Gumbel Distribution Research Articles

Precipitation Study in Flood Zones: San Mateo Atenco, State of Mexico, Mexico Case Study

This work is focused on analyzing the causes of flooding in the sub-basin belonging to the municipality of San Mateo Atenco: Almoloya-Otzolotepec, because the municipal territory is constantly threatened by hydrometeorological phenomena, such as hailstorms, frost and torrential rains. The maximum precipitation was analyzed in neighboring climatological stations and the precipitation at different return periods (2 to 1000) was determined through the Gumbel distribution, and its impact according to the Thiessen polygon method. With the information of the 24-hour intensities, the Intensity Duration Frequency (IDF) curves and the hietogram of the study area were plotted using the alternating block method. The above procedure was applied to the precipitation data from the 9 stations that affect the basin. The approach proposed in this work considers all the precipitation variables for the best approximation of the phenomena that may occur in the basin; it is an innovative model because it considers the weighted averages of precipitation for each area of influence and its surroundings; this information is useful for the implementation of flood protection projects, adequate design of drainage and sewage systems, and a rational use of the resource to guarantee better living conditions for the inhabitants. According to the results obtained, there is a slow hydrological response and the areas with the greatest runoff potential (8383<CN<100) are located towards the central part of the basin where there is a significant concentration of bare soil.

Enhancing probabilistic based real-coded crossover genetic algorithms with authentication of VIKOR multi-criteria optimization method

<p> To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.</p>

A Comparison and Evaluation of Two Commercially Available Metal Artifact Reduction Applications.

The angiography systems A (A) and B (B), both incorporated at our hospital, are equipped with metal artifact reduction (MAR) applications. In clinical practice, it is crucial to understand the characteristics of MAR in both systems given that endovascular treatments are occasionally administered with both. In this study, we compared the artifact reduction effects of MAR on equipment A and B and clarified the differences between the two systems. An artifact evaluation phantom was created using a cylindrical water phantom and an iodine contrast medium. The phantom was imaged, MAR processing was performed on the obtained images, and an isotropic quantitative evaluation of artifacts was performed by extreme value statistical analysis using the Gumbel distribution. The MAR reduction effects were approximately 45% and 40% for equipment A and B at concentrations of 8300 and 6000, respectively. The MAR reduction effect in both devices exhibited different trends depending on the concentration. In clinical procedures that make use of absorbents in medium concentrations of approximately 3000-5000, such as n-butyl-2-cyanoacrylate and Onyx, it is necessary to understand the MAR characteristics of both devices and consider the use of alternative devices as an option.

Rainfall Intensity-Duration-Frequency Relationships: A Robust Foundation for Urban Decision-Making and Flood Management: A Case Study

Ahmedabad, a city in India, experiences varying climatic patterns and is prone to extreme rainfall and relies on established intensity-duration-frequency (IDF) relationships for critical infrastructure planning and flood management. While the city has existing IDF relationships, these curves were established some time ago and still lack well-established IDF Curves. To fill this research gap this study is dedicated to the development of IDF curves for Ahmedabad City, utilizing 45 years of rainfall data (1978 to 2022) sourced from the Indian Meteorological Department (IMD) making our study a pioneering effort in this direction. Employing frequency analysis methodologies, the relationships between rainfall intensity, storm duration, and return periods were established. IDF curves were generated for durations of 5, 10, 15, 30 minutes, and 1, 2, 6, 12 and 24 hours for Ahmedabad City. Short-term rainfall intensities were derived from daily rainfall values using the IMD formula. The empirical approach, Gumbel distribution, and Log Pearson Type-III distribution were applied. The Gumbel method tends to produce slightly higher rainfall intensities for shorter return periods, while the LPT III method exhibits the opposite pattern for longer return periods, such as 25, 50, and 100 years. In general, both approaches yield closely matching results across most return periods. The IDF curves produced in this study offer a versatile set of rainfall scenarios for diverse applications, including the design and modification of hydraulic structures, stormwater management infrastructure, and flood mitigation systems in Ahmedabad City. The outcomes of this research contribute not only to filling a crucial research gap but also empower decision-makers and urban planners with updated and reliable data crucial for enhancing the city’s resilience against extreme rainfall events.

