Statistical Distribution Model Research Articles

Characteristics of physical parameters and predictive modeling of mechanical properties in loess-like silty clay for engineering geology

In the middle and lower reaches of the Yellow River in China, loess-like silty clay is prevalent. This soil type exhibits considerable variability in its compression coefficient α, which can lead to differential soil settlement and consequent damage to buildings and infrastructure, thereby posing safety risks. Despite its significance, research and data on this topic are still limited. This study involves comprehensive measurement and laboratory analysis of over one thousand soil samples collected on-site. It establishes a statistical distribution model for essential parameters, including water content w, wet density ρ, void ratio e, saturation Sr, liquidity index IL, liquid limit WL, plastic limit WP, and plasticity index IP, and explores the probability distribution characteristics of the physical and mechanical parameters of loess-like silty clay. Machine learning prediction models, utilizing Random Forest (RF) and Deep Neural Network (DNN) algorithms, were developed based on an extensive database to forecast the compression coefficient α and compression modulus ES of this soil. The predictive models demonstrated higher accuracy compared to conventional methods and hold significant practical implications for the timely prediction of the mechanical and engineering characteristics of loess-like silty clay. This research provides a robust scientific foundation for engineering design, enhances understanding of the mechanical properties and engineering attributes of this special soil expanse, and reduces the high costs and time consumption associated with engineering geological surveys, as well as the subjectivity of technical and environmental constraints and data interpretation. It serves as a valuable tool for disaster prevention and prediction.

Ultrasound Biomarkers: Contrast-enhanced Ultrasound and Nakagami Imaging to Differentiate Benign and Malignant Choroidal Tumor

Purpose We hypothesized that contrast-enhanced ultrasound (CEUS) using a microbubble technique to quantify microvascular changes and Nakagami imaging for tissue characterization would provide a new approach for diagnosing and differentiating benign and malignant choroidal lesions. Methods Five patients with choroidal melanoma (CM) and five patients with choroidal hemangioma (CH) were selected. Definity®, which contains perflutren microbubbles, was administered as a slow IV bolus (1 ml). CEUS was performed for 1 min postinjection of the contrast agent with ultrasound radiofrequency data acquired from 10 s to 60 s. The contrast value was calculated for the whole tumor region. A gradient magnitude method was used for each postcontrast frames with 1-second interval, and the time-averaged value in pixel intensity gradient of postinjection frames was estimated and reported. Based on the Nakagami statistical distribution model, two Nakagami parameters, m and Ω, where m (shape parameter), representing tissue heterogeneity, and Ω (scale parameter), representing the average energy of backscattered signals, were studied. Results CEUS analysis showed that the time-averaged estimated contrast was significantly higher (p = 0.008) for CH compared to CM. Furthermore, the time-averaged contrast within the normal choroidal region was significantly higher than the choroidal tumor region for both CH and CM (p = 0.001 for CH cases and p < 0.0001 for CM cases). Nakagami analysis showed that the m estimates were significantly higher (p = 0.032) for CH (m = 0.61) than for CM (m = 0.28), indicating that CH is a more heterogeneous tumor than CM. The Ω estimates were significantly higher (p = 0.0019) for CH (Ω = 0.15) compared to CM (Ω = 0.03). These results may be due to the more vascular structures in CH compared to CM. Conclusions Quantitative intensity-based perfusion analysis using CEUS and backscattering tissue analysis using Nakagami imaging can provide valuable insights to differentiate benign and malignant choroidal lesions.

Kriging-based surrogate data-enriching artificial neural network prediction of strength and permeability of permeable cement-stabilized base

Limited test data hinder the accurate prediction of mechanical strength and permeability of permeable cement-stabilized base materials (PCBM). Here we show a kriging-based surrogate model assisted artificial neural network (KS-ANN) framework that integrates laboratory testing, mathematical modeling, and machine learning. A statistical distribution model was established from limited test data to enrich the dataset through the combination of markov chain monte carlo simulation and kriging-based surrogate modeling. Subsequently, an artificial neural network (ANN) model was trained using the enriched dataset. The results demonstrate that the well-trained KS-ANN model effectively captures the actual data distribution characteristics. The accurate prediction of the mechanical strength and permeability of PCBM under the constraint of limited data validates the effectiveness of the proposed framework. As compared to traditional ANN models, the KS-ANN model improves the prediction accuracy of PCBM’s mechanical strength by 21%. Based on the accurate prediction of PCBM’s mechanical strength and permeability by the KS-ANN model, an optimization function was developed to determine the optimal cement content and compaction force range of PCBM, enabling it to concurrently satisfy the requirements of mechanical strength and permeability. This study provides a cost-effective and rapid solution for evaluating the performance and optimizing the design of PCBM and similar materials.

