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The generalized extreme value (GEV) distribution is a popular model for analyzing and forecasting extreme weather data. To increase prediction accuracy, spatial information is often pooled via a latent Gaussian process (GP) on the GEV parameters. Inference for GEV‐GP models is typically carried out using Markov Chain Monte Carlo (MCMC) methods, or using approximate inference methods such as the integrated nested Laplace approximation (INLA). However, MCMC becomes prohibitively slow as the number of spatial locations increases, whereas INLA is applicable in practice only to a limited subset of GEV‐GP models. In this article, we revisit the original Laplace approximation for fitting spatial GEV models. In combination with a popular sparsity‐inducing spatial covariance approximation technique, we show through simulations that our approach accurately estimates the Bayesian predictive distribution of extreme weather events, is scalable to several thousand spatial locations, and is several orders of magnitude faster than MCMC. A case study in forecasting extreme snowfall across Canada is presented. [ABSTRACT FROM AUTHOR]

Structural graph clustering is a data analysis technique that groups nodes within a graph based on their connectivity and structural similarity. The Structural graph clustering SCAN algorithm, a density-based clustering method, effectively identifies core points and their neighbors within areas of high density to form well-defined clusters. However, the clustering quality of SCAN heavily depends on the input parameters, ϵ and μ , making the clustering results highly sensitive to parameter selection. Different parameter settings can lead to significant differences in clustering results, potentially compromising the accuracy of the clusters. To address this issue, a novel structural graph clustering algorithm based on the adaptive selection of density peaks is proposed in this paper. Unlike traditional methods, our algorithm does not rely on external parameters and eliminates the need for manual selection of density peaks or cluster centers by users. Density peaks are adaptively identified using the generalized extreme value distribution, with consideration of the structural similarities and interdependencies among nodes, and clusters are expanded by incorporating neighboring nodes, enhancing the robustness of the clustering process. Additionally, a distance-based structural similarity method is proposed to re-cluster noise nodes to the correct clusters. Extensive experiments on real and synthetic graph datasets validate the effectiveness of our algorithm. The experiment results show that the ADPSCAN has a superior performance compared with several state-of-the-art (SOTA) graph clustering methods. [ABSTRACT FROM AUTHOR]

This study introduced the application of concepts and methods from extreme value theory (EVT) to estimate the probability that daily minimum temperatures exceed springtime critical temperature thresholds for Pinot noir buds and young shoots as a function of springtime phenology. The springtime frost risk estimates were computed spatially for Pinot noir throughout the Willamette Valley (WV) American Viticultural Area (AVA) using a gridded dataset of historical daily minimum surface air temperature data. EVT-based springtime frost risk maps can inform vineyard-management operations by identifying those locations throughout a wine region with a low risk for any cold injury where remedial action is likely not necessary when there is a forecasted frost event. Frost risk estimates were computed for 1991–2021 and 1991–2022 to examine a potentially changed risk profile for springtime frost events throughout the WV AVA due to the April 2022 advective frost event. The April 2022 advective frost event influenced the risk profile throughout the AVA such that an event of its magnitude is now modelled to occur more frequently. The EVT-based risk analysis can be readily updated each year as new data become available. While spatially varying budbreak calculations facilitated computation of the spring frost risk estimates, the EVT approach profiled in this study does not necessarily depend on potentially uncertain predetermined budbreak date estimates. Gridded maps of extreme daily minimum temperature exceedances, reclassified relative to the springtime phenology critical temperature thresholds for Pinot noir, were readily combined with a ripening potential map to identify optimal areas for vineyard site selection throughout the WV AVA. When simultaneously evaluating Pinot noir ripening potential with springtime frost risk using historical data, the limiting factor for vineyard site selection throughout the WV AVA was frost risk, not ripening potential. The study approach is also applicable for other winegrape-growing regions, assessments of winter freeze risk and summertime heatwaves, and with non-gridded observed temperature datasets. [ABSTRACT FROM AUTHOR]

Climate variability, particularly, that of temperature and precipitation, has received a great deal of attention worldwide. In the present work, we have carried out a thorough statistical modelling of precipitation and temperature extremes by taking century-long (1901–2002) datasets into consideration for Himachal Pradesh, India. Globally, the patterns of extreme weather events have changed from longer and hotter heat waves to heavier rains. A fragile ecosphere, climatic change, and the unique geology of Himachal Pradesh have all led to a sharp increase in natural disasters in the hill state over time. The climate of the state varies by altitude. Since precipitation and temperature are the main driving forces behind climate change, quantifying these two variables over a range of return periods is crucial in policymaking for minimizing the potential harm brought on by variations in these atmospheric elements. The statistical modelling of the meteorological data and probabilistic forecasting were done using extreme value theory (EVT), an advanced statistical modelling approach that is widely acknowledged. The generalized extreme value (GEV) analysis approach of EVT is utilized for the probabilistic forecasting of the extremities. The extreme values and their probable occurrence are estimated once every 50, 80, 100, 120, 200, 250, 300, and 500 years, respectively. By estimating the probabilities of extreme events, we can better understand the potential risks and impacts of climate change and develop strategies to manage and mitigate these risks. [ABSTRACT FROM AUTHOR]

