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The Lognormal distribution serves as a fundamental model across various disciplines, offering a versatile framework for analyzing positively skewed data. Lognormal distributions are frequently employed to represent stock prices, as these prices cannot be negative and typically adhere to a multiplicative process. Additionally, this distribution is utilized to model the time until failure for various products. It is also applicable in the analysis of certain environmental variables, such as the concentrations of pollutants. In Bayesian estimation, the choice of prior distribution significantly influences parameter estimation, particularly in scenarios with limited sample sizes. Shrinkage Bayesian estimation methods have emerged as powerful tools to address the challenges of small sample sizes by incorporating prior information effectively. This research conducts a comparative analysis of shrinkage Bayesian estimation methods. Through comprehensive simulations, we investigate the impact of these priors on parameter estimation accuracy by limited sample sizes and initial parameter values. simulation experiments showed that Shrinkage Bayesian estimator method give the best estimators with minimum mean square error comparing with Maximum likelihood estimator. Other simulations can be performed for estimation methods (shrinkage, moments, modified moments). shrinkage Bayesian estimation methods can also be performed on (Weibull, Gamma distribution) distributions and the results compared. [ABSTRACT FROM AUTHOR]

Rainstorm is one of the global meteorological disasters that threaten the safety of transportation infrastructure and the connectivity of transportation system. Aiming to support the resilience assessment of transportation infrastructure in three representative regions: Sichuan–Chongqing, Yangtze River Delta, and Beijing-Tianjin-Hebei-Shandong, rainfall data over 40 years in the three regions are collected, and the temporal distribution of rainfall are analyzed. Prediction equations of rainfall are established. For the purpose of this, the probabilistic density function (PDF) is assigned to the rainfall by fitting the frequency distribution histogram. Using the assigned PDF, the rainfall data are transformed into standard normal space where regression of prediction equations is performed and the prediction accuracy is tested. The results show that: (1) The frequency of rainfall in the three regions follows a lognormal distribution based on which the prediction equations of rainfall can be established in standard normal space. The error of regression shows no remarkable dependence on self-variables, and the significance analysis indicates that the equations proposed in this paper are plausible for predicting rainfalls for the three regions. (2) The Yangtze River Delta region has a higher risk of rainstorm disaster compared to the other two regions according to the frequency of rainfall and the return period of precipitation concentration. (3) Over the period of 1980–2021, the Sichuan–Chongqing region witnessed an increase in yearly rainfall but a decrease in rainstorm disasters, whereas the other two regions experienced a consistent rise in both metrics. [ABSTRACT FROM AUTHOR]

Significant errors often arise when measuring streamflow during high flows and flood events. Such errors conflated by short records of observations may induce bias in the flood frequency estimates, leading to costly engineering design mistakes. This work illustrates how observational (measurement) errors affect the uncertainty of flood frequency estimation. The study used the Bulletin 17 C (US standard) method to estimate flood frequencies of historical peak flows modified to represent the measurement limitations. To perform the modifications, we explored, via Monte Carlo simulation, four hypothetical scenarios that mimic measurement errors, sample size limitations, and their combination. We used a multiplicative noise from a log-normal distribution to simulate the measurement errors and implemented a bootstrap approach to represent the sampling error. Then, we randomly selected M samples from the total N records of the observed peak flows of four gauging stations in Iowa in central USA. The observed data record ranges between 76 and 119 years for watersheds with drainage areas between 500 and 16,000 km2. According to the results, measurement errors lead to more significant differences than sampling limitations. The scenarios exhibited differences with median magnitudes of up to 50%, with some cases reaching differences up to 100% for return periods above 50 years. The results raise a red flag regarding flood frequency estimation that warrants looking for further research on observational errors. [ABSTRACT FROM AUTHOR]

To gain new insights into ground-motion phenomena in New Zealand (NZ), we apply the non-parametric generalized inversion technique (GIT) in the Fourier domain to isolate the systematic source, path, and site effects from 20 813 seismograms, recorded by 693 sensors at 439 unique locations, from 1200 shallow crustal events (M w > 3) during the period 2000–2021. From the inverted source spectra, we derive Brune's stress parameter, ∆σ , which is found to follow a lognormal distribution with a log10 standard deviation of 0.36 or equivalently 0.83 in natural log unit. ∆σ slightly increases with focal depth and is practically independent of earthquake size (i.e. self-similar), but displays a statistically significant spatial clustering. Based on the inverted attenuation, a trilinear geometric-spreading function, and a distance-dependent quality-factor Q (f) model are found to well describe the attenuation in NZ; though a single |$Q(f)$| model is also obtained for the whole distance range: |$Q(f) = 149.1{f}^{0.62}$|⁠. Using the site response decomposed from GIT, we find that the soil classification scheme specified in NZ seismic code, NZS1170.5, has a limited capability in discerning the site-specific frequency-dependent amplification functions in comparison to a non-parametric clustering with the same number of discrete classes. The potential use of the spatial variation in source parameters from this GIT analysis in region-specific physics-based simulations is discussed. [ABSTRACT FROM AUTHOR]

