Generalized Extreme Value Research Articles

Maximum capture problem based on paired combinatorial weibit model to determine park-and-ride facility locations

Park-and-ride (P&R) facilities are key components in encouraging people to use the transit system by allowing them to leave their private vehicles at certain locations. The well-known multinomial logit (MNL) model is often used to develop a random utility maximization–based mathematical programming formulation to determine P&R facility locations. According to the independently and identically distributed (IID) assumption, the MNL model cannot account for the route similarity and user heterogeneity. This study provides a new mixed integer linear programming (MILP) formulation by incorporating a newly developed paired combinatorial weibit (PCW) model to relax the IID assumption for determining the optimal P&R facility location. Specifically, the incorporation of a copula derived from a generalized extreme value (GEV) model addresses the issue of route overlap within the context of the PCW model. In addition, using the Weibull distribution permits the consideration of heterogeneous perception variance. Its two-level tree structure for evaluating the marginal and conditional probabilities allows a linearization scheme to obtain a set of linear constraints. Numerical examples reveal the influence of the IID assumption relaxation on the results. The two probabilities from the tree structure and the binary location variables are combined to present a corresponding PCW model under open/close P&R facility solution. According to the degree of route overlapping and route-specific perception variance, the fare structure, particularly the distance-based scheme, has an impact on the number of P&R users and location at optimum.

Identification of the most suitable probability distributions for ultimate strength of FRP-strengthened X-shaped tubular joints under axial loads

This paper focuses on identifying the most appropriate probability distributions for characterizing the ultimate strength of FRP-strengthened X-shaped tubular joints under axial loads. The study begins by verifying the accuracy of finite element (FE) models through a comparison with experimental results. Subsequently, 218 FE nonlinear static analyses are conducted to generate two reliable datasets for strength ratios. To determine the most suitable probability distribution models, 16 different distributions are fitted to the data, and their accuracy is evaluated using Kolmogorov-Smirnov and Chi-squared goodness-of-fit tests. The findings reveal that the Generalized Extreme Value distribution provides the best fit for describing the ultimate strength under compressive axial load, while the Burr distribution is identified as the most suitable model for tensile axial load. The analysis of probability differences revealed that the proposed probability distribution models for compressive and tensile loads exhibit minimal disparities, with a slight difference of 5.24% and 4.80%, respectively. The identified probability distribution models enhance the reliability and confidence in predicting the behavior and performance of these joints, contributing valuable insights to the field of structural engineering.

Performance Improvement in UAV Communication Systems With Uncertain Solar Energy Supply

In this paper, we study a problem of improving the communication performance in a solar-assisted UAV (unmanned aerial vehicle) communication system (SA-UCS) where UAVs equipped with solar panels are deployed to provide communication services to ground users in a target area. Previous works have ignored the inherent uncertainty in solar energy supply caused by naturally unpredictable weather conditions and UAV vibrations, consequently degrading communication performance in SA-UCSs. To bridge the gap, we propose to explore the extreme value theory to tackle uncertain solar energy supply. Specifically, we formulate a throughput maximization problem that is subject to transmission power, link capacity, UAV position, and minimum residual energy. To handle the uncertainty in solar energy supply, we propose to find the GEV (generalized extreme value) distribution of the minimum amount of harvested solar energy, in order to bound the solar energy supply in extreme cases. To solve the formulated problem, which is in general non-convex, we develop an iterative optimization method that first decomposes the originally formulated problem into two sub-problems being solved alternately at each iteration through employing the successive convex approximation (SCA) technique. We perform extensive simulations using real-world data from the National Solar Radiation Database NSRD18. The simulation results corroborate the throughput enhancement with guaranteed energy supply available for UAV communications. Additionally, the results also show the fast convergence achieved by the developed iterative method.

