Search

For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for the mixture normal distribution based on the generalized extreme value theory. The proposed method is implemented on simulated as well as real-life datasets and its performance is compared with the existing methods. [ABSTRACT FROM AUTHOR]

The premise of extreme value theory focuses on the stochastic behaviour and occurrence of extreme observations in an event that is random. Traditionally for univariate case, the behaviour of the maxima is described either by the types-I, types-II or types-III extreme value distributions, primarily known as the Gumbel, Fréchet or reversed Weibull models. These are all particular cases of the generalized extreme value (GEV) model. However, in real-world scenario, these incidents take place as a consequence of concurrent dependent random events, where the relationship between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the q− generalized extreme value (q−GEV) distribution, as well as the q− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bi-variate (EV) data, arising naturally from independent q−GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model interdependent bivariate observations consisting of extreme values in terms of q−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate q−GEV. Additionally, conventional method to propose the newly defined bivariate (q−GEV) distribution with bivariate q− Gumbel distribution (a special case for ξ→0) has also been established with related inferences and application to climate data.

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. [ABSTRACT FROM AUTHOR]

For a common type of mixture distribution, namely the mixture normal distribution, existing methods for constructing its tolerance interval are unsatisfactory for cases of small sample size and large content. In this study, we propose a method to construct a tolerance interval for the mixture normal distribution based on the generalized extreme value theory. The proposed method is implemented on simulated as well as real-life datasets and its performance is compared with the existing methods.

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.)

Reinforcement corrosion significantly impacts the service life of reinforced concrete structures. The present study investigates the circumferential and longitudinal non-uniformity of steel corrosion in concrete subjected to mechanical load. Results indicate that, in the case of steel corrosion in concrete subjected to mechanical load, the distribution of rust layer thickness around the perimeter of the steel bar is fitted well with a Gaussian distribution. As the corrosion rate gradually increases, the uniform coefficient is linearly proportional to the minimum thickness of the rust layer. With respect to the longitudinal non-uniformity of steel corrosion, load-induced transverse cracks have a significant impact on the non-uniformity of corrosion, leading to the formation of rust peaks near the locations of transverse cracks. In the vicinity of each rust peak, the corrosion rate of the steel bar follows a Gaussian distribution. With respect to the non-uniformity of corrosion along the longitudinal rebar, a Gumbel distribution is identified to fit well, both in the cases of the non-stressed section and the pure bending section, although with dissimilar non-uniform parameters. Crack coefficients (α and β) are introduced to describe the influence of transverse cracks on the longitudinal non-uniformity of steel corrosion. [ABSTRACT FROM AUTHOR]

Analysis of extreme rainfall parameters including rainfall intensities is a fundamental requisite in safe planning, designing, and operating various hydrologic and water engineering projects against storms and floods. In arid and semi-arid regions, such as Oman, sufficient long-term rainfall data with short aggregation are usually not available in most locations across the country. This paper presents the development of intensity duration frequency (IDF) curves using the available rainfall data from 65 meteorological stations situated at different elevations and regions throughout Oman. Gumbel distribution was fitted to the observed data and rainfall intensities were found for various return periods. Rainfall analysis showed the average annual rainfall of 109.21 mm with a standard deviation of 92.82 mm, Skewness coefficient of 1.62 and Kurtosis coefficient of 3.08 for all the studied stations from 1977 to 2017. The statistical analysis showed that the estimated rainfall intensities for various return periods are high in the mountainous region compared to the desert or interior region, and the coastal region of the country. Also, the empirical parameters of IDF formula for all studied stations were established using non-linear regression. Finally, the contour maps for all the parameters were drawn which could be used to determine the IDF relationships for ungauged locations. This study will be useful for the decision makers and practicing hydrologists for planning and design of water resources systems in Oman.