Black carbon (BC) is one of the most important climate forcers with severe health effects. Large uncertainties in radiative forcing estimation and health impact assessment arise from the fact that there is no standardized method to measure BC mass concentration. This study presents a 2-year comparison of three state-of-the-art BC measurement techniques at the high-altitude research station Pic du Midi (PDM) located in the French Pyrenees at an altitude of 2877 m above sea level. A recently upgraded Aethalometer AE33, a thermal-optical analyser Sunset and a single-particle soot photometer SP2 were deployed to measure simultaneously the mass concentration of equivalent black carbon (MeBC), elemental carbon (MEC) and refractory black carbon (MrBC), respectively. Significant deviations in the response of the instruments were observed. All techniques responded to seasonal variations in the atmospheric changes in BC levels and exhibited good correlation during the whole study period. This indicates that the different instruments quantified the same particle type despite the fact that they are based on different physical principles. However the slopes and correlation coefficients varied between instrument pairs. The largest biases were observed for the AE33 with MeBC values that were around 2 times greater than MrBC and MEC values. The principal reasons of such large discrepancy were explained by the mass absorption cross section (MAC) that was too low and C values recommended by the AE33 manufacturer and applied to the absorption coefficients measured by the AE33. In addition, the long-range transport of dust particles at PDM in spring caused significant increases in the bias between AE33 and SP2 by up to a factor 8. The Sunset MEC measurements agreed within around 17 % with the SP2 MrBC values. The largest overestimations of MEC were observed when the total carbon concentrations were below 25 µgCcm-2 , which is probably linked to the incorrect determination of the organic carbon (OC)–EC split point. Another cause of the discrepancy between instruments was found to be the limited detection range of the SP2, which did not allow for the total detection of fine rBC particles. The procedure used to estimate the missing mass fraction of rBC not covered by the measurement range of the SP2 was found to be critical. We found that a time-dependent correction based on fitting the observed rBC size distribution with a multimodal lognormal distribution is needed to accurately estimate MrBC over a larger size range. [ABSTRACT FROM AUTHOR]

The total freeboard, which is the ice layer above water level and includes the snow thickness, is needed to retrieve the ice thickness and ice surface topography. Single-pass interferometric synthetic aperture radar (InSAR) allows for the generation of digital elevation models (DEMs) over the drifting sea ice. However, accurate sea ice DEMs (i.e., the total freeboard) derived from InSAR are impeded due to variation in the penetration of the radar signals into the snow and ice layers. This research introduces a novel methodology for retrieving sea ice DEMs using dual-polarization interferometric SAR images, considering the variation in radar penetration bias across multiple ice types. The accuracy of the method is verified through photogrammetric measurements, demonstrating that the derived DEM has a root-mean-square error of 0.26 m over a 200 km × 19 km area. The method is further applied to broader regions in the Weddell Sea and the Ross Sea, offering new insights into the regional variations of the sea ice topography in the Antarctic. We also characterize the non-Gaussian statistical behavior of the total freeboard using log-normal and exponential-normal distributions. The results suggest that the exponential-normal distribution is superior in the thicker-sea-ice region (average total freeboard > 0.5 m), whereas the two distributions exhibit similar performance in the thinner-ice region (average total freeboard < 0.5 m). These findings offer an in-depth representation of the total freeboard and roughness in the Weddell and Ross seas. The novel methodology introduced here can be conducted on time series data to comprehend the dynamics of the sea ice, including its growth and deformation. [ABSTRACT FROM AUTHOR]

This paper addresses a stochastic job shop scheduling problem with sequence-dependent setup times, aiming to minimize the expected maximum lateness. The stochastic nature is modeled by considering uncertain times between failures (TBF) and uncertain times to repair (TTR). To tackle this problem, a simheuristic approach is proposed, which combines a tabu search (TS) algorithm with Monte Carlo simulation. A total of 320 instances were used to conduct multiple experiments. Instances were generated with two distributions to study the behavior of stochastic TTR and TBF under log-normal and exponential distributions. Firstly, the performance of the simheuristic was evaluated for small instances by comparing it with the simulation of optimal solutions obtained with a mixed-integer linear programming (MILP) model. The simheuristic approach demonstrated an average improvement of around 7% compared to the simulation of MILP model solutions. Secondly, the simheuristic performance was evaluated for medium and large-size instances by comparing it with the simulation of the solutions obtained by the earliest due date (EDD) and process time plus work in the next queue plus negative slack (PT + WINQ + SL) dispatching rules. The results showed an average improvement of around 11% compared to EDD and 14% compared to PT + WINQ + SL. Furthermore, the results highlight that even when the two distributions have the same expected value and coefficient of variation, they can yield different expected maximum lateness values. This emphasizes the importance of precise distribution fitting when solving real cases to achieve effective scheduling performance. [ABSTRACT FROM AUTHOR]

Control charts are widely used in the manufacturing and service sectors to track, regulate, and enhance process output. A manufacturing industry desires to utilize a control chart that has an effective structure and is sensitive to detect infrequent variations in the process. Generally, control charts are developed with the presumption that the understudy quality variable is normally distributed. In actual application, many processes have skewed distributions. The purpose of this study is to use the moving average (MA) charts to track the dispersion of a log‐normal distribution. The design of the proposals is developed and the performance is assessed by run‐length properties. The cumulative distributions of run‐length under in‐control and out‐of‐control are provided to have a broad view of the performance. The simulation findings show that when the value of the log‐normal dispersion parameter is large, the proposed chart is more sensitive to the changes in the dispersion. Additionally, an industrial application is given to illustrate the suggested charts in this research. [ABSTRACT FROM AUTHOR]

Purpose: Image segmentation is one of the most essential tasks in image processing applications. It is a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc. However, an accurate segmentation is a critical task since finding a correct model that fits a different type of image processing application is a persistent problem. This paper develops a novel segmentation model that aims to be a unified model using any kind of image processing application. The proposed precise and parallel segmentation model (PPSM) combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions. Moreover, a parallel boosting algorithm is proposed to improve the performance of the developed segmentation algorithm and minimize its computational cost. To evaluate the effectiveness of the proposed PPSM, different benchmark data sets for image segmentation are used such as Planet Hunters 2 (PH2), the International Skin Imaging Collaboration (ISIC), Microsoft Research in Cambridge (MSRC), the Berkley Segmentation Benchmark Data set (BSDS) and Common Objects in COntext (COCO). The obtained results indicate the efficacy of the proposed model in achieving high accuracy with significant processing time reduction compared to other segmentation models and using different types and fields of benchmarking data sets. Design/methodology/approach: The proposed PPSM combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions. Findings: On the basis of the achieved results, it can be observed that the proposed PPSM–minimum cross-entropy thresholding (PPSM–MCET)-based segmentation model is a robust, accurate and highly consistent method with high-performance ability. Originality/value: A novel hybrid segmentation model is constructed exploiting a combination of Gaussian, gamma and lognormal distributions using MCET. Moreover, and to provide an accurate and high-performance thresholding with minimum computational cost, the proposed PPSM uses a parallel processing method to minimize the computational effort in MCET computing. The proposed model might be used as a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc. [ABSTRACT FROM AUTHOR]

Copyright of Psychological Science is the property of Psychological Science 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.)

