Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania

Emmanuel Iyamuremye; Joseph Mung'atu; Peter Mwita

doi:doi:10.11648/j.ijsd.20190503.14

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Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania

Emmanuel Iyamuremye, Joseph Mung'atu, Peter Mwita

Published in International Journal of Statistical Distributions and Applications (Volume 5, Issue 3)

Received: 31 July 2019 Accepted: 27 August 2019 Published: 10 September 2019

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Abstract

Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.

Published in	International Journal of Statistical Distributions and Applications (Volume 5, Issue 3)
DOI	10.11648/j.ijsd.20190503.14
Page(s)	67-75
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Extreme Value Theory, Generalized Pareto Distribution (GPD), Poisson Generalized Pareto Distribution (Poisson-GPD), Maximum Likelihood Estimation, Likelihood Ration Test, Exceedances

References

[1]	Trends in summer extreme temperatures over the iberian peninsula using nonurban station data. Acero, F., Garc ́ıa, J. A., Gallego, M. C., Parey, S., & Dacunha-Castelle, D. (2014). Journal of Geophysical Research: Atmospheres, 119 (1), 39–53.
[2]	Extreme value analysis of wet and dry periods in sicily. Bordi, I., Fraedrich, K., Petitta, M., & Sutera, A. (2007). Theoretical and Applied Climatology, 87 (1-4), 61–71.
[3]	Extreme value analysis of wet and dry periods in sicily. Bordi, I., Fraedrich, K., Petitta, M., & Sutera, A. (2007). Theoretical and Applied Climatology, 87 (1-4), 61–71.
[4]	Extreme rainfall analysis at ungauged sites in the south of france: comparison of three approaches. Carreau, J., Neppel.
[5]	L., Arnaud, P., & Cantet, P. (2013). Journal de la Societe Francaise de Statistique, 154 (2), 119–138.
[6]	Statistical modelling of recent changes in extreme rainfall in taiwan. Chu, L.-F., McAleer, M., & Wang, S.-H. (2014). International Journal of Environmental Science and Development, 4 (1), 52–55.
[7]	Modelling non-stationary annual maximum flood heights in the lower limpopo river basin of Mozambique. Maposa, D., Cochran, J. J., & Lesaoana, M. (2016). J`amba: Journal of Disaster Risk Studies, 8 (1).
[8]	Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India. Mondal, A. & Mujumdar, P. P. (2015). Journal of Hydrology, 521, 217–231.
[9]	Changes in the extreme daily rainfall in south Korea. Park, J.-S., Kang, H.-S., Lee, Y. S., & Kim, M.-K. (2011). International Journal of Climatology, 31 (15), 2290–2299.
[10]	An introduction to statistical modelling of extreme values. Omey, E., Mallor, F., & Nualart, E. (2009). Application to calculate extreme wind speeds.
[11]	Extreme events in Pakistan. Zahid, M. (2017): Physical processes and impacts of changing climate.
[12]	Effect of the occurrence process of the peaks over threshold on the flood estimates. nz, B. & Bayazit, M. (2001). Journal of Hydrology, 244 (1), 86–96.
[13]	Evidence of trend in return levels for daily rainfall in new Zealand. Withers, C. S. & Nadarajah, S. (2000). Journal of Hydrology (New Zealand), 155–166.
[14]	Statistics of extremes, with applications in environment, insurance, and finance. Smith, R. L. (2003). In Extreme values in finance, telecommunications, and the environment (pp. 20–97). Chapman and Hall/CRC.
[15]	Non homogeneous poisson process modelling of seasonal extreme rainfall events in Tanzania. Ngailo, T., Shaban, N., Reuder, J., Rutalebwa, E., & Mugume, I. (2016b). International Journal of Science and Research (IJSR), 5 (10), 1858–1868.
[16]	Modelling of extreme maximum rainfall using extreme value theory for Tanzania. Ngailo, J., Reuder, J., Rutalebwa, E., Nyimvua, S., & Mesquita, D. (2016a). Int. J. Sci. Innov. Math. Res, 4, 34–45.
[17]	Extremes of daily rainfall in west central Florida. Nadarajah, S. (2005). Climatic change, 69 (2-3), 325–342.
[18]	Long-term changes in the frequency, intensity and duration of extreme storm surge events in southern europe. Cid, A., Meńendez, M., Castanedo, S., Abascal, A. J., M ́endez, F. J., & Medina, R. (2016). Climate dynamics, 46 (5-6), 1503–1516.
[19]	An introduction to statistical modeling of extreme values. Coles, S., Bawa, J., Trenner, L., & Dorazio, P. (2001)., volume 208. Springer.
[20]	Statistics of extremes. Annual Review of Statistics and its Application. Davison, A. C. & Huser, R. (2015), 2, 203–235.
[21]	Statistical modeling of hot spells and heat waves. Furrer, E. M., Katz, R. W., Walter, M. D., & Furrer, R. (2010). Climate Research, 43 (3), 191–205.
[22]	Models for exceedances over high thresholds. Davison, A. C. & Smith, R. L. (1990). Journal of the Royal Statistical Society. Series B (Methodological), 52 (3), 393–442.
[23]	A two-step framework for over-threshold modelling of environmental extremes. Bernardara, P., Mazas, F., Kergadallan, X., & Hamm, L. (2014). Natural Hazards and Earth System Sciences, 14 (3), 635–647.
[24]	Extreme value modeling of precipitation in case studies for china. Ender, M. & Ma, T. (2014). International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 2 (1), 23–36.
[25]	The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Jenkinson (1955). Quarterly Journal of the Royal Meteorological Society, 81 (348), 158–171.
[26]	Statistics of extremes in hydrology. Katz, R. W., Parlange, M. B., & Naveau, P. (2002). Advances in water resources, 25 (8-12), 1287–1304.
[27]	Statistical modeling of extreme rainfall in southwest western Australia. Li, Y., Cai, W., & Campbell, E. (2005). Journal of climate, 18 (6), 852–863.

