Zeitschriftenartikel: „Extremal dependence modeling“

1

Barro, Diakarya. „Extremal Dependence Modeling with Spatial and Survival Distributions“. Journal of Mathematics Research 9, Nr. 1 (23.01.2017): 127. http://dx.doi.org/10.5539/jmr.v9n1p127.

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This paper investigates some properties of dependence of extreme values distributions both in survival and spatial context. Specifically, we prospose a spatial Extremal dependence coefficient for survival distributions. Madogram is characterized in bivariate case and multivariate survival function and the underlying hazard distributions are given in a risky context.

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Huser, Raphaël, und Jennifer L. Wadsworth. „Modeling Spatial Processes with Unknown Extremal Dependence Class“. Journal of the American Statistical Association 114, Nr. 525 (28.06.2018): 434–44. http://dx.doi.org/10.1080/01621459.2017.1411813.

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3

Mallam, Hassane Abba, Natatou Dodo Moutari, Barro Diakarya und Saley Bisso. „Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk“. European Journal of Pure and Applied Mathematics 14, Nr. 3 (05.08.2021): 1057–81. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3951.

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These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.

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4

Apputhurai, P., und A. G. Stephenson. „Accounting for uncertainty in extremal dependence modeling using Bayesian model averaging techniques“. Journal of Statistical Planning and Inference 141, Nr. 5 (Mai 2011): 1800–1807. http://dx.doi.org/10.1016/j.jspi.2010.11.038.

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5

Ressel, Paul. „Stable tail dependence functions – some basic properties“. Dependence Modeling 10, Nr. 1 (01.01.2022): 225–35. http://dx.doi.org/10.1515/demo-2022-0114.

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Abstract We prove some important properties of the extremal coefficients of a stable tail dependence function (“STDF”) and characterise logistic and some related STDFs. The well known sufficient conditions for composebility of logistic STDFs are shown to be also necessary.

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6

Chen, Zaoli, und Gennady Samorodnitsky. „Extremal clustering under moderate long range dependence and moderately heavy tails“. Stochastic Processes and their Applications 145 (März 2022): 86–116. http://dx.doi.org/10.1016/j.spa.2021.12.001.

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7

Olinda, R. A., J. Blanchet, C. A. C. dos Santos, V. A. Ozaki und 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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Li, Jiayi, Zhiyan Cai, Yixuan Liu und Chengxiu Ling. „Extremal Analysis of Flooding Risk and Its Catastrophe Bond Pricing“. Mathematics 11, Nr. 1 (27.12.2022): 114. http://dx.doi.org/10.3390/math11010114.

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Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning.

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Saunina, A. Yu, V. R. Nikitenko, A. A. Chistyakov, M. A. Zvaizgne, A. R. Tameev und A. E. Aleksandrov. „Analytic Modeling of the of J–V Characteristics of Quantum Dot-Based Photovoltaic Cells“. International Journal of Nanoscience 18, Nr. 03n04 (02.04.2019): 1940083. http://dx.doi.org/10.1142/s0219581x19400830.

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An analytic model of [Formula: see text]–[Formula: see text] characteristics of photovoltaic devices based on quantum dot (QD) solids is developed. The model yields the upper estimation of the power conversion efficiency and predicts its extremal dependence on the diffusion length of excitons. The predictive power of our model is approved by the comparison with the experimental data for PbS QD-based solar cells.

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Ferreira, Helena, und Marta Ferreira. „The stopped clock model“. Dependence Modeling 10, Nr. 1 (01.01.2022): 48–57. http://dx.doi.org/10.1515/demo-2022-0101.

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Abstract The extreme value theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological advances allowing an increasingly larger and more efficient data collection, there are sometimes failures in the records, which causes difficulties in statistical inference, especially in the tail where data are scarcer. In this article, we present a model with a simple and intuitive failures scheme, where each record failure is replaced by the last record available. We will study its extremal behavior with regard to local dependence and high values clustering, as well as the temporal dependence on the tail.

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Moretti, Alba Regina, und 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 (01.01.2005): 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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Saminger-Platz, Susanne, Anna Kolesárová, Adam Šeliga, Radko Mesiar und Erich Peter Klement. „New results on perturbation-based copulas“. Dependence Modeling 9, Nr. 1 (01.01.2021): 347–73. http://dx.doi.org/10.1515/demo-2021-0116.

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Abstract A prominent example of a perturbation of the bivariate product copula (which characterizes stochastic independence) is the parametric family of Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some of them perturbing the product copula, while others perturb general copulas. A particularly interesting case is the perturbation of the product based on two functions in one variable where we highlight several special phenomena, e.g., extremal perturbed copulas. The constructions of the perturbations in this paper include three different types of ordinal sums as well as flippings and the survival copula. Some particular relationships to the Markov product and several dependence parameters for the perturbed copulas considered here are also given.

