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Morganti, Paolo Riccardo. "Extreme Value Theory and Auction Models". Abril - Junio 2021 16, nr 2 (22.01.2021): 1–15. http://dx.doi.org/10.21919/remef.v16i2.596.
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The objective of this article is to develop a parametric approach to estimating auctions with incomplete data using Extreme Value Theory (EVT). The methodology is mainly theoretical: we first review that, when only transaction prices can be observed, the distribution of private valuations is irregularly identified. The sample bias produced by nonparametric estimators will affect all functionals of practical interest. We provide simulations for a best-case scenario and a worst-case scenario. Our results show that, compared to nonparametric approaches, the approximation of such functionals developed using EVT produces more accurate results, is easy to compute, and does not require strong assumptions about the unobserved distribution of bidders' valuations. It is recommended that financial operators working with auctions use this parametric approach when facing incomplete datasets. Given the difficult nature of the analysis, this work does not provide large sample properties for the proposed estimators and recommends the use of bootstrapping. This article contributes originally to the literature of structural estimation of auction models providing a useful and robust parametric approximation.
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AghaKouchak, Amir, i Nasrin Nasrollahi. "Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data". Water Resources Management 24, nr 6 (7.08.2009): 1229–49. http://dx.doi.org/10.1007/s11269-009-9493-3.
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Božović, Miloš. "Portfolio Tail Risk: A Multivariate Extreme Value Theory Approach". Entropy 22, nr 12 (17.12.2020): 1425. http://dx.doi.org/10.3390/e22121425.
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This paper develops a method for assessing portfolio tail risk based on extreme value theory. The technique applies separate estimations of univariate series and allows for closed-form expressions for Value at Risk and Expected Shortfall. Its forecasting ability is tested on a portfolio of U.S. stocks. The in-sample goodness-of-fit tests indicate that the proposed approach is better suited for portfolio risk modeling under extreme market movements than comparable multivariate parametric methods. Backtesting across multiple quantiles demonstrates that the model cannot be rejected at any reasonable level of significance, even when periods of stress are included. Numerical simulations corroborate the empirical results.
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Guevara, C. Angelo, i Moshe E. Ben-Akiva. "Sampling of alternatives in Multivariate Extreme Value (MEV) models". Transportation Research Part B: Methodological 48 (luty 2013): 31–52. http://dx.doi.org/10.1016/j.trb.2012.11.001.
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Salvadori, G., i C. De Michele. "Estimating strategies for multiparameter Multivariate Extreme Value copulas". Hydrology and Earth System Sciences 15, nr 1 (17.01.2011): 141–50. http://dx.doi.org/10.5194/hess-15-141-2011.
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Abstract. Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according to different criteria: these may use a single station approach, or a cluster strategy, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.
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Salvadori, G., i C. De Michele. "Estimating strategies for Multiparameter Multivariate Extreme value copulas". Hydrology and Earth System Sciences Discussions 7, nr 5 (4.10.2010): 7563–90. http://dx.doi.org/10.5194/hessd-7-7563-2010.
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Abstract. Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according to different criteria: these may use either a nearest neighbor or a nearest cluster approach, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.
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Han, Yu. "Semi-Parametric Statistical Model for Extreme Value Statistical Models and Application in Automatic Control". Applied Mechanics and Materials 680 (październik 2014): 455–58. http://dx.doi.org/10.4028/www.scientific.net/amm.680.455.
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The frequency that extreme events appear in the life is low,but once it appears,the impact will be significant; many scholars have conducted in depth research and found that statistical theory of extreme value. The theory of extreme statistics plays a more and more important role in many fields such as automatic control, assembly line etc. This paper,makes an in-depth research towards the characteristics and parameter estimation of the extreme value statistical models,as well as the application,mainly analyzes the Bayes parameter estimation method of extreme value distribution,the extreme value distribution theory and Copula function random vector model.
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Cirillo, Pasquale, i Jürg Hüsler. "GENERALIZED EXTREME SHOCK MODELS WITH A POSSIBLY INCREASING THRESHOLD". Probability in the Engineering and Informational Sciences 25, nr 3 (17.05.2011): 419–34. http://dx.doi.org/10.1017/s0269964811000088.
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We propose a generalized extreme shock model with a possibly increasing failure threshold. Although standard models assume that the crucial threshold for the system might only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks might increase the system tolerance to large shock. This is, for example, the case of turbines’ running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the article we show how to link this new model to some nonparametric approaches proposed in the literature.
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Bounceur, Ahcene, Salvador Mir, Reinhardt Euler i Kamel Beznia. "Estimation of Analog/RF Parametric Test Metrics Based on a Multivariate Extreme Value Model". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39, nr 5 (maj 2020): 966–76. http://dx.doi.org/10.1109/tcad.2019.2907923.
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Kyselý, Jan. "A Cautionary Note on the Use of Nonparametric Bootstrap for Estimating Uncertainties in Extreme-Value Models". Journal of Applied Meteorology and Climatology 47, nr 12 (1.12.2008): 3236–51. http://dx.doi.org/10.1175/2008jamc1763.1.
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Abstract The parametric and nonparametric approaches to the bootstrap are compared as to their performance in estimating uncertainties in extreme-value models. Simulation experiments make use of several combinations of true and fitted probability distributions utilized in climatological and hydrological applications. The results demonstrate that for small to moderate sample sizes the nonparametric bootstrap should be interpreted with caution because it leads to confidence intervals that are too narrow and underestimate the real uncertainties involved in the frequency models. Although the parametric bootstrap yields confidence intervals that are slightly too liberal as well, it improves the uncertainty estimates in most examined cases, even under conditions in which an incorrect parametric model is adopted for the data. Differences among three examined types of bootstrap confidence intervals (percentile, bootstrap t, and bias corrected and accelerated) are usually smaller in comparison with those between the parametric and nonparametric versions of bootstrap. It is concluded that the parametric bootstrap should be preferred whenever inferences are based on small to moderate sample sizes (n ≤ 60) and a suitable model for the data is known or can be assumed, including applications to confidence intervals related to extremes in global and regional climate model projections.
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Beirlant, J., G. Matthys i G. Dierckx. "Heavy-Tailed Distributions and Rating". ASTIN Bulletin 31, nr 1 (maj 2001): 37–58. http://dx.doi.org/10.2143/ast.31.1.993.
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AbstractIn this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.
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Degen, Matthias, i Paul Embrechts. "EVT-based estimation of risk capital and convergence of high quantiles". Advances in Applied Probability 40, nr 3 (wrzesień 2008): 696–715. http://dx.doi.org/10.1239/aap/1222868182.