Landslides are one natural disaster in the mountains, causing damage to properties, destruction of infrastructure and loss of life. While landslide deformation and displacement are commonly observed through experimental investigation of the prototype models, this time-consuming approach might involve human errors and inaccurate constitutive models. This study aims to propose a numerical approach based on machine learning for substituting experimental investigation. In pursuit of this objective, the probability-weighted moments (PWMs) for generalised extreme value distribution (GEVD) were implemented to predict the deposit landslide deformation under uniformly increasing rainfall. The deposit landslide of the Dahua was selected as the case study. The accuracy and reliability of the proposed PWM are validated through the maximum likelihood method and the Jenkinson method. The PWM with GEVD is used to derive the progressive failure of the deposit landslide stability under the return period, the pore water pressure variation and the return period's effect. The results show that the proposed solution is suitable for predicting the responses of landslides. Moreover, the results demonstrate the importance of soil density; 30% of the deposited soil was moved when the soil density was 2 g/cm3 besides, and more than 90% were moved at the top of the slope for the soil density equal to 3 g/cm3. [ABSTRACT FROM AUTHOR]

The study investigates the application of Extreme Value Theory in modelling stock prices, aiming to capture the tail behaviour and extreme movements that conventional distributions often fail to represent accurately. The use of Extreme Value Theory has gained considerable attention in the field of finance due to its ability to model rare events, such as financial crises or market crashes. By incorporating Extreme Value Theory, researchers aim to improve risk management, portfolio optimization, and pricing of financial derivatives. In this study, the Log-normal, Weibull, Gamma, and Normal distributions were used to model the stock price closing data, with a specific focus on extreme value distributions. Both graphical explorations and goodness-of-fit criteria were considered together to evaluate the suitability of these distributions. When assessing the data, it was observed that the Weibull distribution provided the best fit for the given stock price closing data. [ABSTRACT FROM AUTHOR]

The heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm CO2$$ {\mathrm{CO}}_2 $$ (pre‐industrial), 700 ppm CO2$$ {\mathrm{CO}}_2 $$ (future conditions), and 1400 ppm CO2$$ {\mathrm{CO}}_2 $$, and compare the results with those obtained using the maximum likelihood approach. [ABSTRACT FROM AUTHOR]

The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the r largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK. [ABSTRACT FROM AUTHOR]

The Akosombo Dam is the largest dam in Ghana and is linked to the world's largest man-made lake by surface area. The top of flood control pool of the dam has been breached a number of times, so it is of interest to know the corresponding probability. The paper fits the generalized extreme value distribution to the extreme water levels – with all three of its parameters (including the shape parameter) accounting for various linear trends, seasonality and cyclic trends with respect to time, the first time such a model has been fitted. The fitted model contains in total 50 parameters. It provided an adequate fit, as evaluated by probability plots, quantile plots, and the Kolmogorov-Smirnov test. It is used to provide return level estimates as well as probabilities of the top of flood control pool of the dam being breached.

Accurate parameter estimation of extreme wind speed distribution is of great importance for the safe utilization and assessment of wind resources. This paper emphatically establishes a novel grey generalized extreme value method for parameter estimation of annual wind speed extremum distribution (AWSED). Considering the uncertainty and frequency characteristics of the parent wind speed, the generalized extreme value distribution (GEVD) is selected as the probability distribution, and the Weibull distribution is utilized as the first-order accumulation generating operator. Then, the GEVD differential equation is derived, and it is transformed into the grey GEVD model using the differential information principle. The least squares method is used to estimate the grey GEVD model parameters, and then a novel estimation method is proposed through grey parameters. A hybrid particle swarm optimization algorithm is used to optimize distribution parameters. The novel method is stable under different sample sizes according to Monte Carlo comparison simulation results, and the suitability for the novel method is confirmed by instance analysis in Wujiaba, Yunnan Province. The new method performs with high accuracy in various indicators, the hypothesis test results are above 95%, and the statistical errors such as MAPE and Wasserstein distance yield the lowest, which are 3.33% and 0.2556, respectively.

Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type $ P(X < Y) $ when both $ X $ and $ Y $ follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value $ \mathbb{H} $-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure $ P(X < Y) $ in selecting financial assets with returns characterized by the distributions $ X $ and $ Y $. Therefore, rather than the conventional approach of comparing the expected values of $ X $ and $ Y $ based on modern portfolio theory, we delve into the metric $ P(X < Y) $ as an alternative parameter for assessing better returns.

