2000.
[11] INGC. “Synthesis report. INGC Climate Change Report: Study on the impact of climate change on disaster risk in Mozambique”.
[van Logchem B and Brito R (ed.)]. INGC, Mozambique, 2009.
[12] Munich Re 2012. TOPICS GEO 2012; Earthquake, flood, nuclear accident; Natural catastrophes 2011 Analyses, assessments, positions.
[13] B. Brian et al., The Economics of Adaptation to Extreme Weather Events in Developing Countries; Working paper 1999, Center for Global Development: www.cgdev.org January 2010.
[14] E.B. Haugen, “Probabilistic Approaches to Design” Aerospace & Mechanical Engineering Department, University Arizona, CCCN: 67-31377. JW1968.
[15] Z. Xu, “Homogeneous stochastic point process model for flood risk analysis. Extreme hydrological Events: Precipitation, Floods and Droughts” Proceedings of the Yokohama Symposium, July 1993. IAHS Publ. no. 213, 1993.
[16] The Chartered Insurance Institute. “Coping with climate change risks and opportunities for insurers”. 2009. Chapter 5, Market failure and climate change: Climate change research report 2009 - 2009.
[17] C. Stuart, “Anticipating catastrophes through extreme value modeling”. Appl. Statist. (2003). 52, Part 4, pp. 405-416. © 2003 Royal Statistical Society. 2003.
[18] D. O. Ernest & W. John, “System Modeling and Response – Theoretical and Experimental Approaches” - ISBN 0-471-03211-5 USA. 1980
[19] B. Magnus et al., “Conceptual Modeling. Prentice Hall Series Computer Science”. ISBN 0-13-514879-0; 1997.
[20] R.-D. Reiss and M. Thomas – Statistical Analysis of Extreme Values. With applications to Insurance, Finance, Hydrology and other fields. Third edition; ISB 978-3-7643-7230-9, Birkhäuser, Varlag Switzerland 2007.
[21] Kotz, S. Nadarajah, S. (2000), “Extreme Value Distributions: Theory and Applications.” London: Imperial College Press. ISBN: 1860942245; 2000.
[22] Mathwave Data Analysis & Simulation: http://www.mathwave.com/ articles/extreme-value-distributions.html.
[23] R. E. Paul and M. Evan, “Climate Change Future. Health, Ecological and Economic Dimensions”. The Center for Health and the Global Environment Harvard Medical School Sponsored by: Swiss Re United Nations Development Programme. 2006.