Impact Evaluation Using Nonstationary Parameters for Historical and Projected Extreme Precipitation

Recent improvements in time series studies of hydro-climatological variables have led to the belief that the effects of nonstationarity are substantial enough to call the idea of traditional stationary approaches into doubt. The mean and variability of annual and seasonal rainfall in Pakistan are changing due to anthropogenic climate change. With the use of stationary and nonstationary frequency analysis techniques, this study set out to assess the impacts of nonstationarity in Southern Punjab, Pakistan, over the historical period of 1970–2015 and the future periods of 2020–2060 and 2060–2100. Four frequency distributions, namely Generalized Extreme Value (GEV), Gumbel, normal, and lognormal, were used. The findings of the nonstationarity impact across Southern Punjab showed different kinds of impacts, such as an increase or reduction in the return level of extreme precipitation. In comparison to other distributions, GEV provided the finest fit. In Bahawalnagar, Bahawalpur, Multan, Rahim Yar Khan and DG. Khan, the annual nonstationarity impacts for the 100-year return level were increased up to 15.2%, 8.7%, 58.3%, 18.7%, and 20%, respectively. Moreover, extreme precipitation was found to be increasing during the historical and projected periods, which may increase floods, while less water availability appeared at a seasonal scale (summer) during 2061–2100. The increased nonstationarity effects emphasized adapting these nonstationarities induced by climate change into the design of water resource structures.

Evaluación de Parámetros de la Distribución Generalizada de Valor Extremo en Precipitaciones del Norte Peruano

Las precipitaciones máximas del norte peruano se comportan de una manera estacional, concentrándose entre los primeros meses del año, sin embargo, pocos estudios han analizado su distribución a lo largo del tiempo mediante un análisis de extremos. El objetivo de la investigación fue evaluar los parámetros de ubicación, escala y forma de la distribución generalizada de valor extremo en precipitaciones máximas del norte peruano correspondientes a las regiones hidrológicas Pacífico 5 y Pacífico 6. Se realizó la recolección de datos de precipitaciones máximas diarias disponibles en las estaciones climáticas de ambas regiones, considerando una cantidad mínima de 15 años de registros por estación y un filtro basado en el análisis estadístico y visual, por lo que se estableció 138 estaciones. Posteriormente se aplicaron los ajustes a momentos ordinarios y a momentos lineales de la distribución generalizada de valor extremo y se utilizó dos tipos de prueba de hipótesis para cada región que ayudaron a validar las similitudes de cada parámetro en ambas regiones. Los resultados muestran diferencias significativas sólo en el parámetro de ubicación, en tanto, al contrastar la altitud, precipitación media y precipitación máxima de cada región hidrológica se determinó que existen altas correlaciones con los parámetros de ubicación y escala. Finalmente, se concluye en que ambas regiones hidrológicas los parámetros de escala y forma muestran un buen desempeño para ambos ajustes a partir de las hipótesis aplicadas y el parámetro de ubicación demostró que la región hidrológica Pacífico 6 es más lluviosa que la región hidrológica Pacífico 5.

Mitigating infectious disease risks through non-stationary flood frequency analysis: a case study in Malaysia based on natural disaster reduction strategy.

The occurrence of floods has the potential to escalate the transmission of infectious diseases. To enhance our comprehension of the health impacts of flooding and facilitate effective planning for mitigation strategies, it is necessary to explore the flood risk management. The variability present in hydrological records is an important and neglecting non-stationary patterns in flood data can lead to significant biases in estimating flood quantiles. Consequently, adopting a non-stationary flood frequency analysis appears to be a suitable approach to challenge the assumption of independent and identically distributed observations in the sample. This research employed the generalized extreme value (GEV) distribution to examine annual maximum flood series. To estimate non-stationary models in the flood data, several statistical tests, including the TL-moment method was utilized on the data from ten stream-flow stations in Johor, Malaysia, which revealed that two stations, namely Kahang and Lenggor, exhibited non-stationary behaviour in their annual maximum streamflow. Two non-stationary models efficiently described the data series from these two specific stations, the control of which could reduce outbreak of infectious diseases when used for controlling the development measures of the hydraulic structures. Thus, the application of these models may help prevent biased prediction of flood occurrences leading to lower number of cases infected by disease.

