scholarly journals Estimation of the Extreme Distribution Model of Economic Losses Due to Outbreaks Using the POT Method with Newton Raphson Iteration

2021 ◽  
Vol 2 (1) ◽  
pp. 37-45
Author(s):  
Riza Adrian Ibrahim ◽  
Sukono Sukono ◽  
Riaman Riaman
Keyword(s):  
Estimation Method ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Model ◽  
Economic Losses ◽  
Extreme Distribution ◽  
Newton Raphson ◽  
The Government ◽  
Raphson Iteration

Extreme distribution is the distribution of a random variable that focuses on determining the probability of small values in the tail areaof the distribution. This distribution is widely used in various fields, one of which is reinsurance. An outbreak catastrophe is non-natural disaster that can pose an extreme risk of economic loss to a country that is exposed to it. To anticipate this risk, the government of a country can insure it to a reinsurance company which is then linkedto bonds in the capital market so that new securities are issued, namely outbreakcatastrophe bonds. In pricing, knowledge of the extreme distribution of economic losses due to outbreak catastrophe is indispensable. Therefore, this study aims to determine the extreme distribution model of economic losses due to outbreak catastrophe whose models will be determined by the approaches and methods of Extreme Value Theory and Peaks Over Threshold, respectively. The threshold value parameter of the model will be estimated by Kurtosis Method, while the other parameters will be estimated with Maximum Likelihood Estimation Method based on Newton-Raphson Iteration. The result of the research obtained is the resulting model of extreme value distribution of economic losses due to outbreak catastrophe that can be used by reinsurance companies as a tool in determining the value of risk in the outbreak catastrophe bonds.

A New Generation of Earthquake Recurrence Models Based on The Extreme Value Theory and Impact on Probabilistic Seismic Hazard Assessments

2021 ◽  
Author(s):  
Anne Dutfoy ◽  
Gloria Senfaute
Keyword(s):  
Seismic Hazard ◽  
Extreme Value Theory ◽  
Generalized Pareto Distribution ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Probabilistic Seismic Hazard ◽  
Universal Method ◽  
Value Analysis

Abstract Probabilistic Seismic Hazard Analysis (PSHA) procedures require that at least the mean activity rate be known, as well as the distribution of magnitudes. Within the Gutenberg-Richter assumption, that distribution is an Exponential distribution, upperly truncated to a maximum possible magnitude denoted $m_{max}$. This parameter is often fixed from expert judgement under tectonics considerations, due to a lack of universal method. In this paper, we propose two innovative alternatives to the Gutenberg-Richter model, based on the Extreme Value Theory and that don't require to fix a priori the value of $m_{max}$: the first one models the tail distribution magnitudes with a Generalized Pareto Distribution; the second one is a variation on the usual Gutenberg-Richter model where $m_{max}$ is a random variable that follows a distribution defined from an extreme value analysis. We use the maximum likelihood estimators taking into account the unequal observation spans depending on magnitude, the incompleteness threshold of the catalog and the uncertainty in the magnitude value itself. We apply these new recurrence models on the data observed in the Alps region, in the south of France and we integrate them into a probabilistic seismic hazard calculation to evaluate their impact on the seismic hazard levels. The proposed new recurrence models introduce a reduction of the seismic hazard level compared to the common Gutenberg-Richter model conventionally used for PSHA calculations. This decrease is significant for all frequencies below 10 Hz, mainly at the lowest frequencies and for very long return periods. To our knowledge, both new models have never been used in a probabilistic seismic hazard calculation and constitute a new promising generation of recurrence models.