Reinforcement corrosion significantly impacts the service life of reinforced concrete structures. The present study investigates the circumferential and longitudinal non-uniformity of steel corrosion in concrete subjected to mechanical load. Results indicate that, in the case of steel corrosion in concrete subjected to mechanical load, the distribution of rust layer thickness around the perimeter of the steel bar is fitted well with a Gaussian distribution. As the corrosion rate gradually increases, the uniform coefficient is linearly proportional to the minimum thickness of the rust layer. With respect to the longitudinal non-uniformity of steel corrosion, load-induced transverse cracks have a significant impact on the non-uniformity of corrosion, leading to the formation of rust peaks near the locations of transverse cracks. In the vicinity of each rust peak, the corrosion rate of the steel bar follows a Gaussian distribution. With respect to the non-uniformity of corrosion along the longitudinal rebar, a Gumbel distribution is identified to fit well, both in the cases of the non-stressed section and the pure bending section, although with dissimilar non-uniform parameters. Crack coefficients (α and β) are introduced to describe the influence of transverse cracks on the longitudinal non-uniformity of steel corrosion.

This paper introduced a relatively new statistical model as an extension of Gumbel distribution, which combines the new alpha power transformation method and Gumbel distribution. Different statistical properties of the proposed model were derived mathematically. Different estimation methods were introduced to estimate proposed model parameters. The behavior of these parameters was checked by using randomly generated data sets and the introduced estimation methods. Two real data sets were analyzed to show how the proposed model fits this data sets than its baseline model and many other well-known and related models.

The constant current accelerated corrosion test was used to study the durability of magnesium oxychloride-coated reinforced concrete (MOCRC) in order to solve the problem of MOCRC's durability. The relative dynamic elastic modulus was utilized as the failure threshold to evaluate the concrete durability, and the collected life data of concrete under different cover thickness were acquired. On the basis of the Gumbel distribution, the probability analysis can be used to study and foretell the life data. The results show that when the durability is evaluated by the relative mass and the relative dynamic modulus of elasticity, the durability of MOCRC with a larger protection layer thickness is better; the relative dynamic modulus of elasticity can better reflect the durability change in MOCRC than the relative mass. When the Gumbel distribution is used for durability analysis, the calculated value of the model and the life data have a relatively high degree of fit, which can provide a reference basis for the durability evaluation of concrete. [ABSTRACT FROM AUTHOR]

In this study, we delve into the realm of image segmentation, a field characterized by a multitude of approaches; one frequently used technique is thresholding-based image segmentation. This process divides intensity levels into different regions based on a specified threshold value. Minimum Cross-Entropy Thresholding (MCET) stands out as an independent objective function that can be applied with any distribution and is regarded as a mean-based thresholding method. In certain cases, images exhibit diverse structures that result in different histogram distributions. Some images possess symmetric histograms, while others feature asymmetric ones. Traditional mean-based thresholding methods are well-suited for symmetric image histograms, relying on Gaussian distribution definitions for mean estimations. However, in situations involving asymmetric distributions, such as left and right-skewed histograms, a different approach is required. In this paper, we propose the utilization of a Maximum Likelihood Estimation (MLE) of Gumbel’s distribution or Extreme Value Type I (EVI) distribution for the objective function of an MCET. Our goal is to introduce a dedicated image-thresholding model designed to enhance the accuracy and efficiency of image-segmentation tasks. This model determines optimal thresholds for image segmentation, facilitating precise data analysis for specific image types and yielding improved segmentation results by considering the impact of mean values on thresholding objective functions. We compare our proposed model with original methods and related studies in the literature. Our model demonstrates better performance in terms of segmentation accuracy, as assessed through both unsupervised and supervised evaluations for image segmentation.

The objective of this study was to analyse the extreme rainfall data of Khartoum, the capital city of Sudan. The study's data consist of monthly rainfall data obtained from the World Bank Climate Change Knowledge Portal for the years 1901 to 2021. The generalized extreme value (GEV) distribution was used to model the annual maximum rainfall using the block maxima method. The model parameters were estimated using the maximum likelihood estimation (MLE) method. We found evidence to suggest that the Gumbel model better fits the maximum rainfall data based on the likelihood ratio test of the GEV and Gumbel models. The return levels of maximum monthly rainfall in Khartoum and their 95 percent confidence intervals were computed for selected return periods: 2, 10, 20, 25, 30, 50, 100, 200, and 500 years. [ABSTRACT FROM AUTHOR]