Flood Inundation mapping and mitigation options in data-scarce region of Beledwayne town in the Wabi Shebele River Basin of Somalia

Somalia has experienced extreme flash floods in recent years across the arid regions causing tremendous loss of lives and properties. However, the flood magnitude, depth, and frequency of occurrence are not yet quantified. This is mainly due to scarce datasets in the area. . In this study, integration of observed and Climate Hazards Infrared Precipitation (CHIRP) satellite rainfall products and remote sensing raster data were used to improve hydrological model simulation outputs. The Hydrologic Engineering Center namely HEC-HMS and HEC-RAS models were used to simulate the rainfall-runoff processes and flood inundation, respectively. The land use, soil, slope and Digital Elevation map (DEM) were used to set-up the models and generate outputs. The HEC-HMS model calibration results depict that the model is able to reproduce the observed streamflow The simulated flows generated by the model predicted good agreement with the observed flow with values of 0.79, 0.74, 0.78, and 0.78 evaluated through the Nash and Sutcliffe Efficiency (NSE), Runoff Volume Error (RVE), coefficient of determination (R2), and percentage error of peak flow (PEPF), respectively. The HEC-RAS model result indicates that the maximum flood depth and velocity were obtained at the floodplain area. The peak flood at 50, 100, and 200-year return period using General Extreme Value (GEV) distribution revealed 384m3s-1, 409m3s-1, and 434m3s-1, respectively. The 100-year peak flood discharge in a specific part of the river revealed a flood depth of 7.53m. The provision of Levees as mitigation measures revealed reduction of the flood extent by 35% and suggested as possible flood protection measures for the study area.

Functional and variables selection in extreme value models for regional flood frequency analysis

The problem of estimating return levels of river discharge, relevant in flood frequency analysis, is tackled by relying on the extreme value theory. The Generalized Extreme Value (GEV) distribution is assumed to model annual maxima values of river discharge registered at multiple gauging stations belonging to the same river basin. The specific features of the data from the Upper Danube basin drive the definition of the proposed statistical model. Firstly, Bayesian P-splines are considered to account for the non-linear effects of station-specific covariates on the GEV parameters. Secondly, the problem of functional and variable selection is addressed by imposing a grouped horseshoe prior to the coefficients to encourage the shrinkage of non-relevant components to zero. A cross-validation study is organized to compare the proposed modeling solution to other models, showing its potential to reduce the uncertainty of the ungauged predictions without affecting their calibration.

Statistical Modeling of Shadows in SAR Imagery

Shadows are a special distortion in synthetic aperture radar (SAR) imaging. They often hamper proper image understanding and target recognition but also offer useful information, and therefore, the statistical modeling of SAR image shadows is imperative. In this endeavor, we systematically deduced the statistical models of shadows in multimodal SAR images, including single-look intensity and amplitude images and multilook intensity and amplitude images in a real domain and complex domain, respectively. In particular, for the filtered SAR image shadow, we introduced the generalized extreme value (GEV) distribution to characterize its statistics. We carried out an experiment on shadows in a real SAR image and conducted chi-square goodness-of-fit tests on the deduced models. Furthermore, we compared the deduced statistical models of shadows with state-of-the-art statistical models of SAR imagery. Finally, suggestions are given for selecting the optimal statistical model of shadows in multimodal SAR images.

Comparative study on characteristics of typhoon gusts in the coastal and offshore areas of the South China Sea

Typhoon gusts are hazardous to buildings and structures in both coastal and offshore areas, but the gust characteristics in the two areas could be quite different. In this study, the observational data from two meteorological stations, one at Shenzhen (coastal) and the other in the offshore area of the South China Sea are used to analyze the typhoon gust-related variables and to find the theoretical distribution model that best describes them. The results show that in both coastal and offshore areas, the probability density distributions of all gust-related variables are non-Gaussian. When fitting the curve of the statistical data, the Gengamma model performs the best, followed by the Lognormal model, and the generalized extreme value (GEV) distribution model. Specifically, the gust factor and turbulence intensity are generally Gengamma- and GEV- distributed, respectively. The distributions exhibit certain differences in different gust variables in coastal and offshore areas. The theoretical probabilistic models perform better in the offshore area than in the coastal area. The gust factor increases linearly with the turbulence intensity, while previous empirical models tend to overestimate it. The gust factor and turbulence intensity are significantly higher in the offshore area than in the coastal area. Slower turbulent dissipation is found in the offshore area during typhoon process. A strong positive correlation is shown between the gust amplitude and the turbulent flux. In both coastal and offshore areas, the larger the gust amplitude is, the more the turbulent flux is transmitted.

