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Journal articles on the topic 'Extreme distribution theory'

Author: Grafiati

Published: 19 February 2023

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1

Balkema, A. A., and L. De Haan. "A convergence rate in extreme-value theory." Journal of Applied Probability 27, no. 3 (1990): 577–85. http://dx.doi.org/10.2307/3214542.

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A uniform convergence rate is determined for maxima of i.i.d. random variables from a distribution in the domain of attraction of the double-exponential distribution. The result is proved under a second-order condition on the underlying distribution parallelling the one given in Smith (1982) for the domain of attraction of the bounded-below and bounded-above families of limit distributions.

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2

Balkema, A. A., and L. De Haan. "A convergence rate in extreme-value theory." Journal of Applied Probability 27, no. 03 (1990): 577–85. http://dx.doi.org/10.1017/s0021900200039127.

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A uniform convergence rate is determined for maxima of i.i.d. random variables from a distribution in the domain of attraction of the double-exponential distribution. The result is proved under a second-order condition on the underlying distribution parallelling the one given in Smith (1982) for the domain of attraction of the bounded-below and bounded-above families of limit distributions.

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3

Syed, Zishan Ali, Mohammad Mohammad Ahmed Almazah, Zahid Iqbal, and Ghulam Raza Khan. "The Risk Analysis and Modeling of Byco Petroleum in Pakistan Using Extreme Value Theory." Mathematical Problems in Engineering 2021 (September 21, 2021): 1–9. http://dx.doi.org/10.1155/2021/2366469.

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The extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. This paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution. L-moment ratio diagram is being used to find the appropriate distributions among the distributions. L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pa

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Hlubinka, Daniel, and Viktor Beneš. "PREDICTION OF THE EXTREMAL SHAPE FACTOR OF SPHEROIDAL PARTICLES." Image Analysis & Stereology 20, no. 2 (2011): 101. http://dx.doi.org/10.5566/ias.v20.p101-104.

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In the stereological unfolding problem for spheroidal particles the extremal shape factor is predicted. The theory of extreme values has been used to show that extremes of the planar shape factor of particle sections tend to the same limit distribution as extremes of the original shape factor for both the conditional and marginal distribution. Attention is then paid to the extreme shape factor conditioned by the particle size. Normalizing constants are evaluated for a parametric model and the numerical procedure is tested on real data from metallography.

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Tamošaitienė, Jolanta, Vahidreza Yousefi, and Hamed Tabasi. "Project Portfolio Construction Using Extreme Value Theory." Sustainability 13, no. 2 (2021): 855. http://dx.doi.org/10.3390/su13020855.

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Choosing proper projects has a great impact on organizational success. Firms have various factors for choosing projects based on their different objectives and strategies. The problem of optimization of projects’ risks and returns is among the most prevalent issues in project portfolio selection. In order to optimize and select proper projects, the amount of projects’ expected risks and returns must be evaluated correctly. Determining the relevant distribution is very important in achieving these expectations. In this research, various types of practical distributions were examined, and consid

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Rieder, H. E., J. Staehelin, J. A. Maeder, et al. "Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory." Atmospheric Chemistry and Physics Discussions 10, no. 5 (2010): 12765–94. http://dx.doi.org/10.5194/acpd-10-12765-2010.

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Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshol

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Rieder, H. E., J. Staehelin, J. A. Maeder, et al. "Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory." Atmospheric Chemistry and Physics 10, no. 20 (2010): 10021–31. http://dx.doi.org/10.5194/acp-10-10021-2010.

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Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshol

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Zhou, Jian, Jixin Wang, and Hongbin Chen. "Mode-decomposing Analysis of the Extreme Load in Hybrid Electric Vehicles Using Extreme Value Theory." Open Mechanical Engineering Journal 10, no. 1 (2016): 136–47. http://dx.doi.org/10.2174/1874155x01610010136.