Accurate parameter estimation of extreme wind speed distribution is of great importance for the safe utilization and assessment of wind resources. This paper emphatically establishes a novel grey generalized extreme value method for parameter estimation of annual wind speed extremum distribution (AWSED). Considering the uncertainty and frequency characteristics of the parent wind speed, the generalized extreme value distribution (GEVD) is selected as the probability distribution, and the Weibull distribution is utilized as the first-order accumulation generating operator. Then, the GEVD differential equation is derived, and it is transformed into the grey GEVD model using the differential information principle. The least squares method is used to estimate the grey GEVD model parameters, and then a novel estimation method is proposed through grey parameters. A hybrid particle swarm optimization algorithm is used to optimize distribution parameters. The novel method is stable under different sample sizes according to Monte Carlo comparison simulation results, and the suitability for the novel method is confirmed by instance analysis in Wujiaba, Yunnan Province. The new method performs with high accuracy in various indicators, the hypothesis test results are above 95%, and the statistical errors such as MAPE and Wasserstein distance yield the lowest, which are 3.33% and 0.2556, respectively. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Beijing University of Technology is the property of Journal of Beijing University of Technology, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type P(X < Y) when both X and Y follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value H-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure P(X < Y) in selecting financial assets with returns characterized by the distributions X and Y. Therefore, rather than the conventional approach of comparing the expected values of X and Y based on modern portfolio theory, we delve into the metric P(X < Y) as an alternative parameter for assessing better returns. [ABSTRACT FROM AUTHOR]

A detailed study has been carried out to reveal signal statistics' impact on analysis sensitivity in laser-induced breakdown spectroscopy (LIBS) measurements. For several signals measured simultaneously, it was demonstrated that space-, spectra- and time-integrated plasma emission followed a normal distribution while the spectra- and time-resolved LIBS signal (atomic line intensity, plasma background emissions) distribution functions were biased compared to a Gaussian distribution function. For the first time in LIBS, the impact of a non-Gaussian distribution function on the limit of detection (LOD)'s determination has been studied in detail for single-shot spectra as well as for averaged spectra. Here, we demonstrated that the non-symmetrical distribution of the LIBS signals influenced the estimated LODs, so knowledge of a LIBS signal's distribution function provides more reliable results, and the analysis sensitivity can be wrongly estimated if Gaussian distribution is presumed. [ABSTRACT FROM AUTHOR]

Abstract A statistical analysis of maximum temperature from twelve weather stations in parts of Guinea is provided. Using maximum likelihood estimation, maximum temperature data was fitted by the Generalized Extreme Value distribution. Data from all of the twelve stations were adequately fit by the Generalized Extreme Value distribution. Return level estimates are provided. Significant trends in maximum temperature were found for four of the stations. The four stations exhibited significant positive trends at the 5% significance level.

Structural graph clustering is a data analysis technique that groups nodes within a graph based on their connectivity and structural similarity. The Structural graph clustering SCAN algorithm, a density-based clustering method, effectively identifies core points and their neighbors within areas of high density to form well-defined clusters. However, the clustering quality of SCAN heavily depends on the input parameters, ϵ and μ, making the clustering results highly sensitive to parameter selection. Different parameter settings can lead to significant differences in clustering results, potentially compromising the accuracy of the clusters. To address this issue, a novel structural graph clustering algorithm based on the adaptive selection of density peaks is proposed in this paper. Unlike traditional methods, our algorithm does not rely on external parameters and eliminates the need for manual selection of density peaks or cluster centers by users. Density peaks are adaptively identified using the generalized extreme value distribution, with consideration of the structural similarities and interdependencies among nodes, and clusters are expanded by incorporating neighboring nodes, enhancing the robustness of the clustering process. Additionally, a distance-based structural similarity method is proposed to re-cluster noise nodes to the correct clusters. Extensive experiments on real and synthetic graph datasets validate the effectiveness of our algorithm. The experiment results show that the ADPSCAN has a superior performance compared with several state-of-the-art (SOTA) graph clustering methods.