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Hassane, Abba Mallam, Barro Diakarya, Yaméogo WendKouni und Saley Bisso. „Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas“. International Journal of Mathematics and Mathematical Sciences 2021 (02.09.2021): 1–9. http://dx.doi.org/10.1155/2021/7648093.

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In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

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SHARMA, KULDEEP, RAGHAVENDRA ASHRIT, R. BHATLA, R. RAKHI, G. R. IYENGAR und E. N. RAJAGOPAL. „Verification of heavy rainfall in NWP models : A case study“. MAUSAM 68, Nr. 4 (02.12.2021): 699–712. http://dx.doi.org/10.54302/mausam.v68i4.772.

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Forecasting of heavy rainfall events is still a challenge even for the most advanced state-of-art high resolution NWP modelling systems. Very often the models fail to accurately predict the track and movement of the low pressure systems leading to large spatial errors in the predicted rain. Quantification of errors in forecast rainfall location and amounts is important for forecasters (to choose a forecast and interpret) and modelers for monitoring the impact of changes and improvements in model physics and dynamics configurations. This study aims to quantify and summarize errors in rainfall forecast for heavy rains associated with a Bay of Bengal (BOB) low pressure systems. The verification analysis is based on three heavy rain events during June to September (JJAS) 2015. The performance of the three deterministic models, NCMRWF’s Global Forecast Systems (NGFS), NCMRWF’s Unified Model (NCUM) and Australian Community Climate and Earth-System Simulator – Global (ACCESS-G) in predicting these heavy rainfall events has been analysed. In addition to standard verification metrics like RMSE, ETS, POD and HK Score, this paper also uses new family of scores like EDS (Extreme Dependency Score), EDI (Extremal Dependence Index) and Symmetric EDI with special emphasis on verification of extreme rainfall to bring out the relative performance of the models for these three rainfall events. The results indicate that Unified modeling framework in NCUM and ACCESS-G by and large performs better than NGFS in rainfall forecasts over India specially at higher lead times. Relatively improved skill in NCUM forecasts can be attributed to (i) improved resolution (~17 km) and (ii) END Game dynamics of NCUM.

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15

Wadsworth, J. L., J. A. Tawn, A. C. Davison und D. M. Elton. „Modelling across extremal dependence classes“. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79, Nr. 1 (17.02.2016): 149–75. http://dx.doi.org/10.1111/rssb.12157.

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16

Leonelli, Manuele, und Dani Gamerman. „Semiparametric bivariate modelling with flexible extremal dependence“. Statistics and Computing 30, Nr. 2 (28.05.2019): 221–36. http://dx.doi.org/10.1007/s11222-019-09878-w.

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17

Nemukula, Murendeni Maurel, Caston Sigauke, Hector Chikoore und Alphonce Bere. „Modelling Drought Risk Using Bivariate Spatial Extremes: Application to the Limpopo Lowveld Region of South Africa“. Climate 11, Nr. 2 (13.02.2023): 46. http://dx.doi.org/10.3390/cli11020046.

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Weather and climate extremes such as heat waves, droughts and floods are projected to become more frequent and intense in several regions. There is compelling evidence indicating that changes in climate and its extremes over time influence the living conditions of society and the surrounding environment across the globe. This study applies max-stable models to capture the spatio–temporal extremes with dependence. The objective was to analyse the risk of drought caused by extremely high temperatures and deficient rainfall. Hopkin’s statistic was used to assess the clustering tendency before using the agglomerative method of hierarchical clustering to cluster the study area into n=3 temperature clusters and n=3 precipitation clusters. For the precipitation and temperature data, the values of Hopkin’s statistic were 0.7317 and 0.8446, respectively, which shows that both are significantly clusterable. Various max-stable process models were then fitted to each cluster of each variable, and the Schlather model with several covariance functions was found to be a good fit on both datasets compared to the Smith model with the Gaussian covariance function. The modelling approach presented in this paper could be useful to hydrologists, meteorologists and climatologists, including decision-makers in the agricultural sector, in enhancing their understanding of the behaviour of drought caused by extremely high temperatures and low rainfall. The modelling of these compound extremes could also assist in assessing the impact of climate change. It can be seen from this study that the size, including the topography of the location (cluster/region), provides important information about the strength of the extremal dependence.

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Zhang, Mingzhi, Hongyu Liu, Jianxu Liu, Chao Chen, Zhaocheng Li, Bowen Wang und Songsak Sriboonchitta. „Modelling Dependency Structures of Carbon Trading Markets between China and European Union: From Carbon Pilot to COVID-19 Pandemic“. Axioms 11, Nr. 12 (05.12.2022): 695. http://dx.doi.org/10.3390/axioms11120695.