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In a hybrid electric vehicle (HEV), the hybrid system, which is equipped with an engine and a motor, is a key component. However, given the multimode characteristics of HEV, the original extreme load of the engine or motor is not independent and the random variables cannot be directly fitted by the extreme value theory (EVT). Thus, this paper proposes a mode-decomposing application method (MDAM) using EVT. Based on the method, three typical distributions, including the Fréchet distribution, the Gumbel distribution, and the Weibull distribution, were combined as a unified expression, and it was

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Cisse, Mamadou, Aliou Diop, Souleymane Bognini, and Nonvikan Karl-Augustt ALAHASSA. "Data Geometry and Extreme Value Distribution." Journal of Mathematics and Statistics Studies 2, no. 2 (2021): 06–15. http://dx.doi.org/10.32996/jmss.2021.2.2.2.

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In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the W

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Perfekt, Roland. "Extreme Value Theory for a Class of Markov Chains with Values in ℝd". Advances in Applied Probability 29, № 1 (1997): 138–64. http://dx.doi.org/10.2307/1427864.

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We consider extreme value theory for a class of stationary Markov chains with values in ℝd. The asymptotic distribution of Mn, the vector of componentwise maxima, is determined under mild dependence restrictions and suitable assumptions on the marginal distribution and the transition probabilities of the chain. This is achieved through computation of a multivariate extremal index of the sequence, extending results of Smith [26] and Perfekt [21] to a multivariate setting. As a by-product, we obtain results on extremes of higher-order, real-valued Markov chains. The results are applied to a freq

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Perfekt, Roland. "Extreme Value Theory for a Class of Markov Chains with Values in ℝd". Advances in Applied Probability 29, № 01 (1997): 138–64. http://dx.doi.org/10.1017/s0001867800027828.

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We consider extreme value theory for a class of stationary Markov chains with values in ℝd. The asymptotic distribution of M n , the vector of componentwise maxima, is determined under mild dependence restrictions and suitable assumptions on the marginal distribution and the transition probabilities of the chain. This is achieved through computation of a multivariate extremal index of the sequence, extending results of Smith [26] and Perfekt [21] to a multivariate setting. As a by-product, we obtain results on extremes of higher-order, real-valued Markov chains. The results are applied to a fr

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SONG, XiaoMeng, JianYun ZHANG, and FanZhe KONG. "Probability distribution of extreme precipitation in Beijing based on extreme value theory." SCIENTIA SINICA Technologica 48, no. 6 (2018): 639–50. http://dx.doi.org/10.1360/n092017-00129.

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Muravev, A. V., A. Yu Bundel, D. B. Kiktev, and A. V. Smirnov. "Verification of radar precipitation nowcasting of significant areas using the generalized Pareto distribution. Part 1: Elements of theory and methods for estimating parameters." Hydrometeorological research and forecasting 3 (September 28, 2022): 6–41. http://dx.doi.org/10.37162/2618-9631-2022-3-6-41.

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The assessments of nowcasting of large precipitation areas accumulated in the last few years at the Hydrometeorological Research Center of the Russian Federation are presented in two parts complemented by a discussion of methodological problems in the first part and application problems in the second part of the paper. The division is largely due to the sharp distinction between the theoretical modeling of extremes with a relatively free choice of assumptions and the statistical analysis of the distribution "tails" in rapidly "impoverishing" samples. The contrast between these parts is exacerb

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Andjelic, Goran, Ivana Milosev, and Vladimir Djakovic. "Extreme value theory in emerging markets." Ekonomski anali 55, no. 185 (2010): 63–105. http://dx.doi.org/10.2298/eka1085063a.

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This paper investigates the performance of extreme value theory (EVT) with the daily stock index returns of four different emerging markets. The research covers the sample representing the Serbian (BELEXline), Croatian (CROBEX), Slovenian (SBI20), and Hungarian (BUX) stock indexes using the data from January 2006 - September 2009. In the paper a performance test was carried out for the success of application of the extreme value theory in estimating and forecasting of the tails of daily return distribution of the analyzed stock indexes. Therefore the main goal is to determine whether EVT adequ

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ANÉ, THIERRY. "TWO-COMPONENT EXTREME VALUE DISTRIBUTION FOR ASIA-PACIFIC STOCK INDEX RETURNS." International Journal of Theoretical and Applied Finance 09, no. 05 (2006): 643–71. http://dx.doi.org/10.1142/s0219024906003792.