Cone-beam computed tomography (CBCT), derived from multidetector row CT (MDCT), has a high spatial resolution and has recently been applied to various organs. One of the severe limitations common to CBCT and MDCT is metal artifacts. In particular, streak metal artifacts (SMAs) between multiple metal materials often hinder diagnosis. However, no studies have quantitatively compared the strength of SMAs in MDCT and CBCT. Nomura et al. reported an evaluation method specialized in SMAs of CBCT using the Gumbel distribution (GD), which can also be applied to SMAs of MDCT (Oral Surg Oral Med Oral Pathol Oral Radiol 131: 494–502, 2021, https://doi.org/10.1016/J.OOOO.2020.08.031). This study aimed to quantitatively compare SMAs occurring between titanium materials on MDCT and CBCT images using the GD-based method. The SMAs were investigated as follows: A hydroxyapatite block was sandwiched between two titanium rods to generate an SMA. They were placed in an acrylic phantom, simulating a human head, and scanned using an MDCT scanner and two CBCT scanners. The obtained images were analyzed using Gumbel plots and location parameters, and the SMA strength was calculated. The results showed that the SMAs on the MDCT images were significantly weaker than those on the CBCT images. In the CBCT scans, a smaller volume CT dose index value caused stronger SMAs. These results indicate that MDCT is more advantageous than CBCT in terms of SMA reduction when bone morphology between titanium materials must be evaluated. The characteristic should be considered in clinical cases. [ABSTRACT FROM AUTHOR]

This paper shows, based on daily records, the modeling of maximum precipitations in each quarter of eighteen meteorological stations located in different parts of Uruguay. We compared the performance of the classic likelihood ratio test with one of the truncated Cráamer-von Mises type. Most of the stations did adjust under the Gumbel distribution with few Fráechet and Weibull cases, obtaining a most appropriate truncated Cráamer-von Mises test performance. From the adjustment in each of the stations and the combination of three statistical techniques (k-means, Kolomgorov-Smirnov test of equality of distributions and test of independence) we concluded that the maximum rainfall throughout the Uruguayan territory is homogeneous with a slight difference between the southern and northern regions. [ABSTRACT FROM AUTHOR]

This paper aims to present simple regressive equations to estimate the parameters of the three-parameter depth–duration–frequency (DDF) curve (3p-DDF), which accurately expresses, for a preassigned return period, the relationship between the rainfall depth and the rainfall duration over large duration ranges, from below 1 h (i.e., tens of minutes) to above 1 h (up to 24 h). These equations are developed to relate their parameters to those of the two-parameter DDF curve (2p-DDF), which can be estimated more easily being based on more readily available data related to rainfall durations above 1 h. In the applications, the regressive equations are first calibrated using recent pluviographic data in northern Italy, Germany, and Sweden. Two validation steps are then carried out to test the equations in terms of estimated rainfall depths using the same data as those used in the calibration step and data of stations from other geographic areas, i.e., Sicily in southern Italy, and from the past century, respectively. The results obtained prove this methodology capable of providing reliable estimation of short-duration rainfalls with various return periods in the absence of measurements with fine temporal resolution. [ABSTRACT FROM AUTHOR]

Flood-vulnerable area identification as a measure of comprehensive flood risk management was investigated in Itang District, Ethiopia, using Probability Distribution and Analytical Hierarchy Process. The former provided a best fit to the extreme value analyses. According to water discharge levels, the region was mapped at 5, 10, 25, 50, and 100 year intervals. The parameters processed were slope, elevation, land-use/land-cover, rainfall, discharge, and soil. Each criterion was evaluated with Analytical Hierarchy Process and mapped by GIS. Data were assorted into very high, high, moderate, low, and very low suitability classes representing 29.7%, 27.8%, 18.5%, 12.7%, and 11.4% inundation areas, respectively. The outcome was found to be extremely useful for evacuation planning, damage assessment, and loss estimation to minimize the disaster effects in the district.

