scholarly journals Application of Extreme Value Theory in Predicting Climate Change Induced Extreme Rainfall in Kenya

2019 ◽  
Vol 8 (4) ◽  
pp. 85
Author(s):  
Faithful C. Onwuegbuche ◽  
Alpha B. Kenyatta ◽  
Steeven B. Affognon ◽  
Exavery P. Enock ◽  
Mary O. Akinade
Keyword(s):  
Climate Change ◽  
Extreme Value Theory ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Return Level ◽  
Return Periods ◽  
Optimal Model ◽  
Return Levels

Climate change has brought about unprecedented new weather patterns, one of which is changes in extreme rainfall. In Kenya, heavy rains and severe flash floods have left people dead and displaced hundreds from their settlements. In order to build a resilient society and achieve sustainable development, it is paramount that adequate inference about extreme rainfall be made. To this end, this research modelled and predicted extreme rainfall events in Kenya using Extreme Value Theory for rainfall data from 1901-2016. Maximum Likelihood Estimation was used to estimate the model parameters and block maxima approach was used to fit the Generalized Extreme Value Distribution (GEVD) while the Peak Over Threshold method was used to fit the Generalized Pareto Distribution (GPD). The Gumbel distribution was found to be the optimal model from the GEVD while the Exponential distribution gave the optimal model over the threshold value. Furthermore, prediction for the return periods of 10, 20, 50 and 100 years were made using the return level estimates and their corresponding confidence intervals were presented. It was found that increase in return periods leads to a corresponding increase in return levels. However, the GPD gave higher return levels for 10 and 20 years compared to GEVD. While, for higher return periods 50 and 100 years, the GEVD gave higher return levels compared to the GPD. Model diagnostics using probability, density, quantile and return level plots indicated that the models provided were a good fit for the data.

scholarly journals Has fire policy decreased the return period of the largest wildfire events in France? A Bayesian assessment based on extreme value theory

2018 ◽  
Vol 18 (10) ◽  
pp. 2641-2651 ◽  
Author(s):  
Guillaume Evin ◽  
Thomas Curt ◽  
Nicolas Eckert
Keyword(s):  
Return Period ◽  
Extreme Value Theory ◽  
Fire Suppression ◽  
Value Theory ◽  
Extreme Value ◽  
Ecological Impacts ◽  
Return Level ◽  
Burned Area ◽  
Return Periods ◽  
Fire Policy

Abstract. Very large wildfires have high human, economic, and ecological impacts so that robust evaluation of their return period is crucial. Preventing such events is a major objective of the new fire policy set up in France in 1994, which is oriented towards fast and massive fire suppression. Whereas this policy is probably efficient for reducing the mean burned area (BA), its effect on the largest fires is still unknown. In this study, we make use of statistical extreme value theory (EVT) to compute return periods of very large BAs in southern France, for two distinct periods (1973 to 1994 and 1995 to 2016) and for three pyroclimatic regions characterized by specific fire activities. Bayesian inference and related predictive simulations are used to fairly evaluate related uncertainties. Results demonstrate that the BA corresponding to a return period of 5 years has actually significantly decreased, but that this is not the case for large return periods (e.g., 50 years). For example, in the most fire-prone region, which includes Corsica and Provence, the median 5-year return level decreased from 5000 to 2400 ha, while the median 50-year return level decreased only from 17 800 to 12 500 ha. This finding is coherent with the recent occurrence of conflagrations of large and intense fires clearly far beyond the suppression capacity of firemen. These fires may belong to a new generation of fires promoted by long-term fuel accumulation, urbanization into the wildland, and ongoing climate change. These findings may help adapt the operational system of fire prevention and suppression to ongoing changes. Also, the proposed methodology may be useful for other case studies worldwide.

scholarly journals Mapping snow depth return levels: smooth spatial modeling versus station interpolation

2010 ◽  
Vol 14 (12) ◽  
pp. 2527-2544 ◽  
Author(s):  
J. Blanchet ◽  
M. Lehning
Keyword(s):  
Snow Depth ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Return Level ◽  
Distribution Fitting ◽  
Regional Variability ◽  
Gev Distribution ◽  
Return Levels

Abstract. For adequate risk management in mountainous countries, hazard maps for extreme snow events are needed. This requires the computation of spatial estimates of return levels. In this article we use recent developments in extreme value theory and compare two main approaches for mapping snow depth return levels from in situ measurements. The first one is based on the spatial interpolation of pointwise extremal distributions (the so-called Generalized Extreme Value distribution, GEV henceforth) computed at station locations. The second one is new and based on the direct estimation of a spatially smooth GEV distribution with the joint use of all stations. We compare and validate the different approaches for modeling annual maximum snow depth measured at 100 sites in Switzerland during winters 1965–1966 to 2007–2008. The results show a better performance of the smooth GEV distribution fitting, in particular where the station network is sparser. Smooth return level maps can be computed from the fitted model without any further interpolation. Their regional variability can be revealed by removing the altitudinal dependent covariates in the model. We show how return levels and their regional variability are linked to the main climatological patterns of Switzerland.