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Financial risk management typically deals with low-probability events in the tails of asset return distributions. To better capture the behavior of these tails, several studies have clearly highlighted that one should rely on a methodology that directly focuses on the tails of the distribution rather than getting the tails as an outcome of modelling the entire density function. Traditional Extreme Value Theory (EVT) distributions, however, provide a good fit for the bulk of the extreme data but usually underestimate a small amount of observations considered as "outliers". Since the main object

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Fałdziński, Marcin, Magdalena Osińska, and Wojciech Zalewski. "Extreme Value Theory in Application to Delivery Delays." Entropy 23, no. 7 (2021): 788. http://dx.doi.org/10.3390/e23070788.

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

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Morganti, Paolo Riccardo. "Extreme Value Theory and Auction Models." Abril - Junio 2021 16, no. 2 (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 devel

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Huang, Whitney K., Michael L. Stein, David J. McInerney, Shanshan Sun, and Elisabeth J. Moyer. "Estimating changes in temperature extremes from millennial-scale climate simulations using generalized extreme value (GEV) distributions." Advances in Statistical Climatology, Meteorology and Oceanography 2, no. 1 (2016): 79–103. http://dx.doi.org/10.5194/ascmo-2-79-2016.

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Abstract. Changes in extreme weather may produce some of the largest societal impacts of anthropogenic climate change. However, it is intrinsically difficult to estimate changes in extreme events from the short observational record. In this work we use millennial runs from the Community Climate System Model version 3 (CCSM3) in equilibrated pre-industrial and possible future (700 and 1400 ppm CO2) conditions to examine both how extremes change in this model and how well these changes can be estimated as a function of run length. We estimate changes to distributions of future temperature extrem

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Gomes, Daniel T., and Lígia Henriques-Rodrigues. "Swimming performance index based on extreme value theory." International Journal of Sports Science & Coaching 14, no. 1 (2018): 51–62. http://dx.doi.org/10.1177/1747954118808068.

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The International Swimming Federation has developed a points system that allows comparisons of results between different events. Such system is important for several reasons, since it is used as a criterion to rank swimmers in awards and selection procedures of national teams. The points system is based entirely on the world record of the correspondent event. Since it is based on only one observation, this work aims to suggest a new system, based on the probability distribution of the best performances in each event. Using extreme value theory, such distribution, under certain conditions, conv

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Christidis, Nikolaos, Peter A. Stott, and Simon J. Brown. "The Role of Human Activity in the Recent Warming of Extremely Warm Daytime Temperatures." Journal of Climate 24, no. 7 (2011): 1922–30. http://dx.doi.org/10.1175/2011jcli4150.1.

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Abstract Formal detection and attribution analyses of changes in daily extremes give evidence of a significant human influence on the increasing severity of extremely warm nights and decreasing severity of extremely cold days and nights. This paper presents an optimal fingerprinting analysis that also detects the contributions of external forcings to recent changes in extremely warm days using nonstationary extreme value theory. The authors’ analysis is the first that attempts to partition the observed change in warm daytime extremes between its anthropogenic and natural components and hence a

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Bhavsar, Suketu P. "A Model for First-Ranked Galaxies in Rich Clusters Using Extreme Value Theory." International Journal of Modern Physics C 08, no. 02 (1997): 253–62. http://dx.doi.org/10.1142/s0129183197000229.

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First-ranked galaxies in rich clusters are among the brightest objects in the Universe. Their extremely uniform luminosities have been the cause of much debate. Are these objects a special class of galaxies or merely the tail end of a distribution? A model can be constructed for the distribution in luminosity of these galaxies using a classical result from extreme value theory by Fisher and Tippett in 1928. Their amazing result on the distribution of extremes and its application in resolving the debate on the nature of the brightest galaxies is discussed here.

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Fayomi, Aisha, Neamat Qutb, and Ohoud Al-Beladi. "The exact extreme value distribution – applied study." International Journal of Advanced Statistics and Probability 5, no. 2 (2017): 87. http://dx.doi.org/10.14419/ijasp.v5i2.7834.