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The exploration of the dependency structure of the Chinese and EU carbon trading markets is crucial to the construction of a globally harmonized carbon market. In this paper, we studied the characteristics of structural interdependency between China’s major carbon markets and the European Union (EU) carbon market before and after the launch of the national carbon emissions trading scheme (ETS) and the occurrence of the new coronavirus (COVID-19) by applying the C-vine copula method, with the carbon trading prices of the EU, Beijing, Shanghai, Guangdong, Shenzhen and Hubei as the research objects. The study shows that there exists a statistically significant dependence between the EU and the major carbon markets in China and their extremal dependences and dependence structures are different at different stages. After the launch of the national carbon ETS, China has become more independent in terms of interdependency with the EU carbon market, and is more relevant between domestic carbon markets. Most importantly, we found that the dependence between the EU and Chinese carbon markets has increased following the outbreak of COVID-19, and tail dependency structures existed before the launch of the national carbon ETS and during the outbreak of the COVID-19. The results of this study provide a basis for the understanding of the linkage characteristics of carbon trading prices between China and the EU at different stages, which in turn can help market regulators and investors to formulate investment decisions and policies.

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Dissanayake, Pushpa, Teresa Flock, Johanna Meier und Philipp Sibbertsen. „Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights“. Mathematics 9, Nr. 21 (05.11.2021): 2817. http://dx.doi.org/10.3390/math9212817.

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The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.

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Wadsworth, J. L., und J. A. Tawn. „Dependence modelling for spatial extremes“. Biometrika 99, Nr. 2 (13.03.2012): 253–72. http://dx.doi.org/10.1093/biomet/asr080.

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21

Hernandez-Campos, Felix, Kevin Jeffay, Cheolwoo Park, J. S. Marron und Sidney I. Resnick. „EXTREMAL DEPENDENCE: INTERNET TRAFFIC APPLICATIONS“. Stochastic Models 21, Nr. 1 (09.02.2005): 1–35. http://dx.doi.org/10.1081/stm-200046446.

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22

Bel, L., J. N. Bacro und Ch Lantuéjoul. „Assessing extremal dependence of environmental spatial fields“. Environmetrics 19, Nr. 2 (2008): 163–82. http://dx.doi.org/10.1002/env.863.

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23

Resnick, Sidney. „The Extremal Dependence Measure and Asymptotic Independence“. Stochastic Models 20, Nr. 2 (31.12.2004): 205–27. http://dx.doi.org/10.1081/stm-120034129.

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24

Kley, Oliver, Claudia Klüppelberg und Sandra Paterlini. „Modelling extremal dependence for operational risk by a bipartite graph“. Journal of Banking & Finance 117 (August 2020): 105855. http://dx.doi.org/10.1016/j.jbankfin.2020.105855.

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25

Davis, Richard A., Thomas Mikosch und Yuwei Zhao. „Measures of serial extremal dependence and their estimation“. Stochastic Processes and their Applications 123, Nr. 7 (Juli 2013): 2575–602. http://dx.doi.org/10.1016/j.spa.2013.03.014.

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26

Winter, Hugo C., und Jonathan A. Tawn. „Modelling heatwaves in central France: a case-study in extremal dependence“. Journal of the Royal Statistical Society: Series C (Applied Statistics) 65, Nr. 3 (22.09.2015): 345–65. http://dx.doi.org/10.1111/rssc.12121.

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27

Le, Phuong Dong, Michael Leonard und Seth Westra. „Modeling Spatial Dependence of Rainfall Extremes Across Multiple Durations“. Water Resources Research 54, Nr. 3 (März 2018): 2233–48. http://dx.doi.org/10.1002/2017wr022231.

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28

Hsieh, Wen-Pin, Yi-Chi Tsao und Chun-Hung Lin. „Thermal Conductivity of Helium and Argon at High Pressure and High Temperature“. Materials 15, Nr. 19 (26.09.2022): 6681. http://dx.doi.org/10.3390/ma15196681.

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Helium (He) and argon (Ar) are important rare gases and pressure media used in diamond-anvil cell (DAC) experiments. Their thermal conductivity at high pressure–temperature (P-T) conditions is a crucial parameter for modeling heat conduction and temperature distribution within a DAC. Here we report the thermal conductivity of He and Ar over a wide range of high P-T conditions using ultrafast time-domain thermoreflectance coupled with an externally heated DAC. We find that at room temperature the thermal conductivity of liquid and solid He shows a pressure dependence of P0.86 and P0.72, respectively; upon heating the liquid, He at 10.2 GPa follows a T0.45 dependence. By contrast, the thermal conductivity of solid Ar at room temperature has a pressure dependence of P1.25, while a T−1.37 dependence is observed for solid Ar at 19 GPa. Our results not only provide crucial bases for further investigation into the physical mechanisms of heat transport in He and Ar under extremes, but also substantially improve the accuracy of modeling the temperature profile within a DAC loaded with He or Ar. The P-T dependences of the thermal conductivity of He are important to better model and constrain the structural and thermal evolution of gas giant planets containing He.