scholarly journals Has fire policy decreased the return period of the largest wildfire events in France? A Bayesian assessment based on extreme value theory

2018 ◽  
Author(s):  
Guillaume Evin ◽  
Thomas Curt ◽  
Nicolas Eckert
Keyword(s):  
Return Period ◽  
Extreme Value Theory ◽  
Fire Suppression ◽  
Value Theory ◽  
Extreme Value ◽  
Ecological Impacts ◽  
Return Level ◽  
Burned Area ◽  
Return Periods ◽  
Fire Policy

Abstract. Very large wildfires have high human, economic and ecological impacts so that robust evaluation of their return period is crucial. Preventing such events is a major objective of the new fire policy set up in France in 1994, which is oriented towards fast and massive fire suppression. Whereas this policy is probably efficient for reducing the mean burned area (BA), its effect on the largest fires is still unknown. In this study, we make use of statistical Extreme Value Theory (EVT) to compute return periods of very large BA in southern France, for two distinct periods (1973 to 1994, and 1995 to 2016) and for three pyroclimatic regions characterized by specific fire activities. Bayesian inference and related predictive simulations are used to fairly evaluate related uncertainties. Results demonstrate that the BA corresponding to a return period of 5 years has actually significantly decreased, but that this is not the case for large return periods (e.g. 50 years). For example, in the most fire-prone region, which includes Corsica and Provence, the median 5-year return level decreased from 5,000 ha. to 2,400 ha., while the median 50-year return level decreased only from 17,800 ha. to 12,500 ha. This finding is coherent with the recent occurrence of conflagrations of large and intense fires clearly far beyond the suppression capacity of firemen. These fires may belong to a new generation of fires promoted by long-term fuel accumulation, urbanization into the wildland, and ongoing climate change. These findings may help adapting the operational system of fire prevention and suppression to ongoing changes. Also, the proposed methodology may be useful for other case studies worldwide.

scholarly journals Mapping snow depth return levels: smooth spatial modeling versus station interpolation

2010 ◽  
Vol 7 (4) ◽  
pp. 6129-6177 ◽  
Author(s):  
J. Blanchet ◽  
M. Lehning
Keyword(s):  
Snow Depth ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Return Level ◽  
Distribution Fitting ◽  
Regional Variability ◽  
Gev Distribution ◽  
Return Levels

Abstract. For adequate risk management in mountainous countries, hazard maps for extreme snow events are needed. This requires the computation of spatial estimates of return levels. In this article we use recent developments in extreme value theory and compare two main approaches for mapping snow depth return levels from in situ measurements. The first one is based on the spatial interpolation of pointwise extremal distributions (the so-called Generalized Extreme Value distribution, GEV henceforth) computed at station locations. The second one is new and based on the direct estimation of a spatially smooth GEV distribution with the joint use of all stations. We compare and validate the different approaches for modeling annual maximum snow depth measured at 100 sites in Switzerland during winters 1965–1966 to 2007–2008. The results show a better performance of the smooth GEV distribution fitting, in particular where the station network is sparser. Smooth return level maps can be computed from the fitted model without any further interpolation. Their regional variability can be revealed by removing the altitudinal dependent covariates in the model. We show how return levels and their regional variability are linked to the main climatological patterns of Switzerland.

scholarly journals Extreme Value Theory in Application to Delivery Delays

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 788
Author(s):  
Marcin Fałdziński ◽  
Magdalena Osińska ◽  
Wojciech Zalewski
Keyword(s):  
Maximum Likelihood ◽  
Extreme Value Theory ◽  
Maximum Likelihood Method ◽  
Rare Events ◽  
Value Theory ◽  
Extreme Value ◽  
Small Sample ◽  
Generalized Extreme Value Distribution ◽  
Return Level ◽  
Likelihood Method

This paper uses the Extreme Value Theory (EVT) to model the rare events that appear as delivery delays in road transport. Transport delivery delays occur stochastically. Therefore, modeling such events should be done using appropriate tools due to the economic consequences of these extreme events. Additionally, we provide the estimates of the extremal index and the return level with the confidence interval to describe the clustering behavior of rare events in deliveries. The Generalized Extreme Value Distribution (GEV) parameters are estimated using the maximum likelihood method and the penalized maximum likelihood method for better small-sample properties. The findings demonstrate the advantages of EVT-based prediction and its readiness for application.

scholarly journals Return Levels Approach and Periods of Currency Crises

2018 ◽  
Vol 10 (3) ◽  
pp. 77
Author(s):  
Mouridi HAMIDOU ◽  
Joseph Mung'atu ◽  
George Orwa
Keyword(s):  
Currency Crises ◽  
Currency Crisis ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Sample Mean ◽  
New Approach ◽  
Gev Distribution ◽  
Return Levels ◽  
Block Maxima