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Extreme value theory is used to develop models for describing the distribution of extreme events. Exact extreme value or compound distri-bution which is based on the theory of the maximum of random variables of random numbers is one of the most important models that are applicable in various situations, for instance of interest, it uses partial duration series (PDF) data to analyze extreme hydrological. As part of our earlier study, the parameters of this model were estimated by two methods, maximum likelihood (ML) and Bayesian- based on non-informative and informative priors. Moreover, a comp

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Onwuegbuche, Faithful C., Alpha B. Kenyatta, Steeven B. Affognon, Exavery P. Enock, and Mary O. Akinade. "Application of Extreme Value Theory in Predicting Climate Change Induced Extreme Rainfall in Kenya." International Journal of Statistics and Probability 8, no. 4 (2019): 85. http://dx.doi.org/10.5539/ijsp.v8n4p85.

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Climate change has brought about unprecedented new weather patterns, one of which is changes in extreme rainfall. In Kenya, heavy rains and severe flash floods have left people dead and displaced hundreds from their settlements. In order to build a resilient society and achieve sustainable development, it is paramount that adequate inference about extreme rainfall be made. To this end, this research modelled and predicted extreme rainfall events in Kenya using Extreme Value Theory for rainfall data from 1901-2016. Maximum Likelihood Estimation was used to estimate the model parameters and bloc

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Carollo, C., I. Astin, and J. Graff. "Vertical structure of extreme currents in the Faroe-Bank Channel." Annales Geophysicae 23, no. 6 (2005): 1977–86. http://dx.doi.org/10.5194/angeo-23-1977-2005.

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Abstract. Extreme currents are studied with the aim of understanding their vertical and spatial structures in the Faroe-Bank Channel. Acoustic Doppler Current Profiler time series recorded in 3 deployments in this channel were investigated. To understand the main features of extreme events, the measurements were separated into their components through filtering and tidal analysis before applying the extreme value theory to the surge component. The Generalized Extreme Value (GEV) distribution and the Generalized Pareto Distribution (GPD) were used to study the variation of surge extremes from n

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Wang, Yingjie, and Xinsheng Liu. "A New Point Process Regression Extreme Model Using a Dirichlet Process Mixture of Weibull Distribution." Mathematics 10, no. 20 (2022): 3781. http://dx.doi.org/10.3390/math10203781.

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The extreme value theory is widely used in economic and environmental domains, it aims to study the stochastic extreme behaviors associated with rare events. In this context, we consider a new mixture model for extremal events analysis, including a Dirichlet process mixture of Weibull (DPMW) distribution below the threshold and the point process (PP) extreme model for the upper tail. This model developed a regression structure for the PP extreme model parameters, which explains the variation of the exceedance through all tail parameters. The estimation of the model parameters is performed unde

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McNeil, Alexander J. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory." ASTIN Bulletin 27, no. 1 (1997): 117–37. http://dx.doi.org/10.2143/ast.27.1.563210.

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AbstractGood estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling extreme historical losses. These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of their application to Danish data on large fire insurance losses.

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Phalitnonkiat, Pakawat, Peter G. M. Hess, Mircea D. Grigoriu, et al. "Extremal dependence between temperature and ozone over the continental US." Atmospheric Chemistry and Physics 18, no. 16 (2018): 11927–48. http://dx.doi.org/10.5194/acp-18-11927-2018.

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Abstract. The co-occurrence of heat waves and pollution events and the resulting high mortality rates emphasize the importance of the co-occurrence of pollution and temperature extremes. Through the use of extreme value theory and other statistical methods, tropospheric surface ozone and temperature extremes and their joint occurrence are analyzed over the United States during the summer months (JJA) using measurements and simulations of the present and future climate and chemistry. Five simulations from the Chemistry-Climate Model Initiative (CCMI) reference experiment using specified dynamic

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Tuia, Devis, and Mikhail Kanevski. "Indoor radon distribution in Switzerland: lognormality and Extreme Value Theory." Journal of Environmental Radioactivity 99, no. 4 (2008): 649–57. http://dx.doi.org/10.1016/j.jenvrad.2007.09.004.