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We discuss some issues regarding the accuracy of a quantile-based estimation of risk capital. In this context, extreme value theory (EVT) emerges naturally. The paper sheds some further light on the ongoing discussion concerning the use of a semi-parametric approach like EVT and the use of specific parametric models such as the g-and-h. In particular, we discusses problems and pitfalls evolving from such parametric models when using EVT and highlight the importance of the underlying second-order tail behavior.
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Degen, Matthias, i Paul Embrechts. "EVT-based estimation of risk capital and convergence of high quantiles". Advances in Applied Probability 40, nr 03 (wrzesień 2008): 696–715. http://dx.doi.org/10.1017/s0001867800002755.
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We discuss some issues regarding the accuracy of a quantile-based estimation of risk capital. In this context, extreme value theory (EVT) emerges naturally. The paper sheds some further light on the ongoing discussion concerning the use of a semi-parametric approach like EVT and the use of specific parametric models such as the g-and-h. In particular, we discusses problems and pitfalls evolving from such parametric models when using EVT and highlight the importance of the underlying second-order tail behavior.
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önalan, ömer. "The modeling of extreme stochastic dependence using copulas and extreme value theory: case study from energy prices". Global Journal of Mathematical Analysis 5, nr 2 (5.06.2017): 29. http://dx.doi.org/10.14419/gjma.v5i2.7256.
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In this paper, we investigate the properties of tail dependence with an approach which is based on the copula models and extreme value theory to obtain a joint distribution function of extreme events and to quantify the dependence between random variables. To achieve this objective, we quantify the large co-movements between the random variables returns which are based on the data set daily quotes of exceeds the threshold value of random variables. In this study, stochastic dependence was modeled by the copulas which it provides a good approach for constructing multivariate probability distributions with flexible marginal’s and different forms of dependence. Choosing the right copula is very important in modeling. The multivariate distributions are easily simulated using the copulas. Finally we can describe the copula family which correctly represents the dependence. To demonstrate the usefulness of the proposed models, we confine our analysis to big price changes of energy commodity spot prices. The empirical findings demonstrated that the copula model which is combined the extreme value theory is a good approach to model the together extreme large changes.
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Moretti, Alba Regina, i Beatriz Vaz de Melo Mendes. "Medindo a Influência do Mercado dos EUA sobre as Interdependências Observadas na América Latina". Brazilian Review of Finance 3, nr 1 (1.01.2005): 123. http://dx.doi.org/10.12660/rbfin.v3n1.2005.1147.
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The modeling of the extremal dependence structure can be made through parametric models classified in two families: Logistic and Mixed, which contain the symmetric and asymmetric models. The bivariate models are very useful in practical applications on the extreme value theory, in particular in a financial area. Considering the strong influence of the North American market on other financial markets, we investigate how does the dependence structure among the Latin American markets change after filtering the influence of the North American market. To remove that influence, we carry on a polynomial regression with GARCH (1,1) errors, and fit the bivariate extreme value models to the pairs of monthly maxima and minima of the standardized regression residuals.
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Basterfield, David, i Thomas Bundt. "Multivariate Stable Distributions and Value at Risk: The Case of the Asian Currency Crisis". Journal of Finance Issues 5, nr 1 (30.06.2007): 187–95. http://dx.doi.org/10.58886/jfi.v5i1.2601.
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This paper explores practical applications of multivariate stable distributions to value at risk modeling during the Asian currency crisis. We fit multivariate stable distributions to daily foreign exchange rate data 1996 through 1998 for six Asian currencies using a rolling estimation procedure and backtest daily marginal and conditional probabilities under 95% and 99% value at risk nulls. We also examine gains in value at risk accuracy from using multivariate stable distributions relative to univariate benchmarks such as generalized autoregressive conditional heteroskedasticity or univariate stable models. We find multivariate stable distributions overstate the probability of extreme losses.
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Cardell, N. Scott. "Variance Components Structures for the Extreme-Value and Logistic Distributions with Application to Models of Heterogeneity". Econometric Theory 13, nr 2 (kwiecień 1997): 185–213. http://dx.doi.org/10.1017/s0266466600005727.
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Two new classes of probability distributions are introduced that radically simplify the process of developing variance components structures for extremevalue and logistic distributions. When one of these new variates is added to an extreme-value (logistic) variate, the resulting distribution is also extreme value (logistic). Thus, quite complicated variance structures can be generated by recursively adding components having this new distribution, and the result will retain a marginal extreme-value (logistic) distribution. It is demonstrated that the computational simplicity of extreme-value error structures extends to the introduction of heterogeneity in duration, selection bias, limited-dependent- and qualitative-variable models. The usefulness of these new classes of distributions is illustrated with the examples of nested logit, multivariate risk, and competing risk models, where important generalizations to conventional stochastic structures are developed. The new models are shown to be computationally simpler and far more tractable than alternatives such as estimation by simulated moments. These results will be of considerable use to applied microeconomic researchers who have been hampered by computational difficulties in constructing more sophisticated estimators.
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Shortridge, Julie E., Seth D. Guikema i Benjamin F. Zaitchik. "Machine learning methods for empirical streamflow simulation: a comparison of model accuracy, interpretability, and uncertainty in seasonal watersheds". Hydrology and Earth System Sciences 20, nr 7 (4.07.2016): 2611–28. http://dx.doi.org/10.5194/hess-20-2611-2016.
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Abstract. In the past decade, machine learning methods for empirical rainfall–runoff modeling have seen extensive development and been proposed as a useful complement to physical hydrologic models, particularly in basins where data to support process-based models are limited. However, the majority of research has focused on a small number of methods, such as artificial neural networks, despite the development of multiple other approaches for non-parametric regression in recent years. Furthermore, this work has often evaluated model performance based on predictive accuracy alone, while not considering broader objectives, such as model interpretability and uncertainty, that are important if such methods are to be used for planning and management decisions. In this paper, we use multiple regression and machine learning approaches (including generalized additive models, multivariate adaptive regression splines, artificial neural networks, random forests, and M5 cubist models) to simulate monthly streamflow in five highly seasonal rivers in the highlands of Ethiopia and compare their performance in terms of predictive accuracy, error structure and bias, model interpretability, and uncertainty when faced with extreme climate conditions. While the relative predictive performance of models differed across basins, data-driven approaches were able to achieve reduced errors when compared to physical models developed for the region. Methods such as random forests and generalized additive models may have advantages in terms of visualization and interpretation of model structure, which can be useful in providing insights into physical watershed function. However, the uncertainty associated with model predictions under extreme climate conditions should be carefully evaluated, since certain models (especially generalized additive models and multivariate adaptive regression splines) become highly variable when faced with high temperatures.