This study introduced the application of concepts and methods from extreme value theory (EVT) to estimate the probability that daily minimum temperatures exceed springtime critical temperature thresholds for Pinot noir buds and young shoots as a function of springtime phenology. The springtime frost risk estimates were computed spatially for Pinot noir throughout the Willamette Valley (WV) American Viticultural Area (AVA) using a gridded dataset of historical daily minimum surface air temperature data. EVT-based springtime frost risk maps can inform vineyard-management operations by identifying those locations throughout a wine region with a low risk for any cold injury where remedial action is likely not necessary when there is a forecasted frost event. Frost risk estimates were computed for 1991–2021 and 1991–2022 to examine a potentially changed risk profile for springtime frost events throughout the WV AVA due to the April 2022 advective frost event. The April 2022 advective frost event influenced the risk profile throughout the AVA such that an event of its magnitude is now modelled to occur more frequently. The EVT-based risk analysis can be readily updated each year as new data become available. While spatially varying budbreak calculations facilitated computation of the spring frost risk estimates, the EVT approach profiled in this study does not necessarily depend on potentially uncertain predetermined budbreak date estimates. Gridded maps of extreme daily minimum temperature exceedances, reclassified relative to the springtime phenology critical temperature thresholds for Pinot noir, were readily combined with a ripening potential map to identify optimal areas for vineyard site selection throughout the WV AVA. When simultaneously evaluating Pinot noir ripening potential with springtime frost risk using historical data, the limiting factor for vineyard site selection throughout the WV AVA was frost risk, not ripening potential. The study approach is also applicable for other winegrape-growing regions, assessments of winter freeze risk and summertime heatwaves, and with non-gridded observed temperature datasets.

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. [ABSTRACT FROM AUTHOR]

Extreme precipitation shows non-stationarity, meaning that its distribution can change with time or other large-scale variables. For a classical frequency-intensity analysis this effect is often neglected. Here, we propose a model including the influence of North Atlantic Oscillation, time, surface temperature and a blocking index. The model features flexibility to use annual maxima as well as seasonal maxima to be fitted in a generalized extreme value setting. To further increase the efficiency of data usage, maxima from different accumulation durations are aggregated so that information for extremes on different time scales can be provided. Our model is trained to individual station data with temporal resolutions ranging from one minute to one day across Germany. Models are chosen with a stepwise BIC model selection and verified with a cross-validated quantile skill index. The verification shows that the new model performs better than a reference model without large-scale information. Also, the new model enables insights into the effect of large-scale variables on extreme precipitation. Results suggest that the probability of extreme precipitation increases with time since 1950 in all seasons. High probabilities of extremes are positively correlated with blocking situations in summer and with temperature in winter. However, they are negatively correlated with blocking situations in winter and temperature in summer. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Southeast University / Dongnan Daxue Xuebao is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness. [ABSTRACT FROM AUTHOR]

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is shown to be minimal in all cases, so that the variability expressed by the standard error becomes the principal reliability metric. Peak-over-threshold (POT) methods are shown to always be more reliable than epoch methods due to the additional sub-epoch data. The generalized asymptotic methods are shown to always be less reliable than the sub-asymptotic methods by a factor that increases with MRI. This study reinforces the previously published theory-based arguments that GEV and GPD are unsuitable models for extreme wind speeds by showing that they also provide the least reliable predictions in practice. A new two-step Weibull-XIMIS hybrid method is shown to have superior reliability.

Progressive first-failure censoring has been widely-used in practice when the experimenter desires to remove some groups of test units before the first-failure is observed in all groups. Practically, some test groups may haphazardly quit the experiment at each progressive stage, which cannot be determined in advance. As a result, in this article, we propose a progressively first-failure censored sampling with random removals, which allows the removal of the surviving group(s) during the execution of the life test with uncertain probability, called the beta-binomial probability law. Generalized extreme value lifetime model has been widely-used to analyze a variety of extreme value data, including flood flows, wind speeds, radioactive emissions, and others. So, when the sample observations are gathered using the suggested censoring plan, the Bayes and maximum likelihood approaches are used to estimate the generalized extreme value distribution parameters. Furthermore, Bayes estimates are produced under balanced symmetric and asymmetric loss functions. A hybrid Gibbs within the Metropolis-Hastings method is suggested to gather samples from the joint posterior distribution. The highest posterior density intervals are also provided. To further understand how the suggested inferential approaches actually work in the long run, extensive Monte Carlo simulation experiments are carried out. Two applications of real-world datasets from clinical trials are examined to show the applicability and feasibility of the suggested methodology. The numerical results showed that the proposed sampling mechanism is more flexible to operate a classical (or Bayesian) inferential approach to estimate any lifetime parameter.