Dating and observing currency crisis periods lie at the heart of much international researchers. This is due to the lack of agreement in one research methodology. Until today, there does not exist a single theory or specific international policy regulation that can explain this phenomenon in global. To identify the periods of currency crisis, many methods have been brought out. Literature first employed a combination of sample mean and standard deviation. Some recent studies have attempted to use extreme value theory (EVT). Although these procedures have been more criticized in most of the literature. These drawbacks of existing approaches give rise to a new approach which is the main goal of this research. The main purpose of this study is to employ return levels technique to date currency crisis periods. The study will discuss only one method the block maxima approach. The stress losses i.e the generalized extreme value (GEV) distribution will be fitted to the annual block maxima to estimate the T-year return levels of extreme exchange market pressure index (EMPI). The parameters of the GEV distribution are estimated using the ML estimator method. Beside, a detailed procedure of the new approach is implemented. A comparison study between our identification approach and the existing conventional approach in the most literature is also conducted. We further illustrate the method by an empirical study on identifying periods of currency crisis of Kenya as case study. For practical implement the study focuses only on one single currency crisis model known as the alternative EMP index model for the intent of arbitrating the performance among various techniques. Results suggest that our new approach (RLDT) is performing better than the conventional method when the return period is considered big. Nonetheless, our technique appears to dominate the existing conventional approaches. This paper covers only a small area of this growing field of research. Hopefully, our investigations to contribute to these efforts by showing that return level dating technique derived from stress-losses model may have a place in the toolbox of economists looking for more accurate techniques in predicting currency crises.

scholarly journals Risk Analysis of Gold Prices in Pakistan Using Extreme Value Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ghulam Raza Khan ◽  
Alanazi Talal Abdulrahman ◽  
Osama Alamri ◽  
Zahid Iqbal ◽  
Maqsood Ahmad
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Risk Measures ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Extreme Stress ◽  
Daily Data ◽  
Peak Over Threshold ◽  
The Impact

Extreme value theory (EVT) is useful for modeling the impact of crashes or situations of extreme stress on investor portfolios. EVT is mostly utilized in financial modeling, risk management, insurance, and hydrology. The price of gold fluctuates considerably over time, and this introduces a risk on its own. The goal of this study is to analyze the risk of gold investment by applying the EVT to historical daily data for extreme daily losses and gains in the price of gold. We used daily gold prices in the Pakistan Bullion Market from August 1, 2011 to July 30, 2021. This paper covers two methods such as Block Maxima (BM) and Peak Over Threshold (POT) modeling. The risk measures which are adopted in this paper are Value at Risk (VaR) and Expected Shortfall (ES). The point and interval estimates of VaR and ES are obtained by fitting the Generalized Pareto (GPA) distribution. Moreover, in this paper, return-level forecasting is also included for the next 5 and 10 years by analyzing the Generalized Extreme Value (GEV) distribution.

scholarly journals Analysis of extreme rainfall in Oti River Basin (West Africa)

2021 ◽  
Author(s):  
Komi S. Klassou ◽  
Kossi Komi
Keyword(s):  
River Basin ◽  
Heavy Rainfall ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Return Periods ◽  
Maximum Rainfall ◽  
Daily Data ◽  
Dry Spell ◽  
Annual Maximum Rainfall

Abstract Understanding how extreme rainfall is changing locally is a useful step in the implementation of efficient adaptation strategies to negative impacts of climate change. This study aims to analyze extreme rainfall over the middle Oti River Basin. Ten moderate extreme precipitation indices as well as heavy rainfall of higher return periods (25, 50, 75, and 100 years) were calculated using observed daily data from 1921 to 2018. In addition, Mann–Kendall and Sen's slope tests were used for trend analysis. The results showed decreasing trends in most of the heavy rainfall indices while the dry spell index exhibited a rising trend in a large portion of the study area. The occurrence of heavy rainfall of higher return periods has slightly decreased in a large part of the study area. Also, analysis of the annual maximum rainfall revealed that the generalized extreme value is the most appropriate three-parameter frequency distribution for predicting extreme rainfall in the Oti River Basin. The novelty of this study lies in the combination of both descriptive indices and extreme value theory in the analysis of extreme rainfall in a data-scarce river basin. The results are useful for water resources management in this area.

Estimated earthquake probabilities in the north circum-Pacific area

1972 ◽  
Vol 62 (6) ◽  
pp. 1397-1410
Author(s):  
A. F. Shakal ◽  
D. E. Willis
Keyword(s):  
Extreme Value Theory ◽  
Probability Model ◽  
Value Theory ◽  
Extreme Value ◽  
Return Periods ◽  
The North ◽  
Aleutian Arc ◽  
Large Earthquakes ◽  
Earthquake Data ◽  
Pacific Area

abstract Gumbel's extreme value theory is applied to the estimation of probabilities of occurrence and return periods for large earthquakes in the north circum-Pacific area, using earthquake data from 1930 through 1971. The probability model of Epstein and Lomnitz is discussed with reference to Gumbel's extreme value theory. Estimated probabilities and expected extremes within individual tectonic blocks are calculated and compared. The area of the Aleutian Arc between 155°W and 167°W is found to have about an 80 per cent probability of an Ms ≧ 8 earthquake by 1980.

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