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Arun, Ashutosh, Md Mazharul Haque, Ashish Bhaskar i Simon Washington. "Transferability of multivariate extreme value models for safety assessment by applying artificial intelligence-based video analytics". Accident Analysis & Prevention 170 (czerwiec 2022): 106644. http://dx.doi.org/10.1016/j.aap.2022.106644.
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Taylor, Stephen. "Clustering Financial Return Distributions Using the Fisher Information Metric". Entropy 21, nr 2 (24.01.2019): 110. http://dx.doi.org/10.3390/e21020110.
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Information geometry provides a correspondence between differential geometry and statistics through the Fisher information matrix. In particular, given two models from the same parametric family of distributions, one can define the distance between these models as the length of the geodesic connecting them in a Riemannian manifold whose metric is given by the model’s Fisher information matrix. One limitation that has hindered the adoption of this similarity measure in practical applications is that the Fisher distance is typically difficult to compute in a robust manner. We review such complications and provide a general form for the distance function for one parameter model. We next focus on higher dimensional extreme value models including the generalized Pareto and generalized extreme value distributions that will be used in financial risk applications. Specifically, we first develop a technique to identify the nearest neighbors of a target security in the sense that their best fit model distributions have minimal Fisher distance to the target. Second, we develop a hierarchical clustering technique that utilizes the Fisher distance. Specifically, we compare generalized extreme value distributions fit to block maxima of a set of equity loss distributions and group together securities whose worst single day yearly loss distributions exhibit similarities.
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Louisor, Jessie, Jérémy Rohmer, Thomas Bulteau, Faïza Boulahya, Rodrigo Pedreros, Aurélie Maspataud i Julie Mugica. "Deriving the 100-Year Total Water Level around the Coast of Corsica by Combining Trivariate Extreme Value Analysis and Coastal Hydrodynamic Models". Journal of Marine Science and Engineering 9, nr 12 (30.11.2021): 1347. http://dx.doi.org/10.3390/jmse9121347.
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As low-lying coastal areas can be impacted by flooding caused by dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents), the analysis of the return period of a single component is not representative of the return period of the total water level at the coast. It is important to assess a joint return period of all the components. Based on a semiparametric multivariate extreme value analysis, we determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and still water level (SWL) exceeded jointly imposed thresholds all along the Corsica Island coasts (Mediterranean Sea). We also considered the covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du). Here, we focus on providing extreme scenarios to populate coastal hydrodynamic models, SWAN and SWASH-2DH, in order to compute the 100-year total water level (100y-TWL) all along the coasts. We show how the proposed multivariate extreme value analysis can help to more accurately define low-lying zones potentially exposed to coastal flooding, especially in Corsica where a unique value of 2 m was taken into account in previous studies. The computed 100y-TWL values are between 1 m along the eastern coasts and a maximum of 1.8 m on the western coast. The calculated values are also below the 2.4 m threshold recommended when considering the sea level rise (SLR). This highlights the added value of performing a full integration of extreme offshore conditions, together with their dependence on hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding.
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Bengtsson, A., i C. Nilsson. "Extreme value modelling of storm damage in Swedish forests". Natural Hazards and Earth System Sciences 7, nr 5 (12.09.2007): 515–21. http://dx.doi.org/10.5194/nhess-7-515-2007.
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Abstract. Forests cover about 56% of the land area in Sweden and forest damage due to strong winds has been a recurring problem. In this paper we analyse recorded storm damage in Swedish forests for the years 1965–2007. During the period 48 individual storm events with a total damage of 164 Mm³ have been reported with the severe storm on 8 to 9 January 2005, as the worst with 70 Mm³ damaged forest. For the analysis, storm damage data has been normalised to account for the increase in total forest volume over the period. We show that, within the framework of statistical extreme value theory, a Poisson point process model can be used to describe these storm damage events. Damage data supports a heavy-tailed distribution with great variability in damage for the worst storm events. According to the model, and in view of available data, the return period for a storm with damage in size of the severe storm of January 2005 is approximately 80 years, i.e. a storm with damage of this magnitude will happen, on average, once every eighty years. To investigate a possible temporal trend, models with time-dependent parameters have been analysed but give no conclusive evidence of an increasing trend in the normalised storm damage data for the period. Using a non-parametric approach with a kernel based local-likelihood method gives the same result.
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Waheed, Saddam Q., Neil S. Grigg i Jorge A. Ramirez. "Development of a Parametric Regional Multivariate Statistical Weather Generator for Risk Assessment Studies in Areas with Limited Data Availability". Climate 8, nr 8 (11.08.2020): 93. http://dx.doi.org/10.3390/cli8080093.
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Risk analysis of water resources systems can use statistical weather generators coupled with hydrologic models to examine scenarios of extreme events caused by climate change. These require multivariate, multi-site models that mimic the spatial, temporal, and cross correlations of observed data. This study developed a statistical weather generator to facilitate bottom-up approaches to assess the impact of climate change on water resources systems for cases of limited data. While existing weather generator models have impressive features, this study suggested a simple weather generator which is straightforward to implement and can employ any distribution function for variables such as precipitation or temperature. It is based on (1) a first-order, two-state Markov chain to simulate precipitation occurrences; (2) the use of Wilks’ technique to produce correlated weather variables at multiple sites with the conservation of spatial, temporal, and cross correlations; (3) the capability to vary the statistical parameters of the weather variables. The model was applied to studies of the Diyala River basin in Iraq, which is a case with limited observed records. Results show that it exhibits high values (e.g., over 0.95) for the Nash–Sutcliffe and Kling–Gupta metric tests, preserves the statistical properties of the observed variables, and conserves the spatial, temporal, and cross correlations among the weather variables in the meteorological stations.
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Budiarti, Retno, Kumala Intansari, I. Gusti Putu Purnaba i Fendy Septyanto. "Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula". JTAM (Jurnal Teori dan Aplikasi Matematika) 7, nr 3 (17.07.2023): 805. http://dx.doi.org/10.31764/jtam.v7i3.15109.
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Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets.
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He, Q., Y. J. Zheng, C. L. Zhang i H. Y. Wang. "MTAD-TF: Multivariate Time Series Anomaly Detection Using the Combination of Temporal Pattern and Feature Pattern". Complexity 2020 (28.10.2020): 1–9. http://dx.doi.org/10.1155/2020/8846608.