A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data

In this paper, we propose a new version of the Gumbel Distribution using a sine technique family. We discuss the key properties of this distribution, such as the probability density function, the cumulative distribution function, the survival function, the hazard function, the cumulative hazard, and the moments. Additionally, we present a method for estimating the distribution's parameters. We then analyze a dataset using the original and generalized distributions, comparing the results and using goodness-of-fit measures to determine which distribution best fits the data. Finally, we provide conclusions based on our findings, with many examples and valid comparisons applied on fuzzy data.

Predicting Vulnerable Road User Behavior With Transformer-Based Gumbel Distribution Networks

Predicting Vulnerable Road User Behavior With Transformer-Based Gumbel Distribution Networks

Parameters and Reliability Estimation of Left Truncated Gumbel Distribution under Progressive Type II Censored with Repairable Mechanical Equipment Data

Parameters and Reliability Estimation of Left Truncated Gumbel Distribution under Progressive Type II Censored with Repairable Mechanical Equipment Data

A COMPARISON OF STATISTICAL DISTRIBUTIONS FOR THE CRUDE BIRTH RATE DATA

Population statistics and demographic are important indicators to show the country's quality of life, social and health, the status of the population, the change in the population structure, and its effect on economic life. In demography, the crude birth rate is used to measure the growth of a population. In this study, we perform the crude birth rate values by statistical regions in Türkiye with some statistical distributions. When the results are compared, the Gumbel distribution provides the best fit to model the crude birth rate values than Normal, Log-Normal, Exponential, Gamma, and Weibull distributions. Among compared distributions, the Gumbel model is the best model to present the CBR data since log likelihood (logL), Akaike information criteria (AIC) and Bayesian information criteria (BIC) values of the Gumbel distribution are the lowest among all models. In addition, the results with the compared distributions are supported by graphs.

ANALYSIS OF EXTREME VALUES FOR DATA PROCESSING OF IN-LINE TECHNICAL DIAGNOSTICS

The pipeline system plays an important role in the structure of enterprises engaged in the transportation of significant volumes of oil and gas over long distances. However, steel pipelines are subject to corrosive factors, which can lead to defects and a reduced service life. Statistical analysis methods have recently been increasingly used to maintain structural reliability and ensure safe operation of equipment, both in the oil and gas industries. One method of statistical modeling is extreme value analysis, which can be used to extrapolate data from random inspection checks to non-investigated areas. The article is devoted to the assessment of the possibility of using statistical methods for analyzing data of in-line technical diagnostics (ITD) to ensure the integrity of trunk pipelines. The ITD results of one section of the export pipeline were used to determine the maximum corrosion rate of the entire length of the pipeline by extrapolating the Gumbel statistical distribution. The algorithm for constructing the Gumbel distribution is given. Plotting the autocorrelation function was used as a method for determining the independence of measurements. The belonging of the analyzed sample to the Gumbel distribution was confirmed by calculating the Anderson-Darling consent criterion. The ITD results of the remaining sections of the oil export pipeline confirmed the possibility of using extreme analysis to determine the maximum corrosion rate and increase the efficiency of pipeline inspection measures. Thus, it was concluded that statistical modeling is able to provide an estimate of the maximum corrosion rate during partial pipeline ITD and, therefore, savings in financial and time resources.

Study on Bond-slip Behavior between Non-uniformly Corroded Reinforcement and Concrete

In order to improve the stress concentration in concrete at steel nodes caused by zero thickness springs, the improved Spring2 nonlinear spring model from ABAQUS is used to simulate the bond-slip behavior between non-uniformly corroded reinforcement and concrete. Based on the collected test results with different stirrup spacing, fitting the influence coefficients of bond stress under stirrup corrosion. With the combination of a non-uniformly corroded rebar distribution model, the refined numerical simulation of the drawing process of reinforced concrete specimens was carried out using ABAQUS. The study shows that the improved nonlinear spring model is better than the zero thickness spring model in terms of computational accuracy and efficiency. The stirrup correction coefficient is approximately linear with the stirrup spacing; the bond-slip relationship considering the effect of stirrup spacing, has a better consistency with the relevant tests in the simulation of the pullout test. Weibull distribution for the fitting of non-uniform corrosion of reinforcement is more reasonable than Gumbel distribution.

Extremes in incomplete samples from moving averages of random variables from the domain of attraction of the Gumbel distribution

We are interested in further extremal properties of the moving average process defined from an i.i.d. noise sequence with common distribution function belonging to the maximum domain of attraction of the Gumbel extreme value distribution and satisfying additionally two specific conditions. In particular, we consider the limiting behavior of a sequence of random vectors consisted of maxima in complete and incomplete samples from this class of moving averages. The point process approach is used to derive the corresponding results.