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Krasilnikov, A. I. „Analysis of the Excess Kurtosis of Two-Component Mixtures of Shifted Non-Gaussian Distributions“. Èlektronnoe modelirovanie 46, Nr. 2 (10.04.2024): 15–34. http://dx.doi.org/10.15407/emodel.46.02.015.

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The dependence of the extremes and zeros of the excess kurtosis on the weight coefficient is researched. Formulas for finding the extrema points, the values of the minimums and maximums of the excess kurtosis are obtained. Conditions on the shift parameter under which the extrema points belong to the interval are determined. Formulas for finding the zeros of the excess kurtosis are obtained and conditions on shift parameter under which the roots of the equation are real and belong to the interval are determined. Examples of calculating extremes and zeros of the excess kurtosis of two-component mixtures of shifted non-Gaussian distributions are considered. The results of the research justify the possibility of practical application of two-component mixtures of shifted distributions for mathematical and computer modeling of an infinite number of non-Gaussian random variables with negative, positive and zero excess kurtosis.

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Tontchev, Nikolay, Normunds Teirumnieks und Emil Yankov. „MODELING THE HARDENING OF CARBON STEELS AFTER QUENCHING AND TEMPERING“. ENVIRONMENT. TECHNOLOGIES. RESOURCES. Proceedings of the International Scientific and Practical Conference 3 (22.06.2024): 456–59. http://dx.doi.org/10.17770/etr2024vol3.8184.

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In the paper, after an overview and defined tasks, a methodology is applied and a model is derived for establishing the dependence of hardness on carbon content, hardness after hardening and tempering temperature after hardening for the entire range of carbon steels from structural to tool steels. The research was based on eight steels and four tempering temperatures formed in a total of 32 combinations. First, one-dimensional dependences of hardness change on carbon content were derived for each annealing temperature, then accuracy was improved with a three-control parameter model. The derived model was examined and its theoretical maximum was corrected. The difference between the theoretical and the real logical maxima amounts to 17.44%. For all specified extremes, the heat treatment modes are defined.

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Sisson, Scott, und Stuart Coles. „Modelling Dependence Uncertainty in the Extremes of Markov Chains“. Extremes 6, Nr. 4 (Dezember 2003): 283–300. http://dx.doi.org/10.1007/s10687-004-4721-3.

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32

Brunner, Manuela I., und Eric Gilleland. „Stochastic simulation of streamflow and spatial extremes: a continuous, wavelet-based approach“. Hydrology and Earth System Sciences 24, Nr. 8 (12.08.2020): 3967–82. http://dx.doi.org/10.5194/hess-24-3967-2020.

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Abstract. Stochastically generated streamflow time series are used for various water management and hazard estimation applications. They provide realizations of plausible but as yet unobserved streamflow time series with the same temporal and distributional characteristics as the observed data. However, the representation of non-stationarities and spatial dependence among sites remains a challenge in stochastic modeling. We investigate whether the use of frequency-domain instead of time-domain models allows for the joint simulation of realistic, continuous streamflow time series at daily resolution and spatial extremes at multiple sites. To do so, we propose the stochastic simulation approach called Phase Randomization Simulation using wavelets (PRSim.wave) which combines an empirical spatio-temporal model based on the wavelet transform and phase randomization with the flexible four-parameter kappa distribution. The approach consists of five steps: (1) derivation of random phases, (2) fitting of the kappa distribution, (3) wavelet transform, (4) inverse wavelet transform, and (5) transformation to kappa distribution. We apply and evaluate PRSim.wave on a large set of 671 catchments in the contiguous United States. We show that this approach allows for the generation of realistic time series at multiple sites exhibiting short- and long-range dependence, non-stationarities, and unobserved extreme events. Our evaluation results strongly suggest that the flexible, continuous simulation approach is potentially valuable for a diverse range of water management applications where the reproduction of spatial dependencies is of interest. Examples include the development of regional water management plans, the estimation of regional flood or drought risk, or the estimation of regional hydropower potential. Highlights. Stochastic simulation of continuous streamflow time series using an empirical, wavelet-based, spatio-temporal model in combination with the parametric kappa distribution. Generation of stochastic time series at multiple sites showing temporal short- and long-range dependence, non-stationarities, and spatial dependence in extreme events. Implementation of PRSim.wave in R package PRSim: Stochastic Simulation of Streamflow Time Series using Phase Randomization.

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Sigauke, Caston, Thakhani Ravele und Lordwell Jhamba. „Extremal Dependence Modelling of Global Horizontal Irradiance with Temperature and Humidity: An Application Using South African Data“. Energies 15, Nr. 16 (17.08.2022): 5965. http://dx.doi.org/10.3390/en15165965.