In the conditions of rising air temperature and changing precipitation regimes in Central Europe and Slovakia over the last two decades, it is necessary to analyse drought, develop high-quality tools for drought detection, and understand its reactions to the emerging drought situation. One of the frequently used meteorological drought indices is the Standardized Precipitation and Evapotranspiration Index (SPEI). Several parameters can be modified in different steps of the calculation process of SPEI. In the article, we analyse the influence of selected adjustable parameters on the index results. Our research has shown that the choice of a statistical distribution (Log-logistic, Pearson III, or Generalized Extreme Value) for fitting water balance can affect the feasibility of calculating distribution parameters (and thus the index) from the provided input data, as well as lead to either underestimation or overestimation of the index. The normality test of SPEI can be used as a tool for the detection and elimination of highly skewed indices and cases when the indices were not well determined by the distribution function. This study demonstrated improved results when using the GEV distribution, despite the common use of the Log-logistic distribution. With the Pearson III distribution, unusually high or low SPEI values (|SPEI| > 6) were detected. [ABSTRACT FROM AUTHOR]

Progressive first-failure censoring has been widely-used in practice when the experimenter desires to remove some groups of test units before the first-failure is observed in all groups. Practically, some test groups may haphazardly quit the experiment at each progressive stage, which cannot be determined in advance. As a result, in this article, we propose a progressively first-failure censored sampling with random removals, which allows the removal of the surviving group(s) during the execution of the life test with uncertain probability, called the beta-binomial probability law. Generalized extreme value lifetime model has been widely-used to analyze a variety of extreme value data, including flood flows, wind speeds, radioactive emissions, and others. So, when the sample observations are gathered using the suggested censoring plan, the Bayes and maximum likelihood approaches are used to estimate the generalized extreme value distribution parameters. Furthermore, Bayes estimates are produced under balanced symmetric and asymmetric loss functions. A hybrid Gibbs within the Metropolis-Hastings method is suggested to gather samples from the joint posterior distribution. The highest posterior density intervals are also provided. To further understand how the suggested inferential approaches actually work in the long run, extensive Monte Carlo simulation experiments are carried out. Two applications of real-world datasets from clinical trials are examined to show the applicability and feasibility of the suggested methodology. The numerical results showed that the proposed sampling mechanism is more flexible to operate a classical (or Bayesian) inferential approach to estimate any lifetime parameter. [ABSTRACT FROM AUTHOR]

The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is shown to be minimal in all cases, so that the variability expressed by the standard error becomes the principal reliability metric. Peak-over-threshold (POT) methods are shown to always be more reliable than epoch methods due to the additional sub-epoch data. The generalized asymptotic methods are shown to always be less reliable than the sub-asymptotic methods by a factor that increases with MRI. This study reinforces the previously published theory-based arguments that GEV and GPD are unsuitable models for extreme wind speeds by showing that they also provide the least reliable predictions in practice. A new two-step Weibull-XIMIS hybrid method is shown to have superior reliability. [ABSTRACT FROM AUTHOR]

The modified Anderson-Darling test statistics have been suggested in testing the highly skewed distributions to detect more possible departures in the right (or left) tail. In this paper, we propose the corresponding modified likelihood ratio test statistics, and compare their performances for the Gumbel distribution with the modified Anderson-Darling test statistics. We also provide the approximate critical values for the generalized extreme value distribution and generalized Pareto distribution where the unknown shape parameter is present. [ABSTRACT FROM AUTHOR]

Due to the temperature rises global warming has become very popular. Increasing of global temperature will disturb the agronomic sector, intensification some of the contagious diseases that may lead to high mortality rates in humans, high demand for electricity, water and food which ultimately affecting the economy of Pakistan. The current research aims to study the best fitted probability distribution that describes the monthly mean temperature (MMT) of four sites in Pakistan are Islamabad, Lahore, Muzaffarabad and Karachi based on secondary data sets which was collected from Pakistan Meteorological department Lahore for the period 1991 to 2020. The Frechet, Weibull and Log-Logistic distributions are applied and the parameters of these distributions are estimated by maximum likelihood and Bayesian estimation methods. Additionally, Log-normal and Generalized Extreme value distribution are considered using the maximum likelihood estimation method to estimate the parameters. Moreover, the graphs of probability density functions also constructed for comparison purposes. The goodness of fit test and model selection criteria such as Kolmogorov-Smirnov test, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are used to measure the accuracy of the predicted data using theoretical probability distributions. The results show that four sites favor the candidate distributions based on the Pvalues of Kolmogorov-Smirnov test at 5 percent level of significance. However, Log-Logistic distribution is the best fitted as compare to other candidate probability distributions based on AIC and BIC values. Furthermore, quantiles are also calculated using maximum likelihood and Bayesian estimation methods and concluded that quantile estimates are closed to the observed MMT series on the basis of Log-Logistic distribution. [ABSTRACT FROM AUTHOR]