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Currently, multivariate time series anomaly detection has made great progress in many fields and occupied an important position. The common limitation of many related studies is that there is only temporal pattern without capturing the relationship between variables and the loss of information leads to false warnings. Our article proposes an unsupervised multivariate time series anomaly detection. In the prediction part, multiscale convolution and graph attention network are mainly used to capture information in temporal pattern with feature pattern. The threshold selection part uses the root mean square error between the predicted value and the actual value to perform extreme value analysis to obtain the threshold. Finally, the model in this paper outperforms other latest models on actual datasets.
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Arthur, William C. "A statistical–parametric model of tropical cyclones for hazard assessment". Natural Hazards and Earth System Sciences 21, nr 3 (10.03.2021): 893–916. http://dx.doi.org/10.5194/nhess-21-893-2021.
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Abstract. We present the formulation of an open-source, statistical–parametric model of tropical cyclones (TCs) for use in hazard and risk assessment applications. The model derives statistical relations for TC behaviour (genesis rate and location, intensity, speed and direction of translation) from best-track datasets, then uses these relations to create a synthetic catalogue based on stochastic sampling, representing many thousands of years of activity. A parametric wind field, based on radial profiles and boundary layer models, is applied to each event in the catalogue that is then used to fit extreme-value distributions for evaluation of return period wind speeds. We demonstrate the capability of the model to replicate observed behaviour of TCs, including coastal landfall rates which are of significant importance for risk assessments.
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Yang, Wei, Liping Zhang, Lijie Shan, Xinchi Chen i Shaodan Chen. "Response of Extreme Hydrological Events to Climate Change in the Water Source Area for the Middle Route of South-to-North Water Diversion Project". Advances in Meteorology 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/2486928.
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As the water source area for the middle route of China’s South-to-North Water Diversion Project, the upper Hanjiang basin is of central concern for future management of the country’s water resources. The upper Hanjiang is also one of the most flood-prone rivers in China. This paper explores the process of extreme floods by using multivariate analysis to characterize flood and precipitation event data in combination, for historical data and simulated data from global climate models. The results suggested that the generalized extreme value and Gamma models better simulated the extreme precipitation and flood volume sequence than the generalized Pareto model for the annual maximum series, while the generalized Pareto distribution model was the best-fit model for peaks over threshold series. For the two-dimensional joint distributions of precipitation and flood volume, the Frank Copula was preferred in simulation of the annual maximum flood series whereas the Gumbel Copula was the most appropriate function to simulate the points over threshold flood series. We concluded that, compared with the traditional univariate approach, multivariate statistical analysis produced flood estimates that were more physically based and statistically sound and carried lower risk for flood design purposes.
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Ma, Jie, Xin Ye i Abdul Rawoof Pinjari. "Practical Method to Simulate Multiple Discrete-Continuous Generalized Extreme Value Model: Application to Examine Substitution Patterns of Household Transportation Expenditures". Transportation Research Record: Journal of the Transportation Research Board 2673, nr 8 (16.04.2019): 145–56. http://dx.doi.org/10.1177/0361198119842819.
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The multiple discrete-continuous generalized extreme value (MDCGEV) model has been derived from multivariate extreme value (MEV)-based stochastic specifications to relax the independence assumption in the multiple discrete-continuous extreme value (MDCEV) model. It is analogous to the situation where a generalized extreme value (GEV) model relaxes the same assumption in a multinomial logit (MNL) model. However, unlike the case of single discrete choice model where substitution patterns can be understood based on elasticity expressions for a change in the value of an explanatory variable, the MDCEV and its variants do not offer closed-form elasticity expressions. The predictions must be compared explicitly under the base case and policy case scenarios. To perform a prediction exercise with MDCEV or its variants, random samples have to be drawn from the relevant stochastic distributions, which is actually not a straightforward task. In this paper, a practical method is proposed for drawing from an MEV distribution and the method is demonstrated to examine substitution patterns in an MDCGEV model for household transportation expenditures. The empirical results show that the cross-elasticities of explanatory variables in the MDCGEV model exhibit more variations than those in MDCEV and multiple discrete-continuous nested extreme value (MDCNEV) models.
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Simpson, E. S., J. L. Wadsworth i J. A. Tawn. "Determining the dependence structure of multivariate extremes". Biometrika 107, nr 3 (7.05.2020): 513–32. http://dx.doi.org/10.1093/biomet/asaa018.
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Summary In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones, and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their utility through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.
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Glasgow, Garrett. "Mixed Logit Models for Multiparty Elections". Political Analysis 9, nr 2 (2001): 116–36. http://dx.doi.org/10.1093/oxfordjournals.pan.a004867.
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Mixed logit (MXL) is a general discrete choice model thus far unexamined in the study of multicandidate and multiparty elections. Mixed logit assumes that the unobserved portions of utility are a mixture of an IID extreme value term and another multivariate distribution selected by the researcher. This general specification allows MXL to avoid imposing the independence of irrelevant alternatives (IIA) property on the choice probabilities. Further, MXL is a flexible tool for examining heterogeneity in voter behavior through random-coefficients specifications. MXL is a more general discrete choice model than multinomial probit (MNP) in several respects, and can be applied to a wider variety of questions about voting behavior than MNP. An empirical example using data from the 1987 British General Election demonstrates the utility of MXL in the study of multicandidate and multiparty elections.
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Galiatsatou, Panagiota, Christos Makris, Yannis Krestenitis i Panagiotis Prinos. "Nonstationary Extreme Value Analysis of Nearshore Sea-State Parameters under the Effects of Climate Change: Application to the Greek Coastal Zone and Port Structures". Journal of Marine Science and Engineering 9, nr 8 (28.07.2021): 817. http://dx.doi.org/10.3390/jmse9080817.
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In the present work, a methodological framework, based on nonstationary extreme value analysis of nearshore sea-state parameters, is proposed for the identification of climate change impacts on coastal zone and port defense structures. The applications refer to the estimation of coastal hazards on characteristic Mediterranean microtidal littoral zones and the calculation of failure probabilities of typical rubble mound breakwaters in Greek ports. The proposed methodology hinges on the extraction of extreme wave characteristics and sea levels due to storm events affecting the coast, a nonstationary extreme value analysis of sea-state parameters and coastal responses using moving time windows, a fitting of parametric trends to nonstationary parameter estimates of the extreme value models, and an assessment of nonstationary failure probabilities on engineered port protection. The analysis includes estimation of extreme total water level (TWL) on several Greek coasts to approximate the projected coastal flooding hazard under climate change conditions in the 21st century. The TWL calculation considers the wave characteristics, sea level height due to storm surges, mean sea level (MSL) rise, and astronomical tidal ranges of the study areas. Moreover, the failure probabilities of a typical coastal defense structure are assessed for several failure mechanisms, considering variations in MSL, extreme wave climates, and storm surges in the vicinity of ports, within the framework of reliability analysis based on the nonstationary generalized extreme value (GEV) distribution. The methodology supports the investigation of future safety levels and possible periods of increased vulnerability of the studied structure to different ultimate limit states under extreme marine weather conditions associated with climate change, aiming at the development of appropriate upgrading solutions. The analysis suggests that the assumption of stationarity might underestimate the total failure probability of coastal structures under future extreme marine conditions.