Logistic regression models are commonly used to explain binary health outcome variable using independent variables such as patient characteristics in medical science and public health research. Although there is no distributional assumption required for independent variables in logistic regression, variables with severely right-skewed distribution such as lab values are often log-transformed to achieve symmetry or approximate normality. However, lab values often have zeros due to limit of detection which makes it impossible to apply log-transformation. Therefore, preprocessing to handle zeros in the observation before log-transformation is necessary. In this study, five methods that remove zeros (shift by 1, shift by half of the smallest nonzero, shift by square root of the smallest nonzero, replace zeros with half of the smallest nonzero, replace zeros with the square root of the smallest nonzero) are investigated in logistic regression setting. To evaluate performances of these methods, we performed a simulation study based on randomly generated data from log-normal distribution and logistic regression model. Shift by 1 method has the worst performance, and overall shift by half of the smallest nonzero method, replace zeros with half of the smallest nonzero method, and replace zeros with the square root of the smallest nonzero method showed comparable and stable performances. [ABSTRACT FROM AUTHOR]

Copyright of Revista Producao Online is the property of Associacao Brasileira de Engenharia de Producao 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 energy saving and carbon reduction in the building industry is closely related to the realization of China's double carbon goal. In this study, a two-dimensional framework for building life cycle carbon emissions was established, which takes into account the early stages of building design such as the feasibility study stage and scheme design stage. Taking 57 residential buildings in Xi'an City as examples, the life cycle carbon emission characteristics of residential buildings in cold areas were introduced. This study found that the life cycle carbon emission intensity is about 45~55 kgCO2/(m2·a). The operation and maintenance stage and building materials production stage accounted for the largest proportion of carbon emissions, and the sum of carbon emissions of the two stages accounted for 92.3% of the total carbon emissions. In addition, based on the probability density function, the carbon emission intensity distributions of the building life cycle, building material production stage, building material transportation stage, and operation and maintenance stage were analyzed, and it was found that each distribution fitting graph was generally in line with a lognormal distribution, and their expected value provided a reference index for carbon emission pre-assessment in the feasibility study stage. Based on the analysis and determination of 11 independent variables that affect the total carbon emissions, such as area, floor number, story height, and number of households, a multiple linear regression model for carbon emission pre-assessment in the design stage of building schemes is proposed. The R2adj of the model is 0.985 and the error is about 10%. The prediction model can provide beneficial guidance for the life cycle carbon emission prediction in the design stage of building projects, so as to reduce carbon emissions by changing building design. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology 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.)

To cope with harsh working conditions, new corrosion-resistant coated steel wires with higher tensile strength have been developed. This study investigates the corrosion characteristics of a new zinc–aluminum alloy-coated steel wire under stress conditions. The particulate corrosion products generated by the oxidation of the coating in the initial stage of corrosion are converted into layer-structured corrosion products at the early stage of corrosion. Moreover, high-stress conditions have a significant influence on the critical conversion time from the coating corrosion stage to the iron matrix corrosion stage. Thus, the uniform corrosion depth (i.e., the mass loss rate) could be fitted with a continuous power function model rather than the previously used two-stage model owing to an ambiguous moment of conversion under stress conditions. The pitting corrosion depth could be fitted with a lognormal distribution in this study. The probability distributions for the aspect ratios of corrosion pits under different stress conditions tended to be consistent. Finally, the block's maximum pitting factor followed a Gumbel distribution with a scale parameter that changed linearly with the stress level and a location parameter related to the square of the stress level. [ABSTRACT FROM AUTHOR]

In this paper we consider a special kind of semicontinous distribution. We try to concern with the situation where the probability of zero observation is associated with the location and scale parameters in lognormal distribution. We first propose a goodness-of-fit test to ensure that the data can be fit by the associated delta-lognormal distribution. Then we define the updated fiducial distributions of the parameters and establish the results that the confidence interval has asymtotically correct level while the significance level of the hypothesis testing is also asymtotically correct. We propose an exact sampling method to sample from the updated fiducial distribution. It can be seen in our simulation study that the inference on the parameters is largely improved. A real data example is also used to illustrate our method. [ABSTRACT FROM AUTHOR]