STATISTICAL INFERENCE IN THE GENERALIZED EXTREME VALUE REGRESSION MODEL BASED ON SIMULATION STUDY

Generalized extreme value (GEV) regression model is widely used when the dependent variable $Y$ represents a rare event. In this case the logistic regression model shows relevant drawbacks. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome $Y$ and a set of potential predictors $\mathbf X$. Maximum likelihood estimators in this model has been proposed, and their asymptotic properties recently established. We conduct a detailed simulation study of its numerical properties. We evaluate its accuracy and the quality of the normal approximation of its asymptotic distribution. We study the quality of the approximation for constructing asymptotic Wald-type tests of hypothesis. Several others aspects of this model, such as the event probabilities still deserve attention. We also propose estimator of this quantity and we investigate its properties both theoretically and via simulations. Based on these results, we provide recommendations about the range of minimum sample size under which a reliable statistical inference on the event probabilities can be obtained in a GEV regression model. A real-data example illustrates the proposed estimators.

Stochastic Model of the Annual Maximum Rainfall Series Using Probability Distributions

Rainfall is a natural process that is often characterized by significant variability and uncertainty. Stochastic models of rainfall typically involve the use of probability distributions to describe the likelihood of different outcomes occurring. This study aimed to model the annual maximum of daily rainfall in Makassar City, Indonesia for the period 1980–2022, specifically focusing on the rainy season (November to April) using probability distributions to estimate return periods. The study used the Generalized Extreme Value (GEVD) and Gumbel distributions. The Kolmogorov-Smirnov test was used to determine the suitability of each distribution, and the likelihood ratio test was employed to determine the best-fit model. The Mann-Kendall test was used to detect any trends in the data. The results indicated that the Gumbel distribution was the best-fit model for data in November, December, January, March, and April, while GEV was appropriate for February. No trends were observed in any of the months. The study then estimated the maximum rainfall for various return periods. January produced the highest maximum rainfall estimates for the 2, 3, and 5-year return periods, while February produced the highest maximum rainfall estimates for the 10 and 20-year return periods. Information about maximum rainfall can be valuable for the government and other stakeholders in developing flood prevention strategies and mitigating the effects of heavy rainfall, particularly during the peak months of the rainy season in Makassar City, which are December, January, and February.

Assessing Flood Risk: LH-Moments Method and Univariate Probability Distributions in Flood Frequency Analysis

This study examines all of the equations necessary to derive the parameters for seven probability distributions of three parameters typically used in flood frequency research, namely the Pearson III (PE3), the generalized extreme value (GEV), the Weibull (W3), the log-normal (LN3), the generalized Pareto Type II (PG), the Rayleigh (RY) and the log-logistic (LL3) distributions, using the higher-order linear moments method (LH-moments). The analysis represents the expansion of previous research whose results were presented in previous materials, and is part of hydrological research aimed at developing a standard for calculating maximum flows based on L-moments and LH-moments. The given methods for calculating the parameters of the examined distributions are used to calculate the maximum flows on Romania’s Prigor River. For both methods, the criterion for selecting the most suitable distribution is represented by the diagram of the L-skewness–L-kurtosis and LH-skewness–LH-kurtosis. The results for Prigor River show that the PG distribution is the best model for the L-moments method, the theoretical values of the statistical indicators being 0.399 and 0.221. The RY distribution is the best model for the LH-moments technique, with values of 0.398 and 0.192 for the two statistical indicators.