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The interaction between global horizontal irradiance (GHI) and temperature helps determine the maximum amount of solar power generated. As temperature increases, GHI increases up to the point that it increases at a decreasing rate and then decreases. Therefore, system operators need to know the maximum possible solar power which can be generated. Using the multivariate adaptive regression splines, extreme value theory and copula models, the present paper seeks to determine the maximum temperature that will result in the generation of the maximum GHI ceteris paribus. The paper also discusses extremal dependence modelling of GHI with temperature and relative humidity (RH) at one radiometric station using South African data from 16 November 2015 to 16 November 2021. Empirical results show that the marginal increases of GHI converge to 0.12 W/m2 when temperature converges to 44.26 °C and the marginal increases of GHI converge to −0.1 W/m2 when RH converges to 103.26%. Conditioning on GHI, the study found that temperature and RH variables have a negative extremal dependence on large values of GHI. Due to the nonlinearity and different structure of the dependence on GHI against temperature and RH, unlike previous literature, we use three Archimedean copula functions: Clayton, Frank and Gumbel, to model the dependence structure. The modelling approach discussed in this paper could be useful to system operators in power utilities who must optimally integrate highly intermittent renewable energies on the grid.

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Budiarti, Retno, Kumala Intansari, I. Gusti Putu Purnaba und 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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BELOSHITSKY, P. V. „STRUCTURAL AND FUNCTIONAL INTERDEPENDENCES OF BIOLOGICAL ORGANISMS IN EXTREME CONDITIONS“. Biotechnologia Acta 15, Nr. 6 (30.12.2022): 36–54. http://dx.doi.org/10.15407/biotech15.06.036.

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Investigations of the adaptation of living organisms/human body to various extreme factors are extremely important. Aim. To characterize and analyze the results of research of structural and functional interdependencies of organisms in extreme conditions. Methods. Comparative analysis of the registered biochemical, physiological characteristics of the body, mathematical modelling of underlying mechanisms on their basis, information and computer technologies. Results. Deviations of organisms’ functions during adaptation processes caused changes in some structures of organism. Significant role of quantitative and qualitative changes of the erythrocyte formation system in the reliability of organisms functioning in extreme conditions in highlands was confirmed. The changes in red and white blood cells reflected largely the relationships between the organisms’ reactivity and resistance. The dependences on degree of rarefaction of the air, mode of climbing, effects of athlete’s training, etc. were revealed. Adaptive hemolysis of erythrocytes, when the biologically active substances were released from blood cells and acted as messengers, were shown to be the triggers capable to change cell metabolism; they played significant roles in reliability of organisms functioning. The set of program models was developed. Results were applied successfully for training of athletes for high-altitude climbing. Conclusions. Results of the studies on the structural and functional interdependencies of organisms in extreme conditions were reviewed and analyzed. Results of mathematical modeling coincided with the results obtained in experiments and observations. In the process of adaptation to hypoxia human organism behaved likes an ultrastable system. Obtained results can be applied in practice.

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Skahill, Brian, Cole Haden Smith und Brook T. Russell. „Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network“. GeoHazards 4, Nr. 4 (16.12.2023): 526–53. http://dx.doi.org/10.3390/geohazards4040030.

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This study utilized a max-stable process (MSP) model with a dependence structure defined via a non-Euclidean distance metric, with the goal of modelling extreme flood data on a river network. The dataset was composed of mean daily discharge observations from 22 United States Geological Survey streamflow gaging stations for river basins in Missouri and Arkansas. The analysis included the application of the elastic-net penalty to automatically build spatially varying trend surfaces to model the marginal distributions. The dependence model accounted for the river distance between hydrologically connected gaging sites and the hydrologic distance, defined as the Euclidean distance between the centers of site’s associated drainage areas, for all stations. Modelling the marginal distributions and spatial dependence among the extremes are two key components for spatially modelling extremes. Among the 16 covariates evaluated for marginal fitting, 7 were selected to spatially model the generalized extreme value (GEV) location parameter (for each gaging station’s contributing drainage basin, its outlet elevation, centroid x coordinate, centroid elevation, area, average basin width, elevation range, and median land surface slope). The three covariates selected for the GEV scale parameter included the area, average basin width, and median land surface slope. The GEV shape parameter was assumed to be constant throughout the entire study area. Comparisons of estimates obtained from the spatial covariate model with their corresponding “at-site” estimates resulted in computed values of 0.95, 0.95, 0.94 and 0.85, 0.84, 0.90 for the coefficient of determination, Nash–Sutcliffe efficiency, and Kling–Gupta efficiency for the GEV location and scale parameters, respectively. Brown–Resnick MSP models were fit to independent multivariate events extracted from a set of common discharge data, transformed to unit Fréchet margins while considering different permutations of the non-Euclidean dependence model. Each of the fitted model’s log-likelihood values indicated improved fits when using hydrologic distance rather than Euclidean distance. They also demonstrated that accounting for flow-connected dependence and anisotropy further improved model fit. In this study, the results from both parts were illustrative; however, further research with larger datasets and more heterogeneous systems is recommended.

