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Hydrological Drought: Water Surface and Duration Curve Indices
Published in Saeid Eslamian, Faezeh Eslamian, Handbook of Drought and Water Scarcity, 2017
Manish Kumar Goyal, Vivek Gupta, Saeid Eslamian
Many probability distribution functions are available in the literature. There are numerous aspects to be considered before selecting a variable. The larger the number of parameters, the more the distribution is adaptive to the data, though, simultaneously, the less reliable is the parameter estimation. So Tallaksen and Lanen [40,41] suggested using a three-parameter distribution in the drought frequency analysis. Many distributions are generally similar in their middle part but are different in the tail [40,41], which represents the outlier events that are generally very extreme. The magnitude of an extreme event is inversely proportional to its return period, though extreme events may have a much fewer number of observations, which generally causes difficulty in selecting the best-fitted probability distribution function. Pickands [31] suggested using a generalized Pareto distribution for the PDS if the upper limit, u, is high enough. Generalized Pareto distribution has its extreme end bounded if the shape parameter is greater than 0, but if the shape parameter becomes 0, then it converts to exponential distribution.
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Published in Eric W. Harmsen, Megh R. Goyal, Flood Assessment, 2017
In an attempt to determine flood occurrence, Birikundavyi et al. [16] used two approaches commonly used for the probabilistic analysis of extreme flood magnitudes that are based on the annual maximum series (AMS) and the partial duration series (PDS). In the AMS approach the highest flood peak in the year is used, while in the PDS approach all those events that exceed a specified value are used. In the study, the Poisson distribution and generalized Pareto distribution (GPD) were used to describe the occurrence of flood and the flood magnitudes. Two neighboring flood peaks were independent if (1) they are separated by at least seven days and (2) the flow between them drops below 50% of the smaller peak.
Fitting flood frequency distributions using the annual maximum series and the peak over threshold approaches
Published in Canadian Water Resources Journal / Revue canadienne des ressources hydriques, 2022
Daniel Caissie, Gabriel Goguen, Nassir El-Jabi, Wafa Chouaib
In the application of the POT analysis, two distributions are fitted, namely the distribution of the occurrence of floods (time arrival) and the distribution of the floods exceedance (magnitudes of floods above the truncation level). The distributions used for the occurrence of floods are generally the Poisson, the binomial or a negative binomial distributions (Önöz and Bayazit 2001; Bhunya et al. 2013). In the case of the flood exceedances, the generalized Pareto distribution or special cases of thereof are often used (Ben-Zvi 2016). Cunnane (1979) looked at the relationship between successive flood peaks using scatter plots (floods that occurred within 5 and 10 days and for flood counts between 1 and 5 floods on average per year). No evidence of autocorrelation was found by the author from the 26 studied hydrometric stations. Most studies have reported that when the truncation level is relatively high (i.e. representing less than 2 floods per year on average), then the independence criteria is generally met (e.g. Cunnane 1973; Taesombut and Yevjevich 1978; Cunnane 1979; Ashkar and Rousselle 1987).
A robust methodology for predicting extreme structural responses of offshore wind turbines
Published in Ships and Offshore Structures, 2021
In order to establish the extreme value distribution by utilising the peak over threshold (POT) method, N load extremes, Lr (r = 1, 2, N) can be extracted from the aforementioned turbine response joint time series (the maximum load from each segment of the time series that lies between two successive upcrossings of a chosen threshold is retained as a load extreme). These extremes can then be used to establish an empirical distribution function, to which a parametric probability distribution model may be fit if desired. The POT method is based on what is called the Generalized Pareto distribution in the following manner: It has been shown that asymptotically, the excess values above a high level will follow a Generalized Pareto distribution if and only if the parent distribution belongs to the domain of attraction of one of the extreme value distributions. The cumulative distribution function of the Generalized Pareto distribution is (Coles (2001); Dargahi-Noubary (1989); Wang (2013, 2016)):for some a, c, L, , , . This distribution is call a Generalized Pareto distribution in which a is called the scale parameter and c is called the shape parameter.
Predicting Bitcoin Return Using Extreme Value Theory
Published in American Journal of Mathematical and Management Sciences, 2021
Mohammad Tariquel Islam, Kumer Pial Das
Researchers have been using EVT for modeling extreme events for many years. McNeil (1998) calculated quantile risk measures for financial return series considering a series of daily returns. Embrechts et al. (1999) showed how extreme value theory could be used as a risk management tool. Bensalah (2000) explained steps in applying extreme value theory to finance. Dey and Das (2020) analyzed extreme federal reserve rates using EVT. McNeil (1997, 1999) provided an overview of the role of EVT in risk management and estimated the tails of loss severity distributions using EVT. Dey and Das (2014, 2016b) and Daspit and Das (2012) modeled extreme hurricane damages using the Generalized Pareto Distribution (GPD). Engeland et al. (2004) introduced a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts. Edwards and Das (2016) used EVT to model extreme earthquakes in the United States. Das and Dey (2016) and Dey and Das (2016a) used EVT to quantify extreme aviation accidents. There are several recent papers dealing with Bitcoin and the cryptocurrency market. For example, Zhang et al. (2021) discussed the properties of Bitcoin and its interplay with other conventional assets for the sake of asset allocation and risk management. Gerritsen et al. (2020) applied a number of trend indicators to assess the profitability of technical trading rules in the bitcoin market. Naeem et al. (2021) examined the asymmetric efficiency of a number of cryptocurrencies, including bitcoin. Kristjanpoller et al. (2020) also examined the asymmetric multifractality between five main cryptocurrencies. Bouri et al. (2020) studied trade uncertainties and hedging abilities of Bitcoin. Bouri et al. (2021) also studied the volatility of Bitcoin returns in light of the US-China trade war. A quantile-based approach to study the impact of volume on Bitcoin returns and volatility was proposed by Balcilar et al. (2017). Bouri et al. (2019) introduced a similar study to understand the impact of trading volume on return and volatility. However, to the best of the authors’ knowledge, no study has been designed to predict bitcoin return using EVT. Osterrieder and Lorenz (2017) provided an extreme value analysis of the returns of bitcoin, where their particular focus was on univariate extreme value analysis. They compared cryptocurrency properties to the traditional exchange rates of the G10 currencies versus the US dollar. Among others, Scaillet et al. (2018) studied the high-frequency jump analysis of the bitcoin market; Athey et al. (2016) worked on bitcoin pricing, adoption, and usage; Moore and Christin (2013) did the empirical analysis of bitcoin exchange risk.