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Olinda, R. A., J. Blanchet, C. A. C. dos Santos, V. A. Ozaki i P. J. Ribeiro Jr. "Spatial extremes modeling applied to extreme precipitation data in the state of Paraná". Hydrology and Earth System Sciences Discussions 11, nr 11 (17.11.2014): 12731–64. http://dx.doi.org/10.5194/hessd-11-12731-2014.
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Abstract. Most of the mathematical models developed for rare events are based on probabilistic models for extremes. Although the tools for statistical modeling of univariate and multivariate extremes are well developed, the extension of these tools to model spatial extremes includes an area of very active research nowadays. A natural approach to such a modeling is the theory of extreme spatial and the max-stable process, characterized by the extension of infinite dimensions of multivariate extreme value theory, and making it possible then to incorporate the existing correlation functions in geostatistics and therefore verify the extremal dependence by means of the extreme coefficient and the Madogram. This work describes the application of such processes in modeling the spatial maximum dependence of maximum monthly rainfall from the state of Paraná, based on historical series observed in weather stations. The proposed models consider the Euclidean space and a transformation referred to as space weather, which may explain the presence of directional effects resulting from synoptic weather patterns. This method is based on the theorem proposed for de Haan and on the models of Smith and Schlather. The isotropic and anisotropic behavior of these models is also verified via Monte Carlo simulation. Estimates are made through pairwise likelihood maximum and the models are compared using the Takeuchi Information Criterion. By modeling the dependence of spatial maxima, applied to maximum monthly rainfall data from the state of Paraná, it was possible to identify directional effects resulting from meteorological phenomena, which, in turn, are important for proper management of risks and environmental disasters in countries with its economy heavily dependent on agribusiness.
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Steinheuer, Julian, i Petra Friederichs. "Vertical profiles of wind gust statistics from a regional reanalysis using multivariate extreme value theory". Nonlinear Processes in Geophysics 27, nr 2 (23.04.2020): 239–52. http://dx.doi.org/10.5194/npg-27-239-2020.
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Abstract. Many applications require wind gust estimates at very different atmospheric height levels. For example, the renewable energy sector is interested in wind and gust predictions at the hub height of a wind power plant. However, numerical weather prediction models typically only derive estimates for wind gusts at the standard measurement height of 10 m above the land surface. Here, we present a statistical post-processing method to derive a conditional distribution for hourly peak wind speed as a function of height. The conditioning variables are taken from the COSMO-REA6 regional reanalysis. The post-processing method was trained using peak wind speed observations at five vertical levels between 10 and 250 m from the Hamburg Weather Mast. The statistical post-processing method is based on a censored generalized extreme value (cGEV) distribution with non-homogeneous parameters. We use a least absolute shrinkage and selection operator to select the most informative variables. Vertical variations of the cGEV parameters are approximated using Legendre polynomials, such that predictions may be derived at any desired vertical height. Further, the Pickands dependence function is used to assess dependencies between gusts at different heights. The most important predictors are the 10 m gust diagnostic, the barotropic and the baroclinic mode of absolute horizontal wind speed, the mean absolute horizontal wind at 700 hPa, the surface pressure tendency, and the lifted index. Proper scores show improvements of up to 60 % with respect to climatology, especially at higher vertical levels. The post-processing model with a Legendre approximation is able to provide reliable predictions of gusts' statistics at non-observed intermediate levels. The strength of dependency between gusts at different levels is non-homogeneous and strongly modulated by the vertical stability of the atmosphere.
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Suleev, Bakhtiar, i Bakyt Kurmasheva. "THEORETICAL FOUNDATIONS OF THE DEVELOPMENT OF A BULLDOZER DESIGN THROUGH THE USE OF MULTIVARIATE PARAMETRIC ANALYSIS". Вестник КазАТК 126, nr 3 (19.06.2023): 74–81. http://dx.doi.org/10.52167/1609-1817-2023-126-3-74-81.
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The article presents the scope, purpose and design of the bulldozer. The main brands of bulldozers used in our republic are given. Their main characteristics are considered, such as: weight, power, blade width and blade height. As a result of the analysis of parametric information, the standard deviation, average value, coefficient of variation, asymmetry and kurtosis were determined. A correlation matrix has been compiled that describes the relationship between the parameters of the machines. Based on the results obtained, a cluster analysis was carried out in the StatGraphics Centurion software. A histogram of the distribution of bulldozer indicators is constructed, with the determination of the left and right boundaries, and the number of models in the interval. Using the obtained parametric analysis data, the equations for determining the coefficient of the technical level were formed. Using the obtained equation, the coefficient of the technical level and the prospective values of the machine parameters are determined.
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Pipan, Tanja, Mary C. Christman i David C. Culver. "Abiotic Community Constraints in Extreme Environments: Epikarst Copepods as a Model System". Diversity 12, nr 7 (7.07.2020): 269. http://dx.doi.org/10.3390/d12070269.
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The general hypothesis that the overall presence or absence of one or more species in an extreme habitat is determined by physico-chemical factors was investigated using epikarst copepod communities as a model system, an example of an extreme environment with specialized, often rare species. The relationship between the presence or absence of epikarst copepods from drips in six Slovenian caves and 12 physico-chemical factors (temperature, conductivity, pH, Ca2+, Na+, K+, Mg2+, NH4+, and Cl−, NO2−, NO3−, and SO42−) was explored. Statistical analyses included principal components analysis, logistic mixed models, stepwise logistic multivariate regression, classification trees, and random forests. Parametric statistical analyses demonstrated the overall importance of two variables—temperature and conductivity. The more flexible statistical approaches, namely categorical trees and random forests, indicate that temperature and concentrations of Ca2+ and Mg2+ were important. This may be because they are essential nutrients or, at least in the case of Ca2+, its importance in molting. The correlation of Cl− and NO3− with copepod abundance may be due to unmeasured variables that vary at the scale of individual cave, but in any case, the values have an anthropogenic component. This contrasts with factors important in individual species’ niche separation, which overlap with the community parameters only for NO3−.