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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 (October 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 valu

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Tanprayoon, Ekapak, Unchalee Tonggumnead, and Sirinapa Aryuyuen. "A New Extension of Generalized Extreme Value Distribution: Extreme Value Analysis and Return Level Estimation of the Rainfall Data." Trends in Sciences 20, no. 1 (2022): 4034. http://dx.doi.org/10.48048/tis.2023.4034.

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This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go

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Liu, Defu, Liping Wang, and Liang Pang. "Theory of multivariate compound extreme value distribution and its application to extreme sea state prediction." Chinese Science Bulletin 51, no. 23 (2006): 2926–30. http://dx.doi.org/10.1007/s11434-006-2186-x.

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Kingsolver, Joel G., and Lauren B. Buckley. "Quantifying thermal extremes and biological variation to predict evolutionary responses to changing climate." Philosophical Transactions of the Royal Society B: Biological Sciences 372, no. 1723 (2017): 20160147. http://dx.doi.org/10.1098/rstb.2016.0147.

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Central ideas from thermal biology, including thermal performance curves and tolerances, have been widely used to evaluate how changes in environmental means and variances generate changes in fitness, selection and microevolution in response to climate change. We summarize the opportunities and challenges for extending this approach to understanding the consequences of extreme climatic events. Using statistical tools from extreme value theory, we show how distributions of thermal extremes vary with latitude, time scale and climate change. Second, we review how performance curves and tolerances

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Coelho, C. A. S., C. A. T. Ferro, D. B. Stephenson, and D. J. Steinskog. "Methods for Exploring Spatial and Temporal Variability of Extreme Events in Climate Data." Journal of Climate 21, no. 10 (2008): 2072–92. http://dx.doi.org/10.1175/2007jcli1781.1.

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Abstract This study presents various statistical methods for exploring and summarizing spatial extremal properties in large gridpoint datasets. Extremal properties are inferred from the subset of gridpoint values that exceed sufficiently high, time-varying thresholds. A simple approach is presented for how to choose the thresholds so as to avoid sampling biases from nonstationary differential trends within the annual cycle. The excesses are summarized by estimating parameters of a flexible generalized Pareto model that can account for spatial and temporal variation in the excess distributions.

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Santos, Eliane Barbosa, Paulo Sérgio Lucio, and Cláudio Moisés Santos e Silva. "Seasonal Analysis of Return Periods for Maximum Daily Precipitation in the Brazilian Amazon." Journal of Hydrometeorology 16, no. 3 (2015): 973–84. http://dx.doi.org/10.1175/jhm-d-14-0201.1.

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Abstract The aim of this study is to estimate the return period of maximum daily precipitation for each season of the year in different subregions of the Brazilian Amazon. For this, the extreme value theory was used, through the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD). The GEV distribution and GPD were applied in precipitation series from homogeneous regions of the Brazilian Amazon. The GEV and GPD goodness of fit were evaluated by the application of the Kolmogorov–Smirnov (KS) test, which compares the cumulative empirical distributions with t

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Wolinski, S., and T. Pytlowany. "Evaluation of Load Values Using the Gumbel Model." Archives of Civil Engineering 58, no. 2 (2012): 199–208. http://dx.doi.org/10.2478/v.10169-012-0012-1.

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Abstract The paper deals with application of the Gumbel model to evaluation of the environmental loads. According to recommendations of Eurocodes, the conventional method of determining return period and characteristic values of loads utilizes the theory of extremes and implicitly assumes that the cumulative distribution function of the annual or other basic period extremes is the Gumbel distribution. However, the extreme value theory shows that the distribution of extremes asymptotically approaches the Gumbel distribution when the number of independent observations in each observation period

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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, no. 2 (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 distrib

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Ibrahim, Mohamad Najib. "Assessment of the Uncertainty Associated with Statistical Modeling of Precipitation Extremes for Hydrologic Engineering Applications in Amman, Jordan." Sustainability 14, no. 24 (2022): 17052. http://dx.doi.org/10.3390/su142417052.