A total of 1,348 endophytic fungal strains were isolated from Ferula ovina, F. galbaniflua, and F. persica. They included Eurotiales (16 species), Pleosporales (11 species), Botryosphaeriales (1 species), Cladosporiales (2 species), Helotiales (6 species), Hypocreales (31 species), Sordariales (7 species), Glomerellales (2 species), and Polyporales (1 species). F. ovina had the richest species composition of endophytic fungi, and the endophytic fungi were most abundant in their roots compared to shoots. Chao, Margalef, Shannon, Simpson, Berger--Parker, Menhinick, and Camargo indices showed that F. ovina roots had the most endophytic fungal species. The frequency distribution of fungal species isolated from Ferula spp. fell into the log-series model, and F. ovina roots had the highest Fisher alpha. The dominance indices showed that there are no dominant species in the endophytic fungal community isolated from Ferula spp., indicating community stability. Evenness values were 0.69, 0.90, 0.94, and 0.57 for endophytic fungi isolated from F. ovina roots, F. ovina shoots, F. galbaniflua roots, and F. persica roots, respectively, indicating a species distribution that tends toward evenness. The fungal species community isolated from each of F. ovina roots, F. ovina shoots, F. galbaniflua roots, and F. persica roots was a diverse species group originating from a homogeneous habitat. Their distribution followed a log-normal distribution, suggesting that the interactions of numerous independent environmental factors multiplicatively control species abundances. Principal component analysis showed that the highest species diversity and dominance were observed in the endophytic fungal community isolated from F. ovina and F. persica roots, respectively. [ABSTRACT FROM AUTHOR]

Aggregate measures play an important role in the analysis of socio-economic phenomena. Various concepts for the construction of aggregate measures have been developed in the source literature. The relative taxonomy method proposed by Wydymus and its modification for the dynamic approach is the subject of interest in the presented article. Measures of central tendency are used in the construction of relative taxonomy method: in the classical version—the arithmetic mean, and in the positional version—the median. It was proposed to apply three robust measures of central tendency: trimmed mean, Winsorized mean, biweight mean. Robust location measures reduce the impact of extreme variable values on the aggregate measure values. The purpose of the article is to examine the usability of the measures of central tendency in ranking a set of objects based on the dynamic relative taxonomy. For this purpose, the degree of compatibility of the rankings of objects in terms of individual variables with the ranking based on the aggregate measure was assess. The rationale for this criterion is that the overall ranking is a resultant of rankings obtained for the individual variables. Kendall's tau correlation coefficient was applied as the measure of rankings compatibility. The empirical data on social cohesion and simulation data were used in the comparative analysis. For both the empirical data and all simulations, the findings collected with robust measures of central tendency are better than the ones obtained using the arithmetic mean. For the simulation data generated from the normal distribution, the highest degree of compatibility of the rankings of objects were achieved for the trimmed mean and the biweight mean. In turn, for the simulation data generated from three distributions (normal, lognormal, and Weibull), significantly better results in assessing the degree of compatibility of the rankings of objects were recorded for the median and the biweight mean. [ABSTRACT FROM AUTHOR]

In this article, we describe the mixrandregret command, which extends the randregret command introduced in Gutiérrez-Vargas, Meulders, and Vandebroek (2021, Stata Journal 21: 626–658) by allowing random coefficients in random regret minimization models. The newly developed mixrandregret command allows the user to specify a combination of fixed and random coefficients in the regret function of the classical random regret minimization model introduced in Chorus (2010, European Journal of Transport and Infrastructure Research 10: 181–196). In addition, the user can specify normal and lognormal distributions for the random coefficients using the appropriate command's options. The models are fit by maximum simulated likelihood estimation using numerical integration to approximate the choice probabilities. [ABSTRACT FROM AUTHOR]

The grain‐size distributions of sediments can yield important information about sediment provenance and sedimentary processes; however, grain‐size distributions are frequently polymodal, rendering analyses difficult. To improve analyses of polymodal grain‐size data, the present study decomposed the grain‐size distributions of bottom surface sediments from Lake Kitaura, a shallow lake in Japan, into lognormal distributions and performed logratio analysis of their mixing proportions. The polymodal grain‐size distributions of the studied samples were separated into four common components at most sites. This logratio analysis revealed clear differences in the characteristics of the spatial distributions of the separated grain‐size components. The logratio values indicated that the three finer components were uniformly deposited within the lake, whereas the coarsest component was spatially diverse, reflecting differences in their sources and sedimentary processes. These results demonstrate the effectiveness of decomposition and logratio analysis of polymodal grain‐size distributions for estimating sedimentary processes. This method can be applied to modern sediments and for palaeoenvironmental reconstructions using sediment cores. [ABSTRACT FROM AUTHOR]

This research investigates exhalation rates of radon (222Rn) and thoron (220Rn) from soil samples in the Jaunsar-Bawar region of the Indian Himalayas. Before sampling, gamma radiation rates were evaluated, ranging from 0.08 to 0.33 µSv/h. The observed 222Rn mass exhalation rates range between 3.56 and 82.08 mBq/kg/h, with an average of 25.67 mBq/kg/h. Additionally, the surface exhalation rate of 220Rn varies from 1.28 to 22.69 Bq/m2/s, averaging 7.90 Bq/m2/s. Projected 220Rn mass emission rates span 154–2356 mBq/kg/s, with a mean of 939 mBq/kg/s. The dataset analysis employs best-fit statistics, revealing the Weibull distribution as the optimal model for gamma dose rate and 220Rn mass emanation rates. Lognormal distribution suits 222Rn mass exhalation rates, and the Gamma distribution excels for 220Rn surface exhalation rates, aligning with log-likelihood estimator indications. [ABSTRACT FROM AUTHOR]

The class of log-symmetric distributions is a generalization of log-normal distribution and includes some well-known distributions such as log-normal, log-logistic, log-Laplace, log-Cauchy, log-power-exponential, log-student-t, log-slash, and Birnbaum-Saunders distributions. In this paper, several characterization results are obtained for log-symmetric distributions based on moments of some functions of the parent distribution and also on the basis of some properties of order statistics. Specifically, when X is identical in distribution with a decreasing continuous function $ h(X) $ h (X) , then a relationship is established between upper and lower order statistics which is then utilized to construct characterization results for log-symmetric distributions in terms of functions of order statistics. The established results can be used for constructing a goodness-of-fit test for log-symmetric distributions. [ABSTRACT FROM AUTHOR]