The heat-related health impacts of extremely high temperatures have become increasingly severe worldwide. Quantitative information on these impacts is necessary to plan and implement adaptation measures. The present study aimed to predict the number of heatstroke ambulance calls (HAC) and ambulance occupancy rate of patients with heatstroke (AORPH) under extremely high temperatures in Tokyo, Japan. Extremely high temperatures were defined as the annual highest value of daily maximum temperature that occurs once every 30 y (30 y temp) or 50 y (50 y temp). Combinations of three greenhouse gas (GHG) emission scenarios and five climate models were adopted to predict the impacts during the base years (1985–2014), mid-21st century (2021–2050), and late 21st century (2071–2100). Furthermore, two types of populations were adopted: fixed and changing. In the case of 50 y temp, the HAC during the peak hour in the base years ranged from 52 to 130 persons across the climate models. In the case of a fixed population, in the late 21st century it ranged from 123 to 2618 persons across the climate models and GHG scenarios. In the case of a changing population, the corresponding values in late 21st century ranged from 128 to 3078 persons. The AORPH during the peak hour ranged from 32% to 80% during the base years for 50 y temp, assuming that all ambulances were dispatched for heatstroke only. In the late 21st century, it ranged from 75% to 1605% in the fixed population case. With population change, the corresponding values in late 21st century ranged from 83% to 1781%. In many scenarios, not all patients with heatstroke could be transported (AORPH > 100%) even if all ambulances have been dispatched. Therefore, adaptation measures that mitigate such an ambulance transport system collapse must be planned and implemented.

Pest outbreaks, harmful algal blooms and population collapses are extreme events with critical consequences for ecosystems. Therefore, understanding the ecological mechanisms underlying these extreme events is crucial. We evaluated theoretical predictions on the size scaling and variance of extreme population abundance by combining (i) the generalized extreme value (GEV) theory and (ii) the resource‐limited metabolic restriction hypothesis for population abundance. Using the phytoplankton data from the L4 station in the English Channel, we showed a negative size scaling of the expected value of maximal density, whose confidence interval included the predicted metabolic scaling (α = −1) supporting theoretical predictions. The role of resources and temperature in the distribution of the size–abundance pattern and residuals was well characterized by the GEV distribution. This comprehensive modelling framework will allow to elucidate community structure and fluctuations and provide unbiased return times estimates, thereby improving the prediction accuracy of the timing of the population outbreaks. [ABSTRACT FROM AUTHOR]

In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has wide applicability in several areas, including hydrology, engineering, science, ecology, and finance. However, the GEV distribution is not suitable for modeling extreme bimodal data. In this paper, we propose an extension of the GEV distribution that incorporates an additional parameter. The additional parameter introduces bimodality and aries tail weight, i.e., this proposed extension is more flexible than the GEV distribution. Inference for the proposed distribution was performed under the likelihood paradigm. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, the proposed distribution is applied to environmental data sets, illustrating their capabilities in challenging cases in extreme value theory. [ABSTRACT FROM AUTHOR]

The potential weight of accumulated snow on the roof of a structure has long been an important consideration in structure design. However, the historical approach of modeling the weight of snow on structures is incompatible for structures with surfaces and geometry where snow is expected to slide off of the structure, such as standalone solar panels. This paper proposes a "storm-level" adaptation of previous structure-related snow studies that is designed to estimate short-term, rather than season-long, accumulations of the snow water equivalent or snow load. One key development associated with this paper includes a climate-driven random forests model to impute missing snow water equivalent values at stations that measure only snow depth in order to produce continuous snow load records. Additionally, the paper compares six different approaches of extreme value estimation on short-term snow accumulations. The results of this study indicate that, when considering the 50-year mean recurrence interval (MRI) for shortterm snow accumulations across different weather station types, the traditional block maxima approach, the mean-adjusted quantile method with a gamma distribution approach, and the peak over threshold Bayesian approach tend to most often provide MRI estimates near the median of all six approaches considered in this study. Further, this paper also shows, via bootstrap simulation, that the peak over threshold extreme value estimation using automatic threshold selection approaches tend to have higher variance compared to the other approaches considered. The results suggest that there is no one-size-fits-all option for extreme value estimation of shortterm snow accumulations, but highlights the potential value from integrating multiple extreme value estimation approaches. [ABSTRACT FROM AUTHOR]