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Jin, Xisong, i Thorsten Lehnert. "Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas". Dependence Modeling 6, nr 1 (7.02.2018): 19–46. http://dx.doi.org/10.1515/demo-2018-0002.
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Abstract Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.
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MacAfee, Allan W., i Samuel W. K. Wong. "Extreme Value Analysis of Tropical Cyclone Trapped-Fetch Waves". Journal of Applied Meteorology and Climatology 46, nr 10 (1.10.2007): 1501–22. http://dx.doi.org/10.1175/jam2555.1.
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Abstract Many of the extreme ocean wave events generated by tropical cyclones (TCs) can be explained by examining one component of the spectral wave field, the trapped-fetch wave (TFW). Using a Lagrangian TFW model, a parametric model representation of the local TC wind fields, and the National Hurricane Center’s hurricane database archive, a dataset of TFWs was created from all TCs in the Atlantic Ocean, Gulf of Mexico, and Caribbean Sea from 1851 to 2005. The wave height at each hourly position along a TFW trajectory was sorted into 2° × 2° latitude–longitude grid squares. Five grid squares (north of Hispaniola, Gulf of Mexico, Carolina coast, south of Nova Scotia, and south of Newfoundland) were used to determine if extreme value theory could be applied to the extremes in the TFW dataset. The statistical results justify accepting that a generalized Pareto distribution (GPD) model with a threshold of 6 m could be fitted to the data: the datasets were mostly modeled adequately, and much of the output information was useful. Additional tests were performed by sorting the TFW data into the marine areas in Atlantic Canada, which are of particular interest to the Meteorological Service of Canada because of the high ocean traffic, offshore drilling activities, and commercial fishery. GPD models were fitted, and return periods and the 95% confidence intervals (CIs) for 10-, 15-, and 20-m return levels were computed. The results further justified the use of the GPD model; hence, extension to the remaining grid squares was warranted. Of the 607 grid squares successfully modeled, the percentage of grid squares with finite lower (upper) values for the 10-, 15-, and 20-m return level CIs were 100 (80), 94 (53), and 90 (16), respectively. The lower success rate of 20-m TFW CIs was expected, given the rarity of 20-m TFWs: of the 5 713 625 hourly TFW points, only 13 958, or 0.24%, were 20 m or higher. Overall, the distribution of the successfully modeled grid squares in the data domain agreed with TFW theory and TC climatology. As a direct result of this study, the summary datasets and return level plots were integrated into application software for use by risk managers. A description of the applications illustrates their use in addressing various questions on extreme TFWs.
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Hammami, Hela, Julie Carreau, Luc Neppel, Sadok Elasmi i Haifa Feki. "Smooth Spatial Modeling of Extreme Mediterranean Precipitation". Water 14, nr 22 (21.11.2022): 3782. http://dx.doi.org/10.3390/w14223782.
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Extreme precipitation events can lead to disastrous floods, which are the most significant natural hazards in the Mediterranean regions. Therefore, a proper characterization of these events is crucial. Extreme events defined as annual maxima can be modeled with the generalized extreme value (GEV) distribution. Owing to spatial heterogeneity, the distribution of extremes is non-stationary in space. To take non-stationarity into account, the parameters of the GEV distribution can be viewed as functions of covariates that convey spatial information. Such functions may be implemented as a generalized linear model (GLM) or with a more flexible non-parametric non-linear model such as an artificial neural network (ANN). In this work, we evaluate several statistical models that combine the GEV distribution with a GLM or with an ANN for a spatial interpolation of the GEV parameters. Key issues are the proper selection of the complexity level of the ANN (i.e., the number of hidden units) and the proper selection of spatial covariates. Three sites are included in our study: a region in the French Mediterranean, the Cap Bon area in northeast Tunisia, and the Merguellil catchment in central Tunisia. The comparative analysis aim at assessing the genericity of state-of-the-art approaches to interpolate the distribution of extreme precipitation events.
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Hitz, Adrien, i Robin Evans. "One-component regular variation and graphical modeling of extremes". Journal of Applied Probability 53, nr 3 (wrzesień 2016): 733–46. http://dx.doi.org/10.1017/jpr.2016.37.
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AbstractThe problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize the Hammersley–Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails.
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Sun, Xudong, Mingxing Zhou i Yize Sun. "Spectroscopy quantitative analysis cotton content of blend fabrics". International Journal of Clothing Science and Technology 28, nr 1 (7.03.2016): 65–76. http://dx.doi.org/10.1108/ijcst-07-2015-0076.
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Purpose – The purpose of this paper is to develop near infrared (NIR) techniques coupled with multivariate calibration methods to rapid measure cotton content in blend fabrics. Design/methodology/approach – In total, 124 and 41 samples were used to calibrate models and assess the performance of the models, respectively. Multivariate calibration methods of partial least square (PLS), extreme learning machine (ELM) and least square support vector machine (LS-SVM) were employed to develop the models. Through comparing the performance of PLS, ELM and LS-SVM models with new samples, the optimal model of cotton content was obtained with LS-SVM model. The correlation coefficient of prediction (r p ) and root mean square errors of prediction were 0.98 and 4.50 percent, respectively. Findings – The results suggest that NIR technique combining with LS-SVM method has significant potential to quantitatively analyze cotton content in blend fabrics. Originality/value – It may have commercial and regulatory potential to avoid time consuming work, costly and laborious chemical analysis for cotton content in blend fabrics.
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Satyanarayana Tani i Andreas Gobiet. "Quantile mapping for improving precipitation extremes from regional climate models". Journal of Agrometeorology 21, nr 4 (10.11.2021): 434–43. http://dx.doi.org/10.54386/jam.v21i4.278.
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The potential of quantile mapping (QM) as a tool for bias correction of precipitation extremes simulated by regional climate models (RCMs) is investigated in this study. We developed an extended version of QM to improve the quality of bias-corrected extreme precipitation events. The extended version aims to exploit the advantages of both non-parametric methods and extreme value theory. We evaluated QM by applying it to a small ensemble of hindcast simulations, performed with RCMs at six different locations in Europe. We examined the quality of both raw and bias-corrected simulations of precipitation extremes using the split sample and cross-validation approaches. The split-sample approach mimics the application to future climate scenarios, while the cross-validation framework is designed to analyse “new extremes”, that is, events beyond the range of calibration of QM. We demonstrate that QM generally improves the simulation of precipitation extremes, compared to raw RCM results, but still tends to present unstable behaviour at higher quantiles. This instability can be avoided by carefully imposing constraints on the estimation of the distribution of extremes. The extended version of the bias-correction method greatly improves the simulation of precipitation extremes in all cases evaluated here. In particular, extremes in the classical sense and new extremes are both improved. The proposed approach is shown to provide a better representation of the climate change signal and can thus be expected to improve extreme event response for cases such as floods in bias-corrected simulations, a development of importance in various climate change impact assessments. Our results are encouraging for the use of QM for RCM precipitation post-processing in impact studies where extremes are of relevance.