Development of Intensity–Duration–Frequency (IDF) Curves over the United Arab Emirates (UAE) Using CHIRPS Satellite-Based Precipitation Products

The recent flooding events in the UAE have emphasized the need for a reassessment of flood frequencies to mitigate risks. The exponential urbanization and climatic changes in the UAE require a reform for developing and updating intensity–duration–frequency (IDF) curves. This study introduces a methodology to develop and update IDF curves for the UAE at a high spatial resolution using CHIRPS (Climate Hazards Group InfraRed Precipitation with Station) data. A bias correction was applied to the CHIRPS data, resulting in an improved capture of extreme events across the country. The Gumbel distribution was the most suitable theoretical distribution for the UAE, exhibiting a strong fit to the observed data. The study also revealed that the CHIRPS-derived IDF curves matched the shape of IDF curves generated using rain gauges. Due to orographic rainfall in the northeastern region, the IDF intensities were at their highest there, while the aridity of inland regions resulted in the lowest intensities. These findings enhance our understanding of rainfall patterns in the UAE and support effective water resource management and infrastructure planning. This study demonstrates the potential of the CHIRPS dataset for IDF curve development, emphasizes the importance of performing bias corrections, and recommends tailoring adjustments to the intended application.

Estimation of multicomponent stress–strength reliability for exponentiated Gumbel distribution

In this paper, the stress–strength reliability R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration.

Implications of rainfall variability on groundwater recharge and sustainable management in South Asian capitals: An in-depth analysis using Mann Kendall tests, continuous wavelet coherence, and innovative trend analysis

Groundwater resources, a critical component of hydrogeological systems, are under increasing pressure due to climate change and anthropogenic activities. South Asia, a region highly vulnerable to climate shocks, has seen over half of its population affected by climate-related disasters in the past two decades. These climate changes, characterized by intensifying heat waves, cyclones, droughts, and flooding, pose significant risks to groundwater resources management. This study aimed to address the recent variability, intensity, and depth of rainfall patterns in the capitals of south Asian countries on a daily, monthly, and annual basis. Mann-Kendal tests (MKT), Innovative Trend Analysis (ITA), and Continuous Wavelet Coherence were conducted to identify trend patterns. The Gumbel distribution of Intensity Depth Frequency (IDF) analysis was performed to analyze the depth and intensity of rainfall patterns for rainfall durations of 5, 10, 15, 30 min, 1–hr, 2–hr, 12–hr and 24–hr for 2, 5, 10, 25, 50, 75 and 100 years return periods. Results of ITA and MKT showed similar trend results for all cities and time scales. Findings suggest that Kotte receives the highest annual rainfall of 1745.28 mm and Kabul the lowest (380.76 mm). MKT showed both positive and negative monthly trends in most of the months, while annual rainfall exhibited positive trends in all cities with a change rate between +0.56 and + 2.34 mm/year. Seasonal trend analysis confirms positive trends for all seasons, except in Delhi, Malé, and Kathmandu in winter. IDF analysis reveals that current rainfall trends will slightly affect the depth and intensity of rainfall events for the various return periods. The study provides valuable insights into the water-energy-food nexus and contributes to the broader discourse on water policy and social aspects of groundwater in the face of climate change.

Actual and design wind loads for overhead transmission lines in the Central European part of Russia

This paper reveals an impact of the climatic loads on the sustainable operation of power grid facilities. An overview is provided considering various international standards related to the design of overhead transmission lines. The aim of the research was to analyze and compare the actual and design values of wind loads for transmission lines located in the Central European part of Russia and operated by the power grid company “Rosseti Center and Volga Region”. An analysis of wind load dynamics has been carried out considering the territory of 9 subjects of Russia and 1983-2022 timeframe. The actual climate data were computed according to the direct measurements of the weather stations. Nomograms of the maximum annual wind speeds are formed utilizing the first limiting Gumbel distribution for two climatic regions of the research area. The retrospective wind loads values were compared against the design values. The results of the study show that climate standards should be updated more frequently as it is the case nowadays, in particular, it relates to revision of existing wind loads or recalculation of wind speed correction factors for the near future.