On The Application of the Extreme Value Theory in Ship’s Strength Calculations - Technical Note

2012 ◽  
Vol 154 (A2) ◽  
Keyword(s):  
Random Process ◽  
Extreme Value Theory ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Technical Note ◽  
Probability Of Exceedance ◽  
Limit Value

A procedure is proposed for application of the extreme value theory (EVT) approach considering not only the maximal value of the corresponding random variable but also its probability of exceedance. It substantially reduces the probability of exceedance of any given limit value used in the case when traditional EVT is applied. Examples are provided to illustrate its application when records of the random process are available.

scholarly journals Dynamic VaR Measurement of Gold Market with SV-T-MN Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Fenglan Li ◽  
Jie Wang ◽  
Liyun Su ◽  
Bao Yang
Keyword(s):  
At Risk ◽  
Extreme Value Theory ◽  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Distribution Model ◽  
Market Return ◽  
Extreme Risk ◽  
Gold Market

VaR (Value at Risk) in the gold market was measured and predicted by combining stochastic volatility (SV) model with extreme value theory. Firstly, for the fat tail and volatility persistence characteristics in gold market return series, the gold price return volatility was modeled by SV-T-MN (SV-T with Mixture-of-Normal distribution) model based on state space. Secondly, future sample volatility prediction was realized by using approximate filtering algorithm. Finally, extreme value theory based on generalized Pareto distribution was applied to measure dynamic risk value (VaR) of gold market return. Through the proposed model on the price of gold, empirical analysis was investigated; the results show that presented combined model can measure and predict Value at Risk of the gold market reasonably and effectively and enable investors to further understand the extreme risk of gold market and take coping strategies actively.

scholarly journals Estimation of Extreme Cable Forces of Cable-Stayed Bridges Based on Monitoring Data and Random Vehicle Models

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yuan Ren ◽  
Zhiyuan Zhu ◽  
Ziyuan Fan ◽  
Qiao Huang
Keyword(s):  
Estimation Method ◽  
Value Theory ◽  
Extreme Value ◽  
Monitoring Data ◽  
Daily Maximum ◽  
Traffic Data ◽  
Cable Force ◽  
Maintenance Decisions ◽  
Cable Forces ◽  
Cable Stayed Bridges

For long-span cable-stayed bridges, cables serve as one of the most important components to guarantee structural integrity. Forces of stay cables indicate not only the performance of cables themselves but also the overall condition of bridges. In order to help stakeholders to make maintenance decisions, an extreme cable force estimation method was proposed based on cable force measurements and traffic data from the weighing system. First, raw monitoring data were preprocessed based on a median filtering to obtain usable cable force signals. The multiresolution wavelet method was used to extract traffic-induced force component from mixed signals. Then, a Monte Carlo-based random vehicle model was developed using traffic data from the weighing system. Based on field temperature measurements and simulation of traffic-induced effects, extreme cable forces with respect to vehicle loads and temperature effects were predicted by extreme value theory. The Generalized Pareto Distribution (GPD) was adopted to establish the probability distribution models of the daily maximum cable force. Then, the extreme value within a return period of 100 years was determined and compared with the design loading demand. Finally, the effectiveness of the proposed method was validated through a cable-stayed bridge in China. As a result, the low-frequency varying component of cable force response had positive correlation with environmental temperatures, and the extreme value of the predicted cable force under prospective traffic volumes was within limit interval value according to the design code. The conclusions can be utilized by bridge owners to make maintenance decisions.

scholarly journals The exact extreme value distribution – applied study

2017 ◽  
Vol 5 (2) ◽  
pp. 87
Author(s):  
Aisha Fayomi ◽  
Neamat Qutb ◽  
Ohoud Al-Beladi
Keyword(s):  
Estimation Method ◽  
Simulated Data ◽  
Daily Rainfall ◽  
Extreme Value Distribution ◽  
Real Data ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Applied Study ◽  
Extreme Value Model

Extreme value theory is used to develop models for describing the distribution of extreme events. Exact extreme value or compound distri-bution which is based on the theory of the maximum of random variables of random numbers is one of the most important models that are applicable in various situations, for instance of interest, it uses partial duration series (PDF) data to analyze extreme hydrological. As part of our earlier study, the parameters of this model were estimated by two methods, maximum likelihood (ML) and Bayesian- based on non-informative and informative priors. Moreover, a comparative study using simulated data showed that the Bayesian based on informative prior is the best estimation method. In this paper, a real data set taken from records of the largest daily rainfall data of Jeddah city in Saudi Arabia is used to fit the model when the parameters are estimated by Bayesian method. A comparative applied study indicates that the exact extreme value model under Bayesian estimates (BE) of its parameters provides appropriate fit for this data set and it is more applicable than the same model when the parameters are estimated by ML method and other three classical extreme value models.