This study proposes a new approach to estimate the parameters of the two-parameter Weibull distribution in the case of complete (uncensored) or doubly Type II censored samples. The proposed estimators have closed forms and can be adapted to Type II right or Type II left censored samples. The new estimators are strongly consistent and the new shape estimator follows asymptotically a normal and the new scale estimator a lognormal distribution. Bias, mean square and efficiency performance of the new estimators are investigated through simulations and compared to some known estimation methods such as maximum likelihood estimation, method of moments, quantile estimation, maximum goodness of fit estimation, L-moments, U-statistics and bias-corrected maximum likelihood. According to the simulations, the newly proposed estimators seem to have good efficiency performance in comparison to the other methods, particularly in small samples. Furthermore, two real data sets are used to illustrate the new estimators. [ABSTRACT FROM AUTHOR]

A digital core technique was utilized for three-dimensional (3D) reconstruction of reef limestone and the maximum-ball algorithm was adopted to extract the pore network model, thus realizing the quantification and 3D visualization of pore throats in reef limestone. Meanwhile, the digital core technology was combined with the fractal theory to calculate the two-dimensional (2D) and 3D fractal dimensions of reef limestone of four different densities. The results show that the slice-by-slice porosity of reef limestone is highly discrete, and the porosity of reef limestone gradually reduces as its density increases. The pore and throat radii of reef limestone of different densities both follow the logarithmic normal distribution while the throat length follows the Gaussian distribution. The coordination number of reef limestone is mainly distributed in the range of 2.73 to 8.65. As the density increases, pore connectivity gradually weakens. The sphericity of reef limestone exhibits a strong exponential correlation with the pore radius The fractal dimension of reef limestone is mainly distributed in the range of 2.392 to 2.697 and tends to decline gradually with the increase in density. [ABSTRACT FROM AUTHOR]

Several studies have been carried out to assess the building's seismic vulnerability, to mitigate the seismic risk in urban areas, which is one of the most devastating natural hazards causing considerable economic and human losses. These studies must be incorporated to improve the planning of urban areas to have resistant and resilient cities in case of disasters. The seismic feedback has shown that the build-back-better concept has a direct impact on the city's economic growth. In this paper, the existing buildings' resilience is assessed, in order to highlight the capacity of these last to keep the functionality when an earthquake occurs. This building's resilience has been determined for three types of structures: masonry, reinforced concrete and steel, according to the reconstruction time, the reconstruction cost and the damage state. This last has been assessed from empirical fragility curves developed using the log normal distribution for five structures typologies (Unreinforced masonry; reinforced masonry; RC frame; RC shear walls/Mixed RC frame-RC shear walls and steel structures). A seismic resilience scenario was performed using a geographic information system (GIS) and applied for the Blida city (Algeria) classified as a high seismic zone according to Algerian seismic regulations. According to the results found, the old districts of the Blida city, built mainly during the so-called pre-code period, will not be resilient in case of disaster. The other districts built later in the low-code and high-code periods will have, respectively, medium and good functionality. [ABSTRACT FROM AUTHOR]

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model. [ABSTRACT FROM AUTHOR]

In many industries, the reliability of a product is often determined by a quantile of a distribution of a product's characteristics meeting a specified requirement. A typical approach to address this is to assume a parametric model and compute a one‐sided confidence bound on the quantile. However, this can become difficult if the sample size is too small to reliably estimate such a parametric model. Linear interpolation between order statistics is a viable nonparametric alternative if the sample size is sufficiently large. In most cases, linear extrapolation from the extreme order statistics can be used, but can result in inconsistent coverage. In this work, we perform an empirical study to generate robust weights for linear extrapolation that greatly improves the accuracy of the coverage across a feasible range of distribution families with positive support. Our method is applied to two industrial datasets. [ABSTRACT FROM AUTHOR]

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages. [ABSTRACT FROM AUTHOR]

To investigate the variation law of corrosion damage of steel wires for bridge cables, the accelerated stress-corrosion test was carried out. The corrosion surface of steel wires was collected by virtue of a three-dimensional topography instrument, and the surface characteristic parameters of steel wires were also statistically analyzed under different corrosion ages and initial strains. Finally, the maximum pit depth of steel wires was estimated by the analysis method of extreme value. The results showed that the stress corrosion intensified the corrosion degree of steel wires under the same corrosion age, and the maximum discrepancy was nearly 20%. However, the high strain level had a lower influence on the growth rate of corrosion degree in the later stage of corrosion. The pit depth of steel wires more conformed to the lognormal distribution under the unstressed condition, while the corrosion depth of steel wires more closely conformed to the normal distribution under the stress condition. The fractal dimension could not only reflect the unevenness of the corrosion surface, but also be used as one of evaluation indicators of corrosion degree. The maximum pit depth obtained from the sampling inspection data was hazardous, and it was safe and feasible to take the results from the analysis method of extreme value. [ABSTRACT FROM AUTHOR]

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As nanoparticle syntheses on a large scale usually yield products with broad size and shape distributions, the properties of nanoparticle-based products need to be tuned after synthesis by narrowing the size and shape distributions or via the removal of undesired fractions. The development of property-selective classification processes requires a universal framework for the quantitative evaluation of multi-dimensional particle fractionation processes. This framework must be applicable to any property and any particle classification process. We extended the well-known one-dimensional methodology commonly used for describing particle size distributions and fractionation processes to the multi-dimensional case to account for the higher complexity of the property distribution and separation functions. In particular, multi-dimensional lognormal distributions are introduced and applied to diameter and length distributions of gold nanorods. The fractionation of nanorods via centrifugation and by orthogonal centrifugal and electric forces is modeled. Moreover, we demonstrate that analytical ultracentrifugation with a multi-wavelength detector (MWL-AUC) is a fast and very accurate method for the measurement of two-dimensional particle size distributions in suspension. The MWL-AUC method is widely applicable to any class of nanoparticles with size-, shape- or composition-dependent optical properties. In addition, we obtained distributions of the lateral diameter and the number of layers of molybdenum disulfide nanosheets via stepwise centrifugation and spectroscopic evaluation of the size fractions. [ABSTRACT FROM AUTHOR]