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Silva, Renato Santos, i Fernando Ferraz Nascimento. "Extreme Value Theory Applied to r Largest Order Statistics Under the Bayesian Approach". Revista Colombiana de Estadística 42, nr 2 (1.07.2019): 143–66. http://dx.doi.org/10.15446/rce.v42n2.70271.
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Extreme Value Theory (EVT) is an important tool to predict efficient gains and losses. Its main areas of analyses are economic and environmental. Initially, for that form of event, it was developed the use of patterns of parametric distribution such as Normal and Gamma. However, economic and environmental data presents, in most cases, a heavy-tailed distribution, in contrast to those distributions. Thus, it was faced a great difficult to frame extreme events. Furthermore, it was almost impossible to use conventional models, making predictions about non-observed events, which exceed the maximum of observations. In some situations EVT is used to analyse only the maximum of some dataset, which provide few observations, and in those cases it is more effective to use the r largest-order statistics. This paper aims to propose Bayesian estimators' for parameters of the r largest-order statistics. During the research, it was used Monte Carlo simulation to analyze the data, and it was observed some properties of those estimators, such as mean, variance, bias and Root Mean Square Error (RMSE). The estimation of the parameters provided inference for its parameters and return levels. This paper also shows a procedure to the choice of the r-optimal to the r largest-order statistics, based on the Bayesian approach applying Markov chains Monte Carlo (MCMC). Simulation results reveal that the Bayesian approach has a similar performance to the Maximum Likelihood Estimation, and the applications were developed using the Bayesian approach and showed a gain in accurary compared with otherestimators.
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Benito Muela, Sonia, Carmen López-Martin i Raquel Arguedas-Sanz. "A comparison of market risk measures from a twofold perspective: accurate and loss function". ACRN Journal of Finance and Risk Perspectives 11, nr 1 (2023): 79–104. http://dx.doi.org/10.35944/jofrp.2022.11.1.005.
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Under the new regulation based on Basel solvency framework, known as Basel III and Basel IV, financial institutions must calculate the market risk capital requirements based on the Expected Shortfall (ES) measure, replacing the Value at Risk (VaR) measure. In the financial literature, there are many papers dedicated to compare VaR approaches but there are few studies focusing in comparing ES approaches. To cover this gap, we have carried out a comprenhensive comparative of VaR and ES models applied to IBEX-35 stock index. The comparison has been carried out from a twofold perspective: accurate risk measure and loss functions. The results indicate that the method based on the conditional Extreme Value Theory (EVT) is the best in estimating market risk, outperforming Parametric method and Filter Historical Simulation.
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Sun, Xudong, i Ke Zhu. "Spectral dimensionality reduction for quantitative analysis of cotton content of blend fabrics". International Journal of Clothing Science and Technology 31, nr 3 (3.06.2019): 326–38. http://dx.doi.org/10.1108/ijcst-07-2018-0091.
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Purpose The purpose of this paper is to initiate investigations to develop near infrared (NIR) spectroscopy coupled with spectral dimensionality reduction and multivariate calibration methods to rapidly measure cotton content in blend fabrics. Design/methodology/approach In total, 124 and 41 samples were used to calibrate models and assess the performance of the models, respectively. The raw spectra are transformed into wavelet coefficients. Multivariate calibration methods of partial least square (PLS), extreme learning machine (ELM) and least square support vector machine (LS-SVM) were employed to develop the models using 100 wavelet coefficients. Through comparing the performance of PLS, ELM and LS-SVM models with new samples, the optimal model of cotton content was obtained with the LS-SVM model. Findings The correlation coefficient of prediction (rp) and root mean square errors of prediction were 0.99 and 4.37 percent, respectively. The results suggest that NIR spectroscopy, combining with the LS-SVM method, has significant potential to quantitatively analyze cotton content in blend fabrics. Originality/value It may have commercial and regulatory potential to avoid time-consuming work, costly and laborious chemical analysis for cotton content in blend fabrics.
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Melina, Sukono, Herlina Napitupulu i Norizan Mohamed. "A Conceptual Model of Investment-Risk Prediction in the Stock Market Using Extreme Value Theory with Machine Learning: A Semisystematic Literature Review". Risks 11, nr 3 (14.03.2023): 60. http://dx.doi.org/10.3390/risks11030060.
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The COVID-19 pandemic has been an extraordinary event, the type of event that rarely occurs but that has major impacts on the stock market. The pandemic has created high volatility and caused extreme fluctuations in the stock market. The stock market can be characterized as either linear or nonlinear. One method that can detect extreme fluctuations is extreme value theory (EVT). This study employed a semisystematic literature review on the use of the EVT method to estimate investment risk in the stock market. The literature used was selected by applying the preferred reporting items for systematic review and meta-analyses (PRISMA) guidelines, sourced from the ScienceDirect.com, ProQuest, and Scopus databases. A bibliometric analysis was conducted to determine the study characteristics and identify any research gaps. The results of the analysis show that studies on this topic are rarely carried out. Research in this field is generally performed only in univariate cases and is very complicated in multivariate cases. Given these limitations, further research could focus on developing a conceptual model that is dynamic and sensitive to extreme fluctuations, with multivariable inputs, in order to predict investment risk. The model developed here considered the variables that affect stock price fluctuations as the input data. The combination of VaR–EVT and machine-learning methods is effective in increasing model accuracy because it combines linear and nonlinear models.
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Rohmer, Jeremy, Pierre Gehl, Marine Marcilhac-Fradin, Yves Guigueno, Nadia Rahni i Julien Clément. "Non-stationary extreme value analysis applied to seismic fragility assessment for nuclear safety analysis". Natural Hazards and Earth System Sciences 20, nr 5 (13.05.2020): 1267–85. http://dx.doi.org/10.5194/nhess-20-1267-2020.