ON THE APPLICATION OF THE EXTREME VALUE THEORY IN SHIP’S STRENGTH CALCULATIONS

2021 ◽  
Vol 154 (A2) ◽  
Author(s):  
L D Ivanov
Keyword(s):  
Random Process ◽  
Extreme Value Theory ◽  
Random Variable ◽  
Value Theory ◽  
Extreme Value ◽  
Probability Of Exceedance ◽  
Limit Value

A procedure is proposed for application of the extreme value theory (EVT) approach considering not only the maximal value of the corresponding random variable but also its probability of exceedance. It substantially reduces the probability of exceedance of any given limit value used in the case when traditional EVT is applied. Examples are provided to illustrate its application when records of the random process are available.

Extremes for high dimensional chaotic systems

2020 ◽  
Author(s):  
Tobias Kuna ◽  
Valerio Lucarini ◽  
Davide Faranda ◽  
Jerouen Wouters ◽  
Viviane Baladi
Keyword(s):  
Dynamical System ◽  
Extreme Value Theory ◽  
Chaotic Systems ◽  
Value Theory ◽  
Extreme Value ◽  
High Impact ◽  
Hitting Times ◽  
High Dimensional ◽  
Physical Measure ◽  
Extreme Distribution

<p>Extremes are related to high impact and serious hazard events and hence their study and prediction have been and continue to be highly relevant for all kind of applications in geoscience and beyond. Extreme value theory is promising to be able to predict them reliably and robustly. In the last fifteen years the classical extreme value theory for stochastic processes has been extended to dynamical systems and has been related to properties of physical measure (statistical properties of the system), return and hitting times. We will review what one can say for highly dimensional perfectly chaotic systems.  We will concentrate on relations between the index of the extreme distribution and invariants of the underlying dynamical system which are stable, in the sense that they will continuously depend on changing parameters in the dynamics.  Furthermore, we explore whether there exists a response theory for extremes, that is, whether the change of extremes can be quantitatilvely expressed  in terms of changing parameters. </p><p> </p>

scholarly journals Bayesian Updates for an Extreme Value Distribution Model of Bridge Traffic Load Effect Based on SHM Data

2021 ◽  
Vol 13 (15) ◽  
pp. 8631
Author(s):  
Xin Gao ◽  
Gengxin Duan ◽  
Chunguang Lan
Keyword(s):  
Probability Model ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Traffic Load ◽  
Monitoring Data ◽  
Distribution Model ◽  
Load Effect ◽  
Tail Distribution

As the distribution function of traffic load effect on bridge structures has always been unknown or very complicated, a probability model of extreme traffic load effect during service periods has not yet been perfectly predicted by the traditional extreme value theory. Here, we focus on this problem and introduce a novel method based on the bridge structural health monitoring data. The method was based on the fact that the tails of the probability distribution governed the behavior of extreme values. The generalized Pareto distribution was applied to model the tail distribution of traffic load effect using the peak-over-threshold method, while the filtered Poisson process was used to model the traffic load effect stochastic process. The parameters of the extreme value distribution of traffic load effect during a service period could be determined by theoretical derivation if the parameters of tail distribution were estimated. Moreover, Bayes’ theorem was applied to update the distribution model to reduce the statistical uncertainty. Finally, the rationality of the proposed method was applied to analyze the monitoring data of concrete-filled steel tube arch bridge suspenders. The results proved that the approach was convenient and found that the extreme value distribution type III might be more suitable as the traffic load effect probability model.

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