Bridging Extremes: The Invertible Bimodal Gumbel Distribution.

This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.

Hydroelastic response of Froude scaled stiffened steel panels exposed to design-critical wave slamming

Stiffened steel panels of offshore ocean structures may experience violent wave impacts which needs to be accounted for in design. The slamming pressures are often measured in scaled wave tank tests and imposed on finite element models to obtain local structural responses. These responses are sometimes high, which has raised the question if hydroelastic effects are properly accounted for. One way to address the uncertainty of hydroelasticity, is to carry out hydroelastic model tests and compare measurements statistically with FEA calculations. This paper presents the hydroelastic model tests required for this type of comparison. Approximate elastic panels representing Froude scaled stiffened steel panels were 3D printed, validated, and then installed in a vertical column in a wave tank. The elastic panels were exposed to design critical wave slamming during irregular wave conditions relevant for the North Atlantic. Two different elastic panels were tested, one strong and one weak panel. The hydroelastic response of the elastic panels are reported in detail and shows that the panel responds with a limited set of frequencies. In most cases the strain time series of the stiffeners and girders obtain its maximum value during the first half period of vibration. Furthermore, the vibration of the panels generally show strong decay after the time of maximum strain. The extreme strains fit reasonably well with the Gumbel distribution. Furthermore, the variability of the extreme strains, measured as the coefficient of variation (COV), is comparable to the variability of slamming pressures from literature, for the strong elastic panel, but is found to be reduced significantly for the weak elastic panel.

Bias and variance reduction of high return levels for extreme hazard modelling

AbstractMany existing extremal data span only a few decades that result in large uncertainty in the estimated shape parameter of the extreme hazard model. This in turn leads to potentially large bias and variance of extrapolated extreme values at high return levels. This paper illustrates a statistical method that helps obtain hazard models that produce estimates at high return levels with reduced bias and variance. This method makes use of the maximum recorded values of extremal data that are independently recorded from a number of observational sites or generated by heterogeneous mechanisms. The logarithmically transformed average recurrence interval of the maximum recorded value at a site is shown to follow the Gumbel (Type I extreme value) distribution; therefore, multiple, say $$m$$ m , observational sites provide a sample of size $$m$$ m log-transformed average recurrence intervals, each from a distinct site. The sample can be treated as a sample from a Gumbel distribution, irrespective of the underlying hazard-generating mechanisms or the statistical hazard models. Application of the method is illustrated by analysis of the extreme wind gust data from automatic weather stations in South Australia and shown to lead to significant reduction of 2.9 m/s in potential bias of the mean and a reduction of 98.1% in variance of the 500-year gust speed at Adelaide Airport. The results are compared to the specifications in the Australian standard AS/NZS 1170.2:2021 and indicate that the standard may have overestimated the wind gust hazard; hence, the specified design wind speeds may fall on the conservative side for South Australia.

The maximum of log‐correlated Gaussian fields in random environment

AbstractWe study the distribution of the maximum of a large class of Gaussian fields indexed by a box and possessing logarithmic correlations up to local defects that are sufficiently rare. Under appropriate assumptions that generalize those in Ding et al., we show that asymptotically, the centered maximum of the field has a randomly‐shifted Gumbel distribution. We prove that the two dimensional Gaussian free field on a super‐critical bond percolation cluster with close enough to 1, as well as the Gaussian free field in i.i.d. bounded conductances, fall under the assumptions of our general theorem.

A New Approach of Presenting Lindley Expontiated Gumbel Distribution with Application to Environmental Data

The Lindley exponentiated Gumbel (LEGu) Distribution, a new family of probability distribution developed for modelling environmental data is introduced in this research paper. The investigation defines the new distribution's basic statistical properties, such as its shape, density function, hazard rate function, moment generation function, and maximum likelihood estimates of its model parameters. The study shows that, in comparison to other baseline distributions and comparators, increasing the number of parameters in the distribution improves its robustness and adaptability, making it more flexible in accommodating different types of data. The model is now more adaptable and can handle a wider range of data sets, making it a useful and effective tool for environmental modelling. The creation of the Lindley exponentiated Gumbel Distribution and the statistical qualities that go along with it bring up new possibilities for the analysis of environmental data, making a significant contribution to the larger initiatives in climate research and decision-making. The results of this study have the potential to advance our comprehension of environmental mechanisms and raise the precision of climate assessments and projections.