Applying Generalized Type-II Hybrid Censored Samples on Generalized and q-Generalized Extreme Value Distributions under Linear Normalization

The generalized extreme value (GEV) distributions have wide applications for describing a variety of random events, such as those that occur during specific survival, financial, or reliability investigations. Also, the q-analogues of GEV distributions, called (q-GEVs), are characterized by their ability to provide more flexibility for modeling, which is due to the influence of the q parameter. In this study, we estimated the parameters of generalized and q-generalized extreme value distributions under linear normalization, called GEVL and q-GEVL, respectively. These parameters were estimated using the maximum likelihood estimator method and are based on the generalized type-II hybrid censored sample (G-Type-II HCS). The confidence intervals for these parameters were evaluated. Also, Shannon entropy was estimated for GEVL and q-GEVL distributions. The accuracy of these parameters and the performance of estimators were demonstrated through a real-life example and a simulation study.

Regression in extremes using the four-parameter Kappa distribution

The four-parameter Kappa distribution (4KD) is known to be flexible and has been used for extreme value analysis, especially in hydrological sciences. This distribution has the great advantage of encompassing the two main distributions of extreme values used in the literature: the Generalized Pareto Distribution (GPD) and the Generalized Extreme Value (GEV) distribution. However, the analyses made in previous works for 4KD in the context of extreme values are based only on models with static parameters, not allowing the capture of covariate effects such as seasonality and location variables in a specific dataset. This study proposes that the inference about the 4KD can be made under the Bayesian paradigm by inserting a regression structure on the parameters to assess possible effects of covariates under the model. This proposal allows us to interpret the parameters and predict extreme events when there are covariates. The estimation of the parameters is performed using Markov Chain Monte Carlo (MCMC) procedures. The model was applied with both approaches in extremes: maximum and exceedance data. In this analysis, the proposed model was compared with models that use a regression structure in the usual extreme values distribution (GEV and GPD), and it presented better results in fit measures.

Flexible loss functions for binary classification in gradient-boosted decision trees: An application to credit scoring

This paper introduces new flexible loss functions for binary classification in Gradient-Boosted Decision Trees (GBDT) that combine Dice-based and cross-entropy-based losses and offer link functions from either a generalized extreme value (GEV) or exponentiated exponential logistic (EEL) distribution. Testing 27 different GBDT models using XGBoost on a Freddie Mac mortgage loan database showed that the choice of the loss function is useful. Specifically, when the class imbalance ratio (IR) is less than 99, using a skewed GEV distribution-based link function in XGBoost enhances discriminatory power and classification accuracy while retaining a simple model structure, which is particularly important in credit scoring applications. In cases where class imbalances are severe, typically between IRs of 99 and 200, we found that an advanced loss function, which is composed of a symmetric hybrid loss function and a link derived from a positively skewed EEL distribution, outperforms other XGBoost variants. Based on our findings, the accuracy improvements of these proposed extensions result in lower misclassification costs, which are especially evident when IR is below 99, which results in higher profitability for the business. Furthermore, the study highlights the transparency associated with GBDT, which is also an integral component of financial applications. Researchers and practitioners can use these insights to create more accurate and discriminative machine learning models, with possible extensions to other GBDT implementations and machine learning techniques that take into account loss functions. The source code for the proposed approach is publicly available at https://github.com/jm-ml/flexible-losses-for-binary-classification-with-GBDT.

Comparison of different statistical methods for prediction of lifetime of electrical connectors with short term tests

Lifetime is an important feature defining the reliability of electrical connectors. In general practice, the lifetime tests required for reliability estimation are time and labor intensive. In our previous work, a data driven method using a statistical process, with an application of probability distributions such as standard normal distribution and generalized extreme value (GEV) distribution with negative skewness to predict degradation paths, was introduced for estimation of the lifetime and FIT rate with the help of electrical contact resistance data collected from short term tests. The proposed method proved its significance by showing the possibility of drastic reduction in the lifetime test duration required for reliability determination. In this work, a non-parametric distribution free method using percentiles of actual measured contact resistances is used for determining the lifetime as against the percentiles of probability distribution used in previous work, thereby simplifying the process further and leading to an even more precise estimation. The lifetimes calculated from parametric and non-parametric methods are compared to highlight the significance of distribution free method in reliability estimation.