Floods are among the most occurring natural hazards that cause severe damage to infrastructure and loss of life. In India, southern Gujarat is affected during the monsoon season, facing multiple flood events in the Damanganga basin. As the basin is one of the data-scarce regions, evaluating the globally available dataset for flood risk mitigation studies in the Damanganga basin is crucial. In the present study, we compared four open-source digital elevation models (DEMs) (SRTM, Cartosat-1, ALOS-PALSAR, and TanDEMX) for hydrodynamic (HD) modeling and flood risk mapping. The simulated HD models for multiple flood events using HEC-RAS v6.3 were calibrated by adopting different roughness coefficients based on land-use land cover, observed water levels at gauge sites, and peak flood depths in the flood plain. In contrast to the previous studies on the Purna river basin (the neighboring basin of Damanganga), the present study shows that Cartosat-1 DEM provides reliable results with the observed flood depth. Furthermore, the calibrated HD model was used to determine the flood risk corresponding to 10, 25, 50, and 100-year return period floods calculated using Gumbel's extreme value (GEV) and log-Pearson type III (LP-III) distribution techniques. Comparing the obtained peak floods corresponding to different return periods with the observed peak floods revealed that the LP-III method gives more reliable estimates of flood peaks for lower return periods, while the GEV method gives comparatively more reliable estimates for higher return period floods. The study shows that evaluating different open-source data and techniques is crucial for developing reliable flood mitigation plans with practical implications. [ABSTRACT FROM AUTHOR]

Copyright of Nativa is the property of Revista Nativa 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.)

The effect of within-year wave climate variability on the predicted extreme significant wave heights for the design of ship structures is examined. The significant wave height data is taken from ERA 5 database along frequent shipping routes. Monthly and annual extreme significant wave heights are extracted, and Gumbel distributions are fitted, respectively, using Maximum Likelihood Estimation. Monthly extreme wave heights are then combined, using the method proposed by Carter and Challenor [(1981). Estimating return values of environmental parameters. Q J R Metereol Soc. 107(451):259–266], to account for the effect of intra-annual climate variability. Long-term extreme values by two methods are compared for individual locations and shipping routes. Consequences on the extreme wave bending moments are explored, comparing the results to IACS rules. It was found that neglecting within-year wave climate variability leads to the underestimation of extreme significant wave heights and wave bending moments by up to 10 %.. [ABSTRACT FROM AUTHOR]

abstract: Updating the basic wind speed map of NBR 6123 –-Wind loading on buildings – is one of the duties of the committee responsible for the revision of this code. Traditionally such maps are elaborated by means of extreme value wind speed data collected at meteorological stations, use of statistical methods for data characterization, and application of mathematical regression to elaborate the territorial maps. However, the spatial distribution of the atmospheric phenomena responsible for strong winds cannot be disregarded. This work presents a proposal for a new wind speed map for NBR 6123 combining a climatological approach and wind speed data recently compiled from hundreds of meteorological stations. A climatological wind map was first produced considering the phenomena which cause strong winds, and used as a basis to draw the isopleths of the basic wind speed map, considering the measured wind speed data. The resulting map shows basic wind speeds ranging from 30 to 48m/s.

The galvanostatic method has been widely used for accelerating the corrosion of reinforcing bars in concrete to complete test studies within a reasonable timeframe. However, which level of current density induces characteristics of steel corrosion spatial variability and the associated structural performance of corroded reinforced concrete (RC) beams that are similar to those observed under natural conditions remains unknown. In this paper, comprehensive experimental research is conducted to compare the characteristics of spatial growth in steel weight loss and crack width and the structural behavior of corroded RC beams by two corrosion-accelerated methods (i.e. galvanostatic method at six current densities and artificial chloride environment method). The effects of these corrosion acceleration methods on Gumbel's location and scale distribution parameters and the associated yield load capacity of corroded RC beams are investigated using Monte Carlo-based two-dimensional finite element analysis. Finally, a suitable current density is recommended to better simulate the steel corrosion distribution and the associated yield load capacity of RC beams in comparison to those observed under an artificial chloride environment. [ABSTRACT FROM AUTHOR]