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Hundhausen, Marie, Hendrik Feldmann, Natalie Laube und Joaquim G. Pinto. „Future heat extremes and impacts in a convection-permitting climate ensemble over Germany“. Natural Hazards and Earth System Sciences 23, Nr. 8 (30.08.2023): 2873–93. http://dx.doi.org/10.5194/nhess-23-2873-2023.

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Abstract. Heat extremes and associated impacts are considered the most pressing issue for German regional governments with respect to climate adaptation. We explore the potential of a unique high-resolution, convection-permitting (2.8 m), multi-GCM (global climate model) ensemble with COSMO-CLM (Consortium for Small-scale Modeling Climate Limited-area Modelling) regional simulations (1971–2100) over Germany regarding heat extremes and related impacts. We find a systematically reduced cold bias especially in summer in the convection-permitting simulations compared to the driving simulations with a grid size of 7 km and parametrized convection. The projected increase in temperature and its variance favors the development of longer and hotter heat waves, especially in late summer and early autumn. In a 2 ∘C (3 ∘C) warmer world, a 26 % (100 %) increase in the heat wave magnitude index is anticipated. Human heat stress (universal thermal climate index (UTCI) > 32 ∘C) and region-specific parameters tailored to climate adaptation revealed a dependency on the major landscapes, resulting in significantly higher heat exposure in flat regions such as the Rhine Valley, accompanied by the strongest absolute increase. A nonlinear, exponential increase is anticipated for parameters characterizing strong heat stress (UTCI > 32 ∘C, tropical nights, very hot days). Providing region-specific and tailored climate information, we demonstrate the potential of convection-permitting simulations to facilitate improved impact studies and narrow the gap between climate modeling and stakeholder requirements for climate adaptation.

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Ossandón, Álvaro, Manuela I. Brunner, Balaji Rajagopalan und William Kleiber. „A space–time Bayesian hierarchical modeling framework for projection of seasonal maximum streamflow“. Hydrology and Earth System Sciences 26, Nr. 1 (12.01.2022): 149–66. http://dx.doi.org/10.5194/hess-26-149-2022.

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Abstract. Timely projections of seasonal streamflow extremes can be useful for the early implementation of annual flood risk adaptation strategies. However, predicting seasonal extremes is challenging, particularly under nonstationary conditions and if extremes are correlated in space. The goal of this study is to implement a space–time model for the projection of seasonal streamflow extremes that considers the nonstationarity (interannual variability) and spatiotemporal dependence of high flows. We develop a space–time model to project seasonal streamflow extremes for several lead times up to 2 months, using a Bayesian hierarchical modeling (BHM) framework. This model is based on the assumption that streamflow extremes (3 d maxima) at a set of gauge locations are realizations of a Gaussian elliptical copula and generalized extreme value (GEV) margins with nonstationary parameters. These parameters are modeled as a linear function of suitable covariates describing the previous season selected using the deviance information criterion (DIC). Finally, the copula is used to generate streamflow ensembles, which capture spatiotemporal variability and uncertainty. We apply this modeling framework to predict 3 d maximum streamflow in spring (May–June) at seven gauges in the Upper Colorado River basin (UCRB) with 0- to 2-month lead time. In this basin, almost all extremes that cause severe flooding occur in spring as a result of snowmelt and precipitation. Therefore, we use regional mean snow water equivalent and temperature from the preceding winter season as well as indices of large-scale climate teleconnections – El Niño–Southern Oscillation, Atlantic Multidecadal Oscillation, and Pacific Decadal Oscillation – as potential covariates for 3 d spring maximum streamflow. Our model evaluation, which is based on the comparison of different model versions and the energy skill score, indicates that the model can capture the space–time variability in extreme streamflow well and that model skill increases with decreasing lead time. We also find that the use of climate variables slightly enhances skill relative to using only snow information. Median projections and their uncertainties are consistent with observations, thanks to the representation of spatial dependencies through covariates in the margins and a Gaussian copula. This spatiotemporal modeling framework helps in the planning of seasonal adaptation and preparedness measures as predictions of extreme spring streamflows become available 2 months before actual flood occurrence.

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Najjari, Vadoud, Tomáš Bacigál und Hasan Bal. „An Archimedean Copula Family with Hyperbolic Cotangent Generator“. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, Nr. 05 (Oktober 2014): 761–68. http://dx.doi.org/10.1142/s0218488514500391.

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Hyperbolic cotangent function is proposed as a generator of new Archimedean copula family and several properties are revealed. To show performance in real data analysis, application to modeling dependence between monthly temperature extremes as well as between flood peak and volume is given.

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Medford, Anthony. „Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models“. Risks 9, Nr. 3 (10.03.2021): 51. http://dx.doi.org/10.3390/risks9030051.

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Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

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Tölle, Merja H., Lukas Schefczyk und Oliver Gutjahr. „Scale dependency of regional climate modeling of current and future climate extremes in Germany“. Theoretical and Applied Climatology 134, Nr. 3-4 (04.11.2017): 829–48. http://dx.doi.org/10.1007/s00704-017-2303-6.