Prediction of Long-Term Offshore Structural Responses Based on Nonlinear Wave Modeling

Wind-generated random wave loads are the dominant loads to consider for maintaining the reliability of fixed offshore structures. Based on probabilistic techniques, the inherent randomness of the wave loading can be used to predict extreme offshore structural response, which is Gaussian in nature. However, researchers have found that the hydrodynamic component and structural dynamics substantially impact the frequency spectrum, leading to a non-Gaussian stochastic offshore structural response. A finite-memory non-linear system (FMNSNL) has been proven to be an efficient approach to evaluate the non-Gaussian stochastic offshore structural response compared to the conventional method, Monte Carlo time simulation. However, the analysis has been conducted based on short-term distribution only. The most satisfactory analysis is based on long-term distribution. Hence, further investigation in this paper will evaluate the long-term probability distribution of extreme offshore structural responses. As a result, a 100-year extreme offshore structural response prediction achieves 80% to 96% accuracy compared to the Monte Carlo time simulation. The probability distribution has been evaluated using the Gumbel distribution function throughout this investigation. Still, there is a little deviation at the tail end of the distribution between the simulated response values and the fitted line. A different distribution function, such as the Generalised Extreme Value (GEV) distribution, is advised for future work.

Extreme Rainfall Modeling through the Lens of Extreme Value Theory: A Case Study of Katsina City, Nigeria

Climate change has conveyed about strange new weather patterns, among others is changes in rainfall extremes. To make adequate inferences about extreme rainfall, it's important to invest in meteorological research. This can include the use of climate models to predict extreme rainfall events with greater accuracy. Additionally, information sharing can help ensure that countries are well-prepared for extreme weather events and can collaborate to address the global challenges posed by climate change. Monthly rainfall record of Katsina city was collected from the Nigerian Meteorological Agency (NiMet), Nigeria. In pursuit of this objective, the study employed Extreme Value Theory to model and forecast extreme rainfall of Katsina city, utilizing rainfall data spanning from 1989 to 2019. The research employed the Maximum Likelihood Estimation method to derive the model parameters. For the Generalized Extreme Value Distribution (GEVD), the block maxima approach was applied, whereas the Generalized Pareto Distribution (GPD) was fitted using the Peak Over Threshold method. The analysis revealed that the optimal model within the GEVD framework was the Frechet distribution, whereas the ordinary Pareto distribution emerged as the optimal model when considering values above the threshold. Additionally, the study included predictions for return periods of 2, 20, and 100 years based on the return level estimates, accompanied by the presentation of their respective confidence intervals. The analysis demonstrated that as the return periods lengthened, there was a proportional increase in the return levels. The study's model diagnostics, involving probability, density, quantile, and return level plots, collectively indicated that the provided models were well-suited for the dataset.

Extreme value modeling with errors-in-variables in detection and attribution of changes in climate extremes

The generalized extreme value (GEV) regression provides a framework for modeling extreme events across various fields by incorporating covariates into the location parameter of GEV distributions. When the covariates are subject to errors-in-variables (EIV) or measurement error, ignoring the EIVs leads to biased estimation and degraded inferences. This problem arises in detection and attribution analyses of changes in climate extremes because the covariates are estimated with uncertainty. It has not been studied even for the case of independent EIVs, let alone the case of dependent EIVs, due to the complex structure of GEV. Here we propose a general Monte Carlo corrected score method and extend it to address temporally correlated EIVs in GEV modeling with application to the detection and attribution analyses for climate extremes. Through extensive simulation studies, the proposed method provides an unbiased estimator and valid inference. In the application to the detection and attribution analyses of temperature extremes in central regions of China, with the proposed method, the combined anthropogenic and natural signal is detected in the change in the annual minimum of daily maximum and the annual minimum of daily minimum.