In the existing multidimensional extensions of the log-normal response time (LNRT) model, the log response times are decomposed into a linear combination of several latent traits. These models are fully compensatory as low levels on traits can be counterbalanced by high levels on other traits. We propose an alternative multidimensional extension of the LNRT model by assuming that the response times can be decomposed into two response time components. Each response time component is generated by a one-dimensional LNRT model with a different latent trait. As the response time components—but not the traits—are related additively, the model is partially compensatory. In a simulation study, we investigate the recovery of the model's parameters. We also investigate whether the fully and the partially compensatory LNRT model can be distinguished empirically. Findings suggest that parameter recovery is good and that the two models can be distinctly identified under certain conditions. The utility of the model in practice is demonstrated with an empirical application. In the empirical application, the partially compensatory model fits better than the fully compensatory model. [ABSTRACT FROM AUTHOR]

Coarse-grained molecular dynamics simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) through the self-assembly of randomly distributed amphiphilic BAB triblock copolymers with hydrophilic A and hydrophobic B blocks in an aqueous solution. The vesiculation pathway consists of several intermediate structures, such as an interconnected network of copolymer aggregates, a cage of cylindrical micelles, and a lamellar cage. The cage-to-vesicle transition occurs at a constant aggregation number and practically eliminates the hydrophobic interfacial area between the B block and solvent. Molecular reorganization underlying the sequence of morphology transitions from a cage-like aggregate to a vesicle is nearly isentropic. The end-to-end distances of isolated copolymer chains in solution and those within a vesicular assembly follow lognormal probability distributions. This can be attributed to the preponderance of folded chain configurations in which the two hydrophobic end groups of a given chain stay close to each other. However, the probability distribution of end-to-end distances is broader for chains within the vesicle as compared with that of a single chain. This is due to the swelling of the folded configurations within the hydrophobic bilayer. Increasing the hydrophobicity of the B block reduces the vesiculation time without qualitatively altering the self-assembly pathway. [ABSTRACT FROM AUTHOR]

The Changzhou ship lock is approaching its capacity limit. In order to quantitatively analyze the influencing factors that restrict the capacity of the Changzhou ship lock, this study proposes an influencing factor analysis method based on principal component analysis (PCA). This method estimates the confidence interval of ship passing time by fitting a lognormal distribution curve, eliminates redundancy in navigability data by combining the hydrological data and cargo load data, and quantitatively analyzes the influencing factors of ship lock capacity under saturated operating conditions. The results show that the influencing factors of Changzhou ship lock capacity are classified according to their influence contribution rate as minimum water depth above the lock sill, operation direction, ship dimensions, draft, loading capacity, and actual load. The research results can provide a theoretical basis for improving the ship lock capacity and have application value for lock scheduling management. [ABSTRACT FROM AUTHOR]

In this study, the ice loads on a scaled four-legged semi-submersible in a broken ice field were measured in a wave tank. Artificial ice models made of paraffin were applied in the experiment. The influence of ice floe properties, type of platform, incident velocity, and incident angle on ice loads was investigated. Shelter effect were observed most effective at a 0° incident angle, followed by a 45° incident angle. A sensitive analysis showed that a square-shaped platform with a narrow column spacing resulted in reduced ice loads in the broken ice field. The shape of floe has limited influence on the ice load under low incident velocity. Additionally, based on the Kolmogorov–Smirnov test, the lognormal distribution model best fit the experimental data of the ice load peak values (at a 5% significance level). The numerical simulation based on Ice-MAS was validated with experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a novel reliability-based network equilibrium problem for mixed traffic flows of human-driven vehicles (HVs) and connected autonomous vehicles (CAVs) with endogenous CAV market penetration and stochastic link capacity degradations. Travelers' perception errors on travel time and their risk-aversive behaviors on mode choice and path choice are incorporated in the model with a hierarchical choice structure. Due to the differences between HVs and CAVs, the perception errors and the safety margin reserved by risk-averse travelers are assumed to be related to the vehicle type. The path travel time distribution is derived by using the moment-matching method based on the assumption that link capacity follows lognormal distribution and link travel times are correlated. Then, the underlying problem is formulated as an equivalent variational inequality problem. A path-based algorithm embedded with the Monte Carlo simulation-based method is proposed to solve the model. Numerical experiments are conducted to illustrate the features of the model and the computational performance of the solution algorithm. [ABSTRACT FROM AUTHOR]

Impedance spectroscopy experiments are able to reveal the fundamental charge transport properties of a wide variety of complex disordered and nano-structured materials provided that appropriate modeling tools are used. In this paper, we present a numerical simulation-based approach to model the dynamical conductivity of networks formed by self-assembled metal nanoparticles. Inter-particle nano-resistance and nano-capacitance are implemented at the nano-scale assuming inter-particle charge transfer and accumulation mechanisms that can be adapted depending on the nature of the nano-particles and the surrounding medium. The actual positions and spatial arrangements of the nanoparticles within the network are taken into consideration, allowing the attributes of percolating conducting routes to be extracted, classified, and compared in terms of path conductance and statistical distribution of path lengths. Our findings are contrasted to those obtained using analytic models, which are commonly used, but rely on strong assumptions about the electric properties of the conducting paths. We address these assumptions and show that in the case of weakly disordered systems, there is a general agreement between numerical simulations and analytic modeling-based approaches. In the case of disordered networks where the nano-particle size and position fluctuations are included, we show that the path length distribution is frequency-dependent and can differ significantly from the lognormal distribution usually assumed in the analytic models. The impedance of individual pathways may be extracted from the numerical simulations; we discovered that the conductance and susceptance of a specific path are frequency-dependent and inversely proportional to the path length only in ordered networks. Strong scattering of conductance values is caused by disorder effects. The developed numerical approach is generic and applies to most nano-devices where charge transport relies on percolation; it allows to bridge the gap between the nano-scale and micro-scale electric characteristics and, thus, permits a deeper understanding of the charge transport properties of nano-structured materials. [ABSTRACT FROM AUTHOR]