We focus on a variety of bivariate models with proportional hazard components. Models with proportional hazard marginals are described together with a selection of models with proportional hazard conditional distributions. The bivariate distributions with marginal proportional hazards distributions are shown to be closely related to certain known bivariate exponential models. Two distinct kinds of conditional specification are investigated. Discussion is provided of cases with hazard function components that are (1) completely unknown, (2) known to belong to given parametric families and (3) completely known. Since the models are designed for use with survival data, it is inevitable that the marginal and conditional distributions will be asymmetric. However, logarithmic transformations in some cases will result in symmetric component distributions. [ABSTRACT FROM AUTHOR]

Floods are among the most occurring natural hazards that cause severe damage to infrastructure and loss of life. In India, southern Gujarat is affected during the monsoon season, facing multiple flood events in the Damanganga basin. As the basin is one of the data-scarce regions, evaluating the globally available dataset for flood risk mitigation studies in the Damanganga basin is crucial. In the present study, we compared four open-source digital elevation models (DEMs) (SRTM, Cartosat-1, ALOS-PALSAR, and TanDEMX) for hydrodynamic (HD) modeling and flood risk mapping. The simulated HD models for multiple flood events using HEC-RAS v6.3 were calibrated by adopting different roughness coefficients based on land-use land cover, observed water levels at gauge sites, and peak flood depths in the flood plain. In contrast to the previous studies on the Purna river basin (the neighboring basin of Damanganga), the present study shows that Cartosat-1 DEM provides reliable results with the observed flood depth. Furthermore, the calibrated HD model was used to determine the flood risk corresponding to 10, 25, 50, and 100-year return period floods calculated using Gumbel’s extreme value (GEV) and log-Pearson type III (LP-III) distribution techniques. Comparing the obtained peak floods corresponding to different return periods with the observed peak floods revealed that the LP-III method gives more reliable estimates of flood peaks for lower return periods, while the GEV method gives comparatively more reliable estimates for higher return period floods. The study shows that evaluating different open-source data and techniques is crucial for developing reliable flood mitigation plans with practical implications.

The constant current accelerated corrosion test was used to study the durability of magnesium oxychloride-coated reinforced concrete (MOCRC) in order to solve the problem of MOCRC’s durability. The relative dynamic elastic modulus was utilized as the failure threshold to evaluate the concrete durability, and the collected life data of concrete under different cover thickness were acquired. On the basis of the Gumbel distribution, the probability analysis can be used to study and foretell the life data. The results show that when the durability is evaluated by the relative mass and the relative dynamic modulus of elasticity, the durability of MOCRC with a larger protection layer thickness is better; the relative dynamic modulus of elasticity can better reflect the durability change in MOCRC than the relative mass. When the Gumbel distribution is used for durability analysis, the calculated value of the model and the life data have a relatively high degree of fit, which can provide a reference basis for the durability evaluation of concrete.

Average annual loss (AAL) is traditionally used as the basis of assessing flood risk and evaluating risk mitigation measures. This research presents an improved implementation to estimate building-specific AAL, with the flood hazard of a building represented by the Gumbel extreme value distribution. AAL is then calculated by integrating the area under the overall loss-exceedance probability curve using trapezoidal Riemann sums. This implementation is compared with existing AAL estimations from flood risk assessment. A sensitivity analysis is conducted to examine the variability in AAL results based on depth-damage function (DDF) choice. To demonstrate the methodology, a one-story single-family residence is selected to assess the financial benefits of freeboard (i.e., increasing lowest floor elevations). Results show that 1 ft. of freeboard results in annual flood risk reduction of over $1,000, while 4 ft of freeboard results in annual flood risk reduction of nearly $2,000. The sensitivity result suggests that the DDF selection is critical, as a large proportion of flood loss is counted below the top of the first floor. The findings of this paper will enhance DDF selection, improve flood loss estimates, encourage homeowners and communities to invest in flood mitigation, and provide government decision-makers with improved information when considering building code changes.