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APA Style

Emmanuel Iyamuremye, Joseph Mung'atu, Peter Mwita. (2019). Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. International Journal of Statistical Distributions and Applications, 5(3), 67-75. https://doi.org/10.11648/j.ijsd.20190503.14

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ACS Style

Emmanuel Iyamuremye; Joseph Mung'atu; Peter Mwita. Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. Int. J. Stat. Distrib. Appl. 2019, 5(3), 67-75. doi: 10.11648/j.ijsd.20190503.14

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AMA Style

Emmanuel Iyamuremye, Joseph Mung'atu, Peter Mwita. Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. Int J Stat Distrib Appl. 2019;5(3):67-75. doi: 10.11648/j.ijsd.20190503.14

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@article{10.11648/j.ijsd.20190503.14,
  author = {Emmanuel Iyamuremye and Joseph Mung'atu and Peter Mwita},
  title = {Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {3},
  pages = {67-75},
  doi = {10.11648/j.ijsd.20190503.14},
  url = {https://doi.org/10.11648/j.ijsd.20190503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190503.14},
  abstract = {Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.},
 year = {2019}
}

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TY  - JOUR
T1  - Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania
AU  - Emmanuel Iyamuremye
AU  - Joseph Mung'atu
AU  - Peter Mwita
Y1  - 2019/09/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190503.14
DO  - 10.11648/j.ijsd.20190503.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 67
EP  - 75
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190503.14
AB  - Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.
VL  - 5
IS  - 3
ER  -

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Author Information

Emmanuel Iyamuremye

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Mung'atu

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Peter Mwita

Department of Mathematics and Statistics, Machakos University, Machakos, Kenya

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APA Style

Emmanuel Iyamuremye, Joseph Mung'atu, Peter Mwita. (2019). Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. International Journal of Statistical Distributions and Applications, 5(3), 67-75. https://doi.org/10.11648/j.ijsd.20190503.14

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ACS Style

Emmanuel Iyamuremye; Joseph Mung'atu; Peter Mwita. Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. Int. J. Stat. Distrib. Appl. 2019, 5(3), 67-75. doi: 10.11648/j.ijsd.20190503.14

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AMA Style

Emmanuel Iyamuremye, Joseph Mung'atu, Peter Mwita. Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania. Int J Stat Distrib Appl. 2019;5(3):67-75. doi: 10.11648/j.ijsd.20190503.14

Copy | Download

@article{10.11648/j.ijsd.20190503.14,
  author = {Emmanuel Iyamuremye and Joseph Mung'atu and Peter Mwita},
  title = {Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {3},
  pages = {67-75},
  doi = {10.11648/j.ijsd.20190503.14},
  url = {https://doi.org/10.11648/j.ijsd.20190503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190503.14},
  abstract = {Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Extreme Value Modelling of Rainfall Using Poisson-generalized Pareto Distribution: A Case Study Tanzania
AU  - Emmanuel Iyamuremye
AU  - Joseph Mung'atu
AU  - Peter Mwita
Y1  - 2019/09/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190503.14
DO  - 10.11648/j.ijsd.20190503.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 67
EP  - 75
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190503.14
AB  - Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.
VL  - 5
IS  - 3
ER  -

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