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Estimates of extreme precipitation are commonly associated with different sources of uncertainty. One of the primary sources of uncertainty in the statistical modeling of precipitation extremes comes from extreme data series (i.e., sampling uncertainty). Therefore, this research aimed to quantify the sampling uncertainty in terms of confidence intervals. In addition, this article examined how the data record length affects predicted extreme precipitation estimates and data set statistics. A nonparametric bootstrap resample was utilized to quantify the precipitation quantile sampling distributi

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Lee, Seyoon, and Joseph H. T. Kim. "Exponentiated generalized Pareto distribution: Properties and applications towards extreme value theory." Communications in Statistics - Theory and Methods 48, no. 8 (2018): 2014–38. http://dx.doi.org/10.1080/03610926.2018.1441418.

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del Castillo, Joan, Jalila Daoudi, and Isabel Serra. "THE FULL TAILS GAMMA DISTRIBUTION APPLIED TO MODEL EXTREME VALUES." ASTIN Bulletin 47, no. 3 (2017): 895–917. http://dx.doi.org/10.1017/asb.2017.9.

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AbstractIn this paper, we introduce the simplest exponential dispersion model containing the Pareto and exponential distributions. In this way, we obtain distributions with support (0, ∞) that in a long interval are equivalent to the Pareto distribution; however, for very high values, decrease like the exponential. This model is useful for solving relevant problems that arise in the practical use of extreme value theory. The results are applied to two real examples, the first of these on the analysis of aggregate loss distributions associated to the quantitative modelling of operational risk.

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Blanchet, J., and M. Lehning. "Mapping snow depth return levels: smooth spatial modeling versus station interpolation." Hydrology and Earth System Sciences Discussions 7, no. 4 (2010): 6129–77. http://dx.doi.org/10.5194/hessd-7-6129-2010.

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Abstract. For adequate risk management in mountainous countries, hazard maps for extreme snow events are needed. This requires the computation of spatial estimates of return levels. In this article we use recent developments in extreme value theory and compare two main approaches for mapping snow depth return levels from in situ measurements. The first one is based on the spatial interpolation of pointwise extremal distributions (the so-called Generalized Extreme Value distribution, GEV henceforth) computed at station locations. The second one is new and based on the direct estimation of a spa

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Blanchet, J., and M. Lehning. "Mapping snow depth return levels: smooth spatial modeling versus station interpolation." Hydrology and Earth System Sciences 14, no. 12 (2010): 2527–44. http://dx.doi.org/10.5194/hess-14-2527-2010.

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Abstract. For adequate risk management in mountainous countries, hazard maps for extreme snow events are needed. This requires the computation of spatial estimates of return levels. In this article we use recent developments in extreme value theory and compare two main approaches for mapping snow depth return levels from in situ measurements. The first one is based on the spatial interpolation of pointwise extremal distributions (the so-called Generalized Extreme Value distribution, GEV henceforth) computed at station locations. The second one is new and based on the direct estimation of a spa

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Deetae, Natthinee. "Analysis and Mathematical Modeling for Flood Surveillance from Rainfall by Extreme Value Theory for Agriculture in Phitsanulok Province, Thailand." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1797–807. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4558.

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Attempts to use the generalized extreme value distribution and generalized Pareto distribution with the maximum likelihood estimates on the extreme rainfall data at one weather station over Phitsanulok province. This paper gathered the rainfall data from January 1987 to December 2021. The estimated return level is 10, 20, 50, and 100 years. The result displays the modeling of the generalized extreme value distribution (GEV); the Gumbel distribution was a fitting proposal for extreme annual rainfall in Phitsanulok province, with μ = 24.95(1.39), σ=22.59(1.06), and ξ=0.03(0.05). In addition, the

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Bhatia, Siddharth, Arjit Jain, and Bryan Hooi. "ExGAN: Adversarial Generation of Extreme Samples." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 6750–58. http://dx.doi.org/10.1609/aaai.v35i8.16834.

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Mitigating the risk arising from extreme events is a fundamental goal with many applications, such as the modelling of natural disasters, financial crashes, epidemics, and many others. To manage this risk, a vital step is to be able to understand or generate a wide range of extreme scenarios. Existing approaches based on Generative Adversarial Networks (GANs) excel at generating realistic samples, but seek to generate typical samples, rather than extreme samples. Hence, in this work, we propose ExGAN, a GAN-based approach to generate realistic and extreme samples. To model the extremes of the

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Chesneau, Christophe. "A note on an extreme left skewed unit distribution: Theory, modelling and data fitting." Open Statistics 2, no. 1 (2021): 1–23. http://dx.doi.org/10.1515/stat-2020-0103.