ABSTRACT Irrigation system capacity is typically defined by analyzing probabilities of non-exceedance of evapotranspiration. The use of mean monthly values of ET0 may lead to underestimation of the required capacity, whereas use of maximum daily values may result in overestimation of required capacity. This study had the following objectives: (1) to analyze a 30-year series of daily ET0 data from Piracicaba, SP, Brazil, to evaluate the suitability of the Gumbel distribution for estimating the maximum values of ET0 organized in periods of up to 30 days; (2) to determine probable maximum values and to select ET0 values considering the irrigation interval and the risk of failure in terms of irrigation system capacity. Daily data from 1990 to 2019 were used to calculate ET0 using the Penman-Monteith model. The Gumbel distribution fitted to the data and was suitable for characterizing the frequency distribution of the maximum ET0. The probable ET0 for designing irrigation systems can then be estimated based on the expected lifespan, irrigation interval, and return period of ET0 maximum values. The higher the anticipated irrigation system lifespan, the higher the return period needed to attain a low risk of failure. Using the average of maximum ET0 values alone leads to underestimation of system capacity and a high risk of failure in terms of irrigation system capacity.

We consider the testing of mutual independence among all entries in a [Formula: see text]-dimensional random vector based on [Formula: see text] independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where [Formula: see text]. We further show that the two tests are rate-optimal in terms of power against sparse alternatives and that they outperform competitors in simulations, especially when [Formula: see text] is large.

In Malaysia, the increment of annual rainfall patterns is causing frequent floods, mainly in Sabah and Sarawak. Limbang river basin was selected as a case study due to it was facing of high-risk flooding problem mainly during the transition of climate. This study was aimed to estimate the frequency of rainfall under various return periods and to identify the best fit model probability distribution of annual maximum rainfall based on twenty-four hours sample in Limbang. The three statistical models were used, which are Gumbel, Log-Pearson type III, and Log-Normal. Based on the goodness of fit tests, Chi-Square, Kolmogorov Smirnov test, and the Log-Normal was found to be the best fit model for the station of Panduran. The Log-Pearson type III was found to be the best-fit distribution model for the rest of the stations, which occupies almost more than 90%. The maximum values of expected rainfall were calculated using the best fit probability distributions and could be used by a design engineer in the future.

High-frequency mechanical impact (HFMI) is an efficient post-weld treatment technique that enhances fatigue strength in metallic welded structures. Steel or steel-concrete composite road bridges, where the fatigue limit state often governs the design, compose one category of structures that can benefit from the application of this technology. To assert an improvement in fatigue strength using HFMI, the induced compressive residual stresses must be stable. Therefore, the maximum service stresses that can be allowed on HFMI-treated joints should be controlled to avoid the relaxation of the induced beneficial compressive stresses by HFMI treatment. Using statistical analysis of recorded traffic, this paper compares the measured maximum traffic loads to those generated by a load model. More than 870,000 and 470,000 recorded vehicles from traffic measurements in Sweden and the Netherlands are used in this analysis. To capture the characteristic bending moment, the daily maxima of the resulting measured load effect are combined with the extreme value distribution of the bending moment. In addition, it is found that the characteristic load combination is the best-studied option to assess the maximum stress in HFMI-treated weldments in road bridges. [ABSTRACT FROM AUTHOR]

An epidemiological study is carried out in several countries analyzing the first wave of the COVID-19 pandemic using the SIR model and Gumbel distribution. The equations of the SIR model are solved exactly using the proper time as a parameter. The physical time is obtained by integration of the inverse of the infected function over proper time. Some properties of the solutions of the SIR model are studied such as time scaling and the asymmetry, which allows to obtain the basic reproduction number from the data. Approximations to the solutions of the SIR model are studied using Gumbel distributions by least squares fit or by adjusting the maximum of the infected function. Finally, the parameters of the SIR model and the Gumbel function are extracted from the death data and compared for the different countries. It is found that ten of the selected countries are very well described by the solutions of the SIR model, with a basic reproduction number between 3 and 8. [ABSTRACT FROM AUTHOR]

Copyright of Kirkuk University Journal for Scientific Studies is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 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.)