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Abstract. Fragility curves (FCs) are key tools for seismic probabilistic safety assessments that are performed at the level of the nuclear power plant (NPP). These statistical methods relate the probabilistic seismic hazard loading at the given site to the required performance of the NPP safety functions. In the present study, we investigate how the tools of non-stationary extreme value analysis can be used to model in a flexible manner the tail behaviour of the engineering demand parameter as a function of the considered intensity measure. We focus the analysis on the dynamic response of an anchored steam line and of a supporting structure under seismic solicitations. The failure criterion is linked to the exceedance of the maximum equivalent stress at a given location of the steam line. A series of three-component ground-motion records (∼300) were applied at the base of the model to perform non-linear time history analyses. The set of numerical results was then used to derive a FC, which relates the failure probability to the variation in peak ground acceleration (PGA). The probabilistic model of the FC is selected via information criteria completed by diagnostics on the residuals, which support the choice of the generalised extreme value (GEV) distribution (instead of the widely used log-normal model). The GEV distribution is here non-stationary, and the relationships of the GEV parameters (location, scale and shape) are established with respect to PGA using smooth non-linear models. The procedure is data-driven, which avoids the introduction of any a priori assumption on the shape or form of these relationships. To account for the uncertainties in the mechanical and geometrical parameters of the structures (elastic stiffness, damping, pipeline thicknesses, etc.), the FC is further constructed by integrating these uncertain parameters. A penalisation procedure is proposed to set to zero the variables of little influence in the smooth non-linear models. This enables us to outline which of these parametric uncertainties have negligible influence on the failure probability as well as the nature of the influence (linear, non-linear, decreasing, increasing, etc.) with respect to each of the GEV parameters.
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Gioia, Andrea, Maria Francesca Bruno, Vincenzo Totaro i Vito Iacobellis. "Parametric Assessment of Trend Test Power in a Changing Environment". Sustainability 12, nr 9 (9.05.2020): 3889. http://dx.doi.org/10.3390/su12093889.
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In the context of climate and environmental change assessment, the use of probabilistic models in which the parameters of a given distribution may vary in accordance with time has reinforced the need for appropriate procedures to recognize the “statistical significance” of trends in data series arising from stochastic processes. This paper introduces a parametric methodology, which exploits a measure based on the Akaike Information Criterion (AICΔ), and a Rescaled version of the Generalized Extreme Value distribution, in which a linear deterministic trend in the position parameter is accounted for. A Monte Carlo experiment was set up with the generation of nonstationary synthetic series characterized by different sample lengths and covering a wide range of the shape and scale parameters. The performances of statistical tests based on the parametric AICΔ and the non-parametric Mann-Kendall measures were evaluated and compared with reference to observed ranges of annual maxima of precipitation, peak flow, and wind speed. Results allow for sensitivity analysis of the test power and show a strong dependence on the trend coefficient and the L-Coefficient of Variation of the parent distribution from the upper-bounded to the heavy-tailed special cases. An analysis of the sample variability of the position parameter is also presented, based on the same generation sets.
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Naveau, Philippe, Alexis Hannart i Aurélien Ribes. "Statistical Methods for Extreme Event Attribution in Climate Science". Annual Review of Statistics and Its Application 7, nr 1 (9.03.2020): 89–110. http://dx.doi.org/10.1146/annurev-statistics-031219-041314.
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Changes in the Earth's climate have been increasingly observed. Assessing the likelihood that each of these changes has been caused by human influence is important for decision making on mitigation and adaptation policy. Because of their large societal and economic impacts, extreme events have garnered much media attention—have they become more frequent and more intense, and if so, why? To answer such questions, extreme event attribution (EEA) tries to estimate extreme event likelihoods under different scenarios. Over the past decade, statistical methods and experimental designs based on numerical models have been developed, tested, and applied. In this article, we review the basic probability schemes, inference techniques, and statistical hypotheses used in EEA. To implement EEA analysis, the climate community relies on the use of large ensembles of climate model runs. We discuss, from a statistical perspective, how extreme value theory could help to deal with the different modeling uncertainties. In terms of interpretation, we stress that causal counterfactual theory offers an elegant framework that clarifies the design of event attributions. Finally, we pinpoint some remaining statistical challenges, including the choice of the appropriate spatio-temporal scales to enhance attribution power, the modeling of concomitant extreme events in a multivariate context, and the coupling of multi-ensemble and observational uncertainties.
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Hassouneh, Islam, Teresa Serra i Štefan Bojnec. "Nonlinearities in the Slovenian apple price transmission". British Food Journal 117, nr 1 (5.01.2015): 461–78. http://dx.doi.org/10.1108/bfj-03-2014-0109.
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Purpose – The purpose of this paper is to assess price linkages and patterns of transmission among producer and consumer markets for apple in Slovenia. Design/methodology/approach – Non-linear error correction models are applied. Non-linearities are allowed by means of threshold and multivariate local linear regression estimation techniques. Monthly prices over the period 2000-2011 are used in the empirical application. Findings – Both techniques provide evidence of non-linearities in price adjustments. Findings suggest that producer and consumer prices tend to increase rather than decrease. Results also indicate that parametric threshold approaches may have difficulties in adequately representing price behavior dynamics. Originality/value – The main contribution of this work to the literature relies on the fact that this is the first attempt to assess vertical price transmission in the apple sector in Central and Eastern European Country markets. Further, it is the first attempt to use multivariate local linear regression techniques in this context.
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Shortridge, J. E., S. D. Guikema i B. F. Zaitchik. "Empirical streamflow simulation for water resource management in data-scarce seasonal watersheds". Hydrology and Earth System Sciences Discussions 12, nr 10 (28.10.2015): 11083–127. http://dx.doi.org/10.5194/hessd-12-11083-2015.
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Abstract. In the past decade, certain methods for empirical rainfall–runoff modeling have seen extensive development and been proposed as a useful complement to physical hydrologic models, particularly in basins where data to support process-based models is limited. However, the majority of research has focused on a small number of methods, such as artificial neural networks, despite the development of multiple other approaches for non-parametric regression in recent years. Furthermore, this work has generally evaluated model performance based on predictive accuracy alone, while not considering broader objectives such as model interpretability and uncertainty that are important if such methods are to be used for planning and management decisions. In this paper, we use multiple regression and machine-learning approaches to simulate monthly streamflow in five highly-seasonal rivers in the highlands of Ethiopia and compare their performance in terms of predictive accuracy, error structure and bias, model interpretability, and uncertainty when faced with extreme climate conditions. While the relative predictive performance of models differed across basins, data-driven approaches were able to achieve reduced errors when compared to physical models developed for the region. Methods such as random forests and generalized additive models may have advantages in terms of visualization and interpretation of model structure, which can be useful in providing insights into physical watershed function. However, the uncertainty associated with model predictions under climate change should be carefully evaluated, since certain models (especially generalized additive models and multivariate adaptive regression splines) became highly variable when faced with high temperatures.