Modeling of extreme events is important in many scientific fields, including environmental and civil engineering, and impacts and risk assessments. Among available methods, statistical models that allow estimating extremes' frequency and intensity are regularly used in procedures to anticipate potential changes in extreme events. Extreme value theory provides a theoretical basis for statistical estimation of extreme events using frequency analysis. The challenge in modeling is knowing when to use the block maxima method or the peaks-over-threshold (POT) method. Each has its drawbacks. POT describes the main characteristics of the observed extreme series; the threshold selection is always challenging and might affect the accuracy of the simulated results and the credibility of changes in extreme values. To encompass this challenge, mixture models offer more flexibility to represent samples with nonhomogeneous data. This study presents the gamma generalized Pareto (GGP) mixture model for estimating risk occurrence of hydroclimatic extremes. The model was developed in its general form, whereas the observed hydrometeorological extreme events depend on multidimensional covariates. A maximum likelihood algorithm is proposed to estimate the parameters with a constraint on the shape parameter of the generalized Pareto (GP) distribution. A Monte Carlo (MC) simulation compared the proposed model with the classical POT approach, with a fixed threshold, and the annual maximum series of streamflow. The approach was applied using a daily hydrological data set from an observed station located in the Saint John River at Fort Kent (01AD002), New Brunswick, Canada. The results show a flexibility to model extremes for dependent or nonstationary time series and adequately describes the central part of the observed frequencies, as well as the tails. [ABSTRACT FROM AUTHOR]

The risk-return relationship is of fundamental significance in the field of economics and finance. It is used to structure investment strategies, allocate resources, as well as assist in the construction of policy and regulatory frameworks. The accurate forecast of the risk-return relationship ensures sound financial decisions, whereas an inaccurate one can underestimate risk and thus lead to losses. The GARCH-M approach is one of the foremost models used in South African literature to investigate the risk-return relationship. This study made a novel and significant contribution, on a local and international level, as it was the first study to investigate GARCH-M type models with different innovation distributions. This study analyzed the JSE ALSI returns of the South African market for the sample period from 05 October 2004 to 05 October 2021. Results revealed that the EGARCH (1, 1)-M with the Skewed Student-t distribution (Skew-t) is optimal relative to the standard GARCH, APARCH and GJR. However, the EGARCH-M Skew-t failed to capture the financial data's asymmetric, volatile and random nature. To improve forecast accuracy, this study applied different nonnormal innovation distributions: the Pearson Type Ⅳ distribution (PIVD), Generalized Extreme Value distribution (GEVD), Generalized Pareto distribution (GPD) and Stable. Model diagnostics revealed that the nonnormal innovation distributions adequately captured asymmetry. The Value at Risk and backtesting procedure found that the PIVD, followed by Stable, outperformed the Extreme Value Theory distributions (GEVD and GPD). Thus, investors, risk managers and policymakers would opt to use the EGARCH-M in combination with the PIVD when modelling the risk-return relationship. The main contribution of this study was to confirm that applying GARCH type models with the conventional and normal type distributions, to a volatile emerging market, is considered ineffective. Therefore, this study recommended the exploration of other innovation distributions, that were not included in the scope of this study, for future research purposes.

The maximum electromagnetic field formed in the electrically large enclosures for a given input power has always been the focus of electromagnetic compatibility issues such as radiation sensitivity and shielding effectiveness. To model the maximums in a simple manner, the electrically large enclosure can be regarded as a reverberation chamber (RC), thus the generalized extreme value (GEV) theory based framework is used for both undermoded and overmoded frequencies. Since the mechanical stirrer is not easy to be installed like that for RC, frequency stirring and mechanical stirring related configurations are discussed, and the corresponding results have confirmed the validity of frequency stirring with the estimate of the parameters in GEV distribution. As for the maximum field, a comparison has been made between GEV distribution and IEC 61000-4-21, and the corresponding results have also highlighted that the maximum field can be assessed by frequency stirring configuration, and by GEV distribution with a desired confidence.

This article introduces the R package evgam. The package provides functions for fitting extreme value distributions. These include the generalized extreme value and generalized Pareto distributions. The former can also be fitted through a point process representation. Package evgam supports quantile regression via the asymmetric Laplace distribution, which can be useful for estimating high thresholds, sometimes used to discriminate between extreme and non-extreme values. The main addition of package evgam is to let extreme value distribution parameters have generalized additive model forms, the smoothness of which can be objectively estimated using Laplace's method. Illustrative examples fitting various distributions with various specifications are given. These include daily precipitation accumulations for part of Colorado, US, used to illustrate spatial models, and daily maximum temperatures for Fort Collins, Colorado, US, used to illustrate temporal models.

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Globally, changes in hydroclimate extremes such as extreme precipitation events influence water resources, natural environments, and human health and safety. During recent decades, India has observed an enormous increase in rainfall extremes during the summer monsoon (June to September) seasons. However, future extreme rainfall events have significant uncertainty at the regional scale. Consequently, a comprehensive study is needed to evaluate the extreme rainfall events at a regional river basin level in order to understand the geomorphological characteristics and pattern of rainfall events. In the above purview, the current research focuses on changes in extreme rainfall events obtained through observed gridded datasets and future scenarios of climate models derived through the Coupled Model Intercomparison Project (CMIP). The results highlight a significant rise in the extremes of precipitation events during the first half of the 21st century. In addition, our study concludes that accumulated precipitation will increase by five days in the future, while the precipitation maxima will increase from 200 to 300 mm/day at the 2-year, 50-year, and 100-year return periods. Finally, it is found that during the middle of the 21st century the 23.37% number of events will increase over the TRB at the 90th percentile. [ABSTRACT FROM AUTHOR]