Marketing scholars often compare groups that occur naturally (e.g., socioeconomic status) or due to random assignment of participants to study conditions. These scholars often report group means, standard deviations, and effect sizes. Although such summary information can be helpful, it can misinform marketing practitioners' decisions. To avoid this problem, scholars should also report the probability that one group's member will score higher than another group's member, and by various amounts. In this vein, newly conceived gain-probability diagrams can depict relevant, concise, and easy-to-comprehend probabilistic information. These diagrams' nuanced perspective can contradict traditional significance test and effect size implications. [ABSTRACT FROM AUTHOR]

Background: Belarus and Ukraine were the countries most affected by the consequences of the Chornobyl nuclear power plant in 1986. A study of perinatal mortality in Belarus found a highly statistically significant increase in the 1990s in the most contaminated oblast Gomel but no increase during this period in the rest of Belarus. As a possible mechanism to interpret this increase as a late Chornobyl effect, it has been suggested that strontium-90 contained in Chornobyl fallout, incorporated during menarche, impairs the immune system of pregnant women which in turn increases perinatal mortality. In the present study, this hypothesis is tested using data from Ukraine. Methods: Annual data on perinatal mortality, in the period 1981–2006 were provided by the Ministry of Public Health of Ukraine. Trends in perinatal mortality rates in the most contaminated regions of Ukraine (Kyiv and Zhytomyr oblasts and the city of Kyiv; study region) were compared with rates in the rest of Ukraine (control region). To identify any differences in perinatal mortality trends between the study and control regions, the ratios of perinatal mortality rates in the study region to the rates in the control region were analyzed using the calculated strontium concentration as a predictor. Results: A trend analysis of perinatal mortality rates in Ukraine revealed two bell-shaped deviations from a long-term exponential trend with maxima at the beginning and end of the 1990s. The same pattern was found in the data from the study and control regions, but the deviations were almost three times higher in the study region than in the control region. An analysis of the ratios of perinatal mortality rates in the study region to the rates in the control region (odds ratios) showed an increase and decrease during the 1990s which was approximated by a lognormal density distribution. The calculated strontium concentration, when used as a predictor, also fitted the data well. Thus, the data from Ukraine confirms the results from Belarus. The analysis of the odds ratios revealed about 1000 excess perinatal deaths in the study region in the period 1990–2004. The corresponding figure for Ukraine as a whole was estimated at 3500 perinatal deaths. Conclusion: It is hypothesized that the observed increase in perinatal mortality in the 1990s may be a late effect of incorporated strontium-90 on the immune system of pregnant women. The analysis is based on a theoretical model, as no data on strontium concentrations were available; the results should therefore be interpreted with caution. An updated study for Belarus would be desirable to corroborate the results. [ABSTRACT FROM AUTHOR]

The efficiency of estimating the numerical characteristics of the family of the lognormal law of distribution of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, methods for discretizing the range of values of a random variable based on the Sturgess, Brooks-Carruther, Heinhold-Gaede formulas and the formula proposed by the authors of this article are used. Data arrays have been formed that make it possible to estimate the numerical characteristics of the distribution laws of random variables, taking into account their discrete values. Based on the transformed data sets, estimates of mathematical expectation, standard deviation, asymmetry and kurtosis coefficients were calculated. Estimates of the numerical characteristics of the considered distribution laws for a continuous and discrete random variable with different volumes of initial statistical data are compared. The effectiveness of methods for estimating the numerical characteristics of the family of the lognormal distribution law from the initial statistical data and from the results of transformations of these data using known discretization formulas has been established. The reliability of the comparison of the effectiveness indicators of the studied methods was confirmed using the Kolmogorov-Smirnov criterion. It is shown that the discretization formula proposed by the authors of this article is more efficient in comparison with the traditional Sturgess, Brooks-Carruther, and Heinhold-Gaede discretization formulas. [ABSTRACT FROM AUTHOR]

In this paper, taking into account the inevitable impact of environmental perturbations on disease transmission, we primarily investigate a stochastic model for measles infection with nonlinear incidence. The transmission rate in this model follows a logarithmic normal distribution influenced by an Ornstein--Uhlenbeck (OU) process. To analyze the dynamic properties of the stochastic model, our first step is to establish the existence and uniqueness of a global solution for the stochastic equations. Next, by constructing appropriate Lyapunov functions and utilizing the ergodicity of the OU process, we establish sufficient conditions for the existence of a stationary distribution, indicating the prevalence of the disease. Furthermore, we provide sufficient conditions for disease elimination. These conditions are derived by considering the interplay between the model parameters and the stochastic dynamics. Finally, we validate the theoretical conclusions through numerical simulations, which allow us to assess the practical implications of the established conditions and observe the dynamics of the stochastic model in action. By combining theoretical analysis and numerical simulations, we gain a comprehensive understanding of the stochastic model's behavior, contributing to the broader understanding of measles transmission dynamics and the development of effective control strategies. [ABSTRACT FROM AUTHOR]