In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements satisfying the so-called Lyapunov condition. Under an appropriated normalization, the joint law of the extremal singular values converges in distribution, as the matrix dimension tends to infinity, to an independent product of Rayleigh and Gumbel laws. The latter implies that a normalized condition number converges in distribution to a Fréchet law as the dimension of the matrix increases. [ABSTRACT FROM AUTHOR]

High-frequency mechanical impact (HFMI) is an efficient post-weld treatment technique that enhances fatigue strength in metallic welded structures. Steel or steel-concrete composite road bridges, where the fatigue limit state often governs the design, compose one category of structures that can benefit from the application of this technology. To assert an improvement in fatigue strength using HFMI, the induced compressive residual stresses must be stable. Therefore, the maximum service stresses that can be allowed on HFMI-treated joints should be controlled to avoid the relaxation of the induced beneficial compressive stresses by HFMI treatment. Using statistical analysis of recorded traffic, this paper compares the measured maximum traffic loads to those generated by a load model. More than 870,000 and 470,000 recorded vehicles from traffic measurements in Sweden and the Netherlands are used in this analysis. To capture the characteristic bending moment, the daily maxima of the resulting measured load effect are combined with the extreme value distribution of the bending moment. In addition, it is found that the characteristic load combination is the best-studied option to assess the maximum stress in HFMI-treated weldments in road bridges.

This paper aims to present simple regressive equations to estimate the parameters of the three-parameter depth–duration–frequency (DDF) curve (3p-DDF), which accurately expresses, for a preassigned return period, the relationship between the rainfall depth and the rainfall duration over large duration ranges, from below 1 h (i.e., tens of minutes) to above 1 h (up to 24 h). These equations are developed to relate their parameters to those of the two-parameter DDF curve (2p-DDF), which can be estimated more easily being based on more readily available data related to rainfall durations above 1 h. In the applications, the regressive equations are first calibrated using recent pluviographic data in northern Italy, Germany, and Sweden. Two validation steps are then carried out to test the equations in terms of estimated rainfall depths using the same data as those used in the calibration step and data of stations from other geographic areas, i.e., Sicily in southern Italy, and from the past century, respectively. The results obtained prove this methodology capable of providing reliable estimation of short-duration rainfalls with various return periods in the absence of measurements with fine temporal resolution.

Worldwide, COVID-19 coronavirus disease is spreading rapidly in a second and third wave of infections. In this context of increasing infections, it is critical to know the probability of a specific number of cases being reported. We collated data on new daily confirmed cases of COVID-19 breakouts in: Argentina, Brazil, China, Colombia, France, Germany, India, Indonesia, Iran, Italy, Mexico, Poland, Russia, Spain, U.K., and the United States, from the 20th of January, 2020 to 28th of August 2021. A selected sample of almost ten thousand data is used to validate the proposed models. Generalized Extreme-Value Distribution Type 1-Gumbel and Exponential (1, 2 parameters) models were introduced to analyze the probability of new daily confirmed cases. The data presented in this document for each country provide the daily probability of rate incidence. In addition, the frequencies of historical events expressed as a return period in days of the complete data set is provided.

This paper introduced a relatively new statistical model as an extension of Gumbel distribution, which combines the new alpha power transformation method and Gumbel distribution. Different statistical properties of the proposed model were derived mathematically. Different estimation methods were introduced to estimate proposed model parameters. The behavior of these parameters was checked by using randomly generated data sets and the introduced estimation methods. Two real data sets were analyzed to show how the proposed model fits this data sets than its baseline model and many other well-known and related models. [ABSTRACT FROM AUTHOR]

Let $X_1,X_2, \ldots, X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density f. Under some conditions on f, we obtain a Poisson limit theorem, as $n \to \infty$ , for the number of large probability kth-nearest neighbor balls of $X_1,\ldots, X_n$. Our result generalizes Theorem 2.2 of 11, which refers to the special case $k=1$. Our proof is completely different since it employs the Chen–Stein method instead of the method of moments. Moreover, we obtain a rate of convergence for the Poisson approximation. [ABSTRACT FROM AUTHOR]