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Krasilnikov, A. I. „Analysis of Cumulant Coefficients of Two-Component Mixtures of Shifted Non-Gaussian Distributions“. Èlektronnoe modelirovanie 43, Nr. 5 (04.10.2021): 73–92. http://dx.doi.org/10.15407/emodel.43.05.073.

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The dependence of the cumulant coefficients of two-component mixtures of shifted non- Gaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have extrema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered.

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Sverdlov, Viktor A., Thomas Windbacher, Franz Schanovsky und Siegfried Selberherr. „Mobility Modeling in Advanced MOSFETs with Ultra-Thin Silicon Body under Stress“. Journal of Integrated Circuits and Systems 4, Nr. 2 (21.11.2009): 55–60. http://dx.doi.org/10.29292/jics.v4i2.298.

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We use a two-band k·p model to describe the subband structure in strained silicon thin films. The model provides the dependence of the conductivity effective mass on strain and film thickness. The conductivity mass decreases along tensile stress in [110] direction applied to a (001) film. This conductivity mass decrease ensures the mobility enhancement in MOSFETs even with extremely thin silicon films. The two-band k·p model also describes the dependence of the non-parabolicity parameter on film thickness and strain. The influence of the subband structure modification on the mobility in advanced MOSFETs with strained ultra-thin silicon body is investigated. It is shown that an increase of subband non-parabolicity in thin films with strain reduces the mobility enhancement due to the conductivity mass modification, especially at higher strain values.

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Yang, Qing, L. Ruby Leung, Sara A. Rauscher, Todd D. Ringler und Mark A. Taylor. „Atmospheric Moisture Budget and Spatial Resolution Dependence of Precipitation Extremes in Aquaplanet Simulations“. Journal of Climate 27, Nr. 10 (09.05.2014): 3565–81. http://dx.doi.org/10.1175/jcli-d-13-00468.1.

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Abstract This study investigates the moisture budgets and resolution dependency of precipitation extremes in an aquaplanet framework based on the Community Atmosphere Model, version 4 (CAM4). Moisture budgets from simulations using two different dynamical cores, the Model for Prediction Across Scales-Atmosphere (MPAS-A) and High Order Method Modeling Environment (HOMME), but the same physics parameterizations suggest that during precipitation extremes the intensity of precipitation is approximately balanced by the vertical advective moisture transport. The resolution dependency in extremes from simulations at their native grid resolution originates from that of vertical moisture transport, which is mainly explained by changes in dynamics (related to vertical velocity ω) with resolution. When assessed at the same grid scale by area-weighted averaging the fine-resolution simulations to the coarse grids, simulations with either dynamical core still demonstrate resolution dependency in extreme precipitation with no convergence over the tropics, but convergence occurs at a wide range of latitudes over the extratropics. The use of lower temporal frequency data (i.e., daily vs 6 hourly) reduces the resolution dependency. Although thermodynamic (moisture) changes become significant in offsetting the effect of dynamics when assessed at the same grid scale, especially over the extratropics, changes in dynamics with resolution are still large and explain most of the resolution dependency during extremes. This suggests that the effects of subgrid-scale variability of ω and vertical moisture transport during extremes are not adequately parameterized by the model at coarse resolution. The aquaplanet framework and analysis described in this study provide an important metric for assessing sensitivities of cloud parameterizations to spatial resolution and dynamical cores under extreme conditions.

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Rust, H. W. „The effect of long-range dependence on modelling extremes with the generalised extreme value distribution“. European Physical Journal Special Topics 174, Nr. 1 (Juli 2009): 91–97. http://dx.doi.org/10.1140/epjst/e2009-01092-8.

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Lamarche, Leslie J., und Roman A. Makarevich. „A modeling study of asymmetries in plasma irregularity characteristics near gradient reversals“. Annales Geophysicae 34, Nr. 9 (31.08.2016): 709–23. http://dx.doi.org/10.5194/angeo-34-709-2016.

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Abstract. Asymmetries in plasma density irregularity generation between the leading and trailing edges of the large-scale plasma density structures in the high-latitude ionosphere are investigated. A model is developed that evaluates the gradient-drift instability (GDI) growth rate differences across the gradient reversal that is applicable at all propagation directions and for the broad range of altitudes spanning the entire lower ionosphere. In particular, the model describes asymmetries that would be observed by an oblique scanning radar near density structures in the polar cap such as elongated polar patches. The dependencies on the relative orientations between the directions of the gradient reversal, plasma convection, and wave propagation are examined at different altitudinal regions. At all altitudes, the largest asymmetries are expected for observations along the gradient reversals, e.g., when an elongated structure is oriented along the radar boresight. The convection direction that results in the strongest asymmetries exhibits a strong dependence on the altitude, with the optimal convection being parallel to the gradient reversal in the E region, perpendicular to it in the F region, and at some angle between these extremes in the transitional region. Implications for observations of polar patches by oblique scanning radars within the Super Dual Auroral Radar Network are discussed. It is demonstrated that the wave propagation direction relative to the prevalent convection and gradient directions plays a critical role in controlling both the irregularity growth rate and its asymmetries near gradient reversals.