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Abstract In probability and statistics, unit distributions are used to model proportions, rates, and percentages, among other things. This paper is about a new one-parameter unit distribution, whose probability density function is defined by an original ratio of power and logarithmic functions. This function has a wide range of J shapes, some of which are more angular than others. In this sense, the proposed distribution can be thought of as an “extremely left skewed alternative” to the traditional power distribution. We discuss its main characteristics, including other features of the probabi

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Cui, Yu, Qing He, Zhenhua Zhang, and Zhiguo Li. "USING EXTREME VALUE THEORY TO IDENTIFY RAILCAR ASYMMETRIC WHEEL WEAR AND ITS BENEFIT ANALYSIS." Transport 34, no. 5 (2019): 569–78. http://dx.doi.org/10.3846/transport.2019.11657.

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Railcar asymmetric wheel wear leads to severe wear on one wheel but mild wear on the other wheel. The consequences of the asymmetric wheel include accelerated wear, mechanical failure and downtime, and high financial penalties. Therefore, identifying the asymmetric wheel wear is critical not only for cost effective maintenance but also for safe operations. Fortunately, the increasing amount of various wayside detectors is instrumented along the railway that can monitor the health of railcar components and log plenty of detailed information about railroad operations. One can use this informatio

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Wang, Wei, Yuling Song, Jun Chen, and Shuaibing Shi. "Dynamic reliability prediction of vehicular suspension structure with damping random uncertainties." Journal of Vibration and Control 25, no. 3 (2018): 549–58. http://dx.doi.org/10.1177/1077546318788710.

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This research is conducted such that a two degrees of freedom nonlinear stochastic vibration model of vehicular suspension structure with random bilinear damping forces and cubic nonlinear restoring forces is established. Based on extreme value theory (EVT) and Monte Carlo integration method (MCIM), a novel method of predicting the failure probabilities of the maximum amplitude responses of suspension structure is proposed. The extreme value distribution functions of amplitude responses, which are analytical expressed by underlying amplitude distribution functions, are acquired by using EVT. I

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Masingi, Vusi Ntiyiso, and Daniel Maposa. "Modelling Long-Term Monthly Rainfall Variability in Selected Provinces of South Africa: Trend and Extreme Value Analysis Approaches." Hydrology 8, no. 2 (2021): 70. http://dx.doi.org/10.3390/hydrology8020070.

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Extreme rainfall events have made significant damages to properties, public infrastructure and agriculture in some provinces of South Africa notably in KwaZulu-Natal and Gauteng among others. The general global increase in the frequency and intensity of extreme precipitation events in recent years is raising a concern that human activities might be heavily disturbed. This study attempts to model long-term monthly rainfall variability in the selected provinces of South Africa using various statistical techniques. The study investigates the normality and stationarity of the underlying distributi

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Gupta, Vijay K., Oscar J. Mesa, and E. Waymire. "Tree-dependent extreme values: the exponential case." Journal of Applied Probability 27, no. 1 (1990): 124–33. http://dx.doi.org/10.2307/3214600.

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The length of the main channel in a river network is viewed as an extreme value statistic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses an interesting contrast to the classical independent theory. Equivalently, the distribution of the extinction time for a binary branching process given a large number of progeny is sought. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n–1/2L given M = n

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Gupta, Vijay K., Oscar J. Mesa, and E. Waymire. "Tree-dependent extreme values: the exponential case." Journal of Applied Probability 27, no. 01 (1990): 124–33. http://dx.doi.org/10.1017/s002190020003847x.

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The length of the main channel in a river network is viewed as an extreme value statistic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses an interesting contrast to the classical independent theory. Equivalently, the distribution of the extinction time for a binary branching process given a large number of progeny is sought. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n–1/2 L given M =

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Medford, Anthony. "Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models." Risks 9, no. 3 (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 A

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