Historical changes and possible future projections of temperature extremes in China, in terms of return values of annual extreme temperatures, are examined based on daily maximum and minimum temperatures from station observations and multiple models of the fifth and sixth phases of the Coupled Model Intercomparison Project (CMIP). The observations suggest that increases in temperature extremes are largely attributable to the changing mean climate, while the varying natural variability also has an important impact, which depends on the index of the variability. The models simulate warm extremes reasonably well but underestimate the spatial heterogeneity and temporal trend of cold extremes in China. In comparison, Coupled Model Intercomparison Project Phase 6 (CMIP6) models have higher skill in simulating temperature extremes in China, showing smaller biases and intermodel variability. MRI‐ESM2‐0 and NorESM2‐LM from CMIP6 and GFDL‐ESM2M and NorESM1‐M from CMIP5 are selected as reference models based on the better performance in reproducing observed temperature extremes in China. In the future, projections from CMIP6 multimodel ensemble (MME, represented as the multimodel median) and reference models all show a continued uptick in temperature extremes, with statistically significant increases in warm extremes mainly in the north and increases in cold extremes prominent in most parts of China. Different individual models, which have similar historical simulations, yield divergent future trends of temperature extremes, which may be associated with different climate sensitivities of models. In addition, MME usage should be treated with caution since its smoothing on spatial heterogeneity and possible information from poor models. Plain Language Summary: Given the serious hazards of extreme temperature events, understanding changes in extreme temperatures and effectively predicting their future changes are critical to climate mitigation and adaptation. According to station observations and model data from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and 6 (CMIP6), we find besides the varying temperature mean, the varying temperature variance also has an important impact on changes in extreme temperatures, and CMIP6 models have overall better performance than CMIP5 models in reproducing changes in extreme temperatures in China. Our results also emphasize that good performances in historical simulation cannot guarantee better projections in the future and projections of extreme temperatures from the multimodel ensemble sacrifice the spatial heterogeneity relative to individual reference models. Key Points: The impact of the varying natural variability on changes in temperature extremes depends on the variability indexCMIP6 models perform better than CMIP5 in simulating temperature extremes changes in ChinaMultimodel ensemble projections of extreme temperatures sacrifice spatial heterogeneity [ABSTRACT FROM AUTHOR]

Ozone pollution in China has become increasingly severe in recent years. Considering the damage that extreme ozone pollution may cause and the fact that the occurrence of extreme ozone pollution among different locations may be related, this paper uses hourly ozone concentration data from national monitoring stations to investigate the co-movement of extreme ozone pollution in the Beijing-Tianjin-Hebei (BTH) Region. The extreme dependence analysis is adopted to assess such extreme co-movements between different cities. The co-occurrences of extreme ozone pollution at the same time or with certain time differences in the region are analyzed. City groups suffering simultaneous extreme pollution and those where the pollution occurs with certain time differences are identified under certain criteria. Furthermore, the order in which cities experience extreme ozone pollution is determined. With the publication of the New Three-year Action Plan for Winning the Blue Sky War, our results may be important for improving the joint early-warning and emergency response mechanism at city levels in the BTH Region. [ABSTRACT FROM AUTHOR]

A detailed study has been carried out to reveal signal statistics’ impact on analysis sensitivity in laser-induced breakdown spectroscopy (LIBS) measurements. For several signals measured simultaneously, it was demonstrated that space-, spectra- and time-integrated plasma emission followed a normal distribution while the spectra- and time-resolved LIBS signal (atomic line intensity, plasma background emissions) distribution functions were biased compared to a Gaussian distribution function. For the first time in LIBS, the impact of a non-Gaussian distribution function on the limit of detection (LOD)’s determination has been studied in detail for single-shot spectra as well as for averaged spectra. Here, we demonstrated that the non-symmetrical distribution of the LIBS signals influenced the estimated LODs, so knowledge of a LIBS signal’s distribution function provides more reliable results, and the analysis sensitivity can be wrongly estimated if Gaussian distribution is presumed.

This study applied the theory of statistical analysis, Extreme Value Theory (EVT), with dengue fever cases reported between 2010 and 2019 from the Department of Disease Control Bureau of Epidemiology, Ministry of Health, Nakhon Sawan region. From the results of this study, it showed that the highest monthly recurrence values of dengue fever for Nakhon Sawan province in every 5, 10, and 20 years were 43.1725, 54.6569, and 68.1125 per 100,000 populations, respectively. [ABSTRACT FROM AUTHOR]