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TWUMASIANKRAH, SAMPSON, WILHEMINA ADOMA PELS und SARALEES NADARAJAH. „Modeling rainfall extremes along the coastal and Northern parts of Ghana“. MAUSAM 75, Nr. 2 (24.03.2024): 433–42. http://dx.doi.org/10.54302/mausam.v75i2.5875.

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The main objective of the study was to determine the appropriate distribution for extreme rainfall along the coastal and northern sectors of Ghana. For stakeholders and policymakers to make appropriate risk-mitigating measures to lessen the damage caused by flood and drought, it is necessary to make proper inferences about extreme rainfall. In this study, we used both the multivariate and univariate extreme value data analysis approaches. The Generalized Extreme Value (GEV) with the Block Maxima approach and Generalized Pareto Distribution (GPD) with the Peak over the threshold (that is all excesses and decluster peaks approaches) were used in this study. Historical gridded monthly maximum rainfall data from 1970 to 2020 were obtained from the Climatic Research Unit and were grouped as the coastal and northern stations. The Maximum Likelihood Estimation method was used to estimate the model parameters, and both the unit root test and the Mann-Kendall tests were used to test for trend in the data. With the multivariate extreme modelling approach, the logistic bivariate GEV model was chosen as the “best” model. However, the dependence value was 0.965, so the extreme rainfall should be modelled independently using the univariate extreme value approaches. Hence, based on the information criteria and analysis of deviance approaches, the GEV distribution was considered the “best” fit for the extreme rainfall dataset for the northern part of Ghana. In contrast, the GPD distribution was the “best” fit for the coastal station. Comparatively, for the volume of rainfall in the year 2020, the extreme rainfall is expected to be higher in the coastal station of Ghana in the next two years. Also, extreme rainfall in 2 years would not exceed the maximum occurrence of rainfall (279.267), which happened in September 2020 at the northern station of Ghana.

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Maîtrejean, Guillaume, Patrick Terriault und Vladimir Brailovski. „Density Dependence of the Macroscale Superelastic Behavior of Porous Shape Memory Alloys: A Two-Dimensional Approach“. Smart Materials Research 2013 (19.09.2013): 1–13. http://dx.doi.org/10.1155/2013/749296.

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Porous Shape Memory Alloys (SMAs) are of particular interest for many industrial applications, as they combine intrinsic SMA (shape memory effect and superelasticity) and foam characteristics. The computational cost of direct porous material modeling is however extremely high, and so designing porous SMA structure poses a considerable challenge. In this study, an attempt is made to simulate the superelastic behavior of porous materials via the modeling of fully dense structures with material properties modified using a porous/bulk density ratio scaling relation. Using this approach, direct modeling of the porous microstructure is avoided, and only the macroscale response of the model is considered which contributes to a drastic reduction of the computational cost. Foam structures with a gradient of porosity are also studied, and the prediction made using the fully dense material model is shown to be in agreement with the mesoscale porous material model.

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Yue, Miaocong, Huayong Liu, Xinghua Chang, Laiping Zhang und Tianyu Li. „TGN: A Temporal Graph Network for Physics Prediction“. Applied Sciences 14, Nr. 2 (19.01.2024): 863. http://dx.doi.org/10.3390/app14020863.

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Long-term prediction of physical systems on irregular unstructured meshes is extremely challenging due to the spatial complexityof meshes and the dynamic changes over time; namely, spatial dependence and temporal dependence. Recently, graph-based next-step prediction models have achieved great success in the task of modeling complex high-dimensional physical systems. However, due to these models ignoring the temporal dependence, they inevitably suffer from the effects of error accumulation. To capture the spatial and temporal dependence simultaneously, we propose a temporal graph network (TGN) to predict the long-term dynamics of complex physical systems. Specifically, we introduce an Encode-Process-Decode architecture to capture spatial dependence and create low-dimensional vector representations of system states. Additionally, a temporal model is introduced to learn the dynamic changes in the low-dimensional vector representations to capture temporal dependence. Our model can capture spatiotemporal correlations within physical systems. On some complex long-term prediction tasks in fluid dynamics, such as airfoil flow and cylinder flow, the prediction error of our method is significantly lower than the competitive GNN baseline. We show accurate phase predictions even for very long prediction sequences.

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Durieu, Olivier, und Yizao Wang. „Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise“. Stochastic Processes and their Applications 143 (Januar 2022): 55–88. http://dx.doi.org/10.1016/j.spa.2021.10.007.

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