For aircraft serving in coastal environments, the aluminum alloy skin is exposed to high temperature, humidity, and salt environment for a long time. Pitting and exfoliation will affect its normal service life. In this article, static salt spray experiments and electrochemical tests were carried out on 2198‐T8 Al–Li alloy in nine different corrosive environments. The effects of salt concentration, temperature, and humidity on the corrosion behavior were analyzed and compared. The relationship between corrosion environment parameters and pits was established. The results show that, under the same corrosion environment, the length, width, and depth of the pits all follow the log‐normal distribution; compared with the salt concentration and humidity, the increase in temperature has the most obvious promotion on the corrosion rate. Based on the frequency statistics of pit size and electrochemical test results, the pit morphology was simplified to a semiellipsoid geometric model, and the pit size in different corrosive environments was predicted. The predicted size data all fall within the 1.5‐fold dispersion region. [ABSTRACT FROM AUTHOR]

The intermittency of gravity wave potential energy (GWPE) in the upper troposphere and stratosphere was investigated using the Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) temperature data over three typical mountains (Tibetan Plateau, Rocky Mountains, and Andes). These typical mountains have high sea level elevations but different land–sea contrast. The probability density function (PDF) of GWPE has the independent variable of GWPE and dependent variable of occurrence probability of GWPE over a region. Our analysis showed that the PDFs of GWPE over these three mountains roughly followed lognormal distributions in all heights and months. But, the key parameters (mean value and standard deviation) of lognormal distribution varied with heights and months. Above each mountain, the two key parameters exhibited similar temporal and spatial distributions. They had the largest values around the tropopause region, smaller values in the lower stratosphere (~20–30 km), and larger values in the upper stratosphere (~35–45 km). The intermittency of GWs is represented as the ratio of the GWPE at 50th percentile to the GWPE at 90th percentile. The weakest intermittency was at ~20–30 km (above the zonal mean winds of zero) over the Tibetan Plateau and Rocky Mountains in all months and over the Andes from November to March, respectively. Generally, the weakest intermittency (~0.4) occurred in the region where the key parameters were the smallest around summer. The key parameters of lognormal distribution were dominated by annual variation over the Andes throughout the height range, 8–50 km. However, the semiannual variations are also significant in the lower stratosphere over the Tibetan Plateau and Rocky Mountains. The seasonal variations in the intermittency were not as obvious as those of the key parameters. The lognormal distributions and the intermittencies derived here provide an observational constraint on the tunable parameters in GW parameterization schemes. [ABSTRACT FROM AUTHOR]

The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) on board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite has been widely used in climate and environment studies to obtain the vertical profiles of atmospheric aerosols. To retrieve the vertical profile of aerosol extinction, the CALIOP algorithm assumes column-averaged lidar ratios based on a clustering of aerosol optical properties measured at surface stations. On one hand, these lidar ratio assumptions may not be appropriate or representative at certain locations. One the other hand, the two-wavelength design of CALIOP has the potential to constrain aerosol size information, which has not been considered in the operational algorithm. In this study, we present a modified inversion algorithm to simultaneously retrieve aerosol extinction and effective radius profiles using two-wavelength elastic lidars such as CALIOP. Specifically, a lookup table is built to relate the lidar ratio with the Ångström exponent calculated using aerosol extinction at the two wavelengths, and the lidar ratio is then determined iteratively without a priori assumptions. The retrieved two-wavelength extinction at each layer is then converted to the particle effective radius assuming a lognormal distribution. The algorithm is tested on synthetic data, Raman lidar measurements and then finally the real CALIOP backscatter measurements. Results show improvements over the CALIPSO operational algorithm by comparing with ground-based Raman lidar profiles. [ABSTRACT FROM AUTHOR]

Background: It is mandatory to label food products with the 14 main allergens in the EU. Reasonable allergen labeling requires knowledge of population‐based thresholds derived from food challenges. The aim of this study was to evaluate the threshold‐distribution in clinically verified food allergic patients for allergens mandatory for labeling. Methods: All positive open oral food challenges and double‐blind placebo‐controlled food challenges (DBPCFC) performed at the Allergy Center, Odense University Hospital, Denmark (2000–2022) were included. For each included challenge, the cumulative threshold (LOAEL) was obtained and NOAEL estimated. Data were modelled as an interval censored log‐normal distribution. Results: Overall, 38 of all 2612 challenges (1.5%) in 1229 patients (717 male, 986 children) reacted to <5 mg protein. The majority of the most sensitive patients reacted with a Sampson severity score of 2–3. Using interval censored log‐normal models only five groups (hens´ egg, fish, peanut, milk, tree‐nuts) elicited reactions after ingestion of 0.5 mg protein and in low frequencies of the population. Hen's egg was the most potent allergen, with reactivity to <0.5 mg protein in 0.24% [0.13–0.44%] of egg allergic patients while the estimated fraction of allergic patients reacting to a eliciting dose on 0.5 mg protein for most other allergens were below 0.04%. Conclusion: Our data demonstrates that the majority of food allergic patients as expected tolerating traces of allergenic foods without developing severe allergic symptoms and signs. Hen's egg appears to be the food most likely to elicit reactions in the most sensitive individuals at very low doses. [ABSTRACT FROM AUTHOR]

The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriate distribution and discriminating among them for a given data to best fit is an important issue. Further, when the data are observed in the presence of some censoring scheme the problem becomes more challenging. In this paper, we address the problem of selecting a more appropriate distribution by discriminating based on the random samples drawn in the presence of type-II censoring. We consider the difference of the maximized log-likelihood functions, and compute the asymptotic distribution of the discrimination statistic. We further propose a modified discriminating approach, and compute the probabilities of correct selection to check the performance of the discrimination procedure. Finally, simulation study is conducted, and two real data sets are analysed for the illustration purpose. [ABSTRACT FROM AUTHOR]