DMR_Kmeans: Identifying Differentially Methylated Regions Based on k-means Clustering and Read Methylation Haplotype Filtering

Introduction:: Differentially methylated regions (DMRs), including tissue-specific DMRs and disease-specific DMRs, can be used in revealing the mechanisms of gene regulation and screening diseases. Up until now, many methods have been proposed to detect DMRs from bisulfite sequencing data. In these methods, differentially methylated CpG sites and DMRs are usually identified based on statistical tests or distribution models, which neglect the joint methylation statuses provided in each read and result in inaccurate boundaries of DMRs. Methods:: In this paper, a method, named DMR_Kmeans, is proposed to detect DMRs based on kmeans clustering and read methylation haplotype filtering. In DMR_Kmeans, for each CpG site, the k-means algorithm is used to cluster the methylation levels from two groups, and the methylation difference of the CpG is measured based on the different distributions in clusters. Methylation haplotypes of reads are employed to extract the methylation patterns in a candidate region. Finally, DMRs are identified based on the methylation differences and the methylation patterns in candidate regions. Result:: Comparing the performance of DMR_Kmeans and eight DMR detection methods on the whole genome bisulfite sequencing data of six pairs of tissues, the results show that DMR_Kmeans achieves higher Qn and Ql, and more overlapped promoters than other methods when given a certain threshold of methylation difference greater than 0.4, which indicates that the DMRs predicted by DMR_Kmeans with accurate boundaries contain less CpGs with small methylation differences than those by other methods. Conclusion:: Furthermore, it suggests that DMR_Kmeans can provide a DMR set with high quality for downstream analysis since the total length of DMRs predicted by DMR_Kmeans is longer and the total number of CpG sites in the DMRs is greater than those of other methods.

Application of the Parametric Bootstrap Method for Confidence Interval Estimation and Statistical Analysis of PM2.5 in Bangkok

Research in epidemiology and health science indicates that exposure to particles with an aerodynamic diameter of less than 2.5 µm (PM2.5) causes harmful health consequences. Probability density functions (pdf) are utilized to analyze the distribution of pollutant data and study the occurrence of high-concentration occurrences. In this study, PM2.5 concentrations (in μg/m^3 ) were recorded daily from January 2011 to December 2022 at 12 air quality monitoring locations in Bangkok. The study utilized two-parameter distributions such as gamma, inverse Gaussian, lognormal, log-logistic, Weibull, and Pearson type V to identify the most suitable statistical distribution model for PM2.5 in Bangkok. The Anderson-Darling test result indicates that the inverse Gaussian and Pearson type V distributions are the most appropriate probability density functions for the daily average PM2.5 concentration at stations in Bangkok. The projected 98th percentile of daily PM2.5 levels at two locations is higher than the 24-hour threshold for daily PM2.5 concentrations in Thailand, posing significant health risks. Additionally, the two parametric bootstrap methods used to estimate confidence intervals for the median, namely percentile bootstrap and simple bootstrap, indicate that two stations have poor air quality for those with sensitive health conditions.

On the directional nature of celestial object’s fall on the earth (Part 1: Distribution of fireball shower, meteor fall &amp; crater on earth’s surface)

Abstract This paper investigates the directional distribution of extraterrestrial objects (meteors, fireballs, and craters) impacting Earth’s surface, and introduces a novel directional statistical mixture model to analyze their falls, validated through rigorous testing. First, we address whether these falls follow non-uniform directional patterns by explicitly employing directional statistical tools for analyzing such data. Using projection techniques for longitude and latitude and more importantly, a general spherical statistical approach, we statistically investigate the suitability of the von Mises distribution and its spherical version, the von Mises Fisher distribution, (a maximum entropy distribution for directional data). Moreover, leveraging extensive datasets encompassing meteor falls, fireball showers, and craters, we propose and validate a novel mixture von Mises-Fisher model for comprehensively analyzing extraterrestrial object falls. Our study reveals distinct statistical characteristics across datasets: fireball falls exhibit non-uniformity, while meteor craters suggest a potential for both uniform and von Mises distributions with a preference for the latter after further refinement. Meteor landings deviate from a single directional maximum entropic distribution; we demonstrate the effectiveness of an optimal 13-component mixture von Mises-Fisher distribution for accurate modeling. Similar analyses resulted in 3- and 6-component partitions for fireball and crater datasets. This research presents valuable insights into the spatial patterns and directional statistical distribution models governing extraterrestrial objects’ fall on Earth, useful for various future works.

A New Synthetic Aperture Radar Ship Detector Based on Clutter Intensity Statistics in Complex Environments

In complex environments, the clutter statistical characteristics of synthetic aperture radar (SAR) are inconstant, and the constant detection performance of a false alarm rate (CFAR) detector based on a clutter statistical model is also hard to achieve. As a result, the overestimated threshold leads to a degradation in detection probability. To this end, this paper proposes a SAR ship detector different from CFAR detectors, which is independent of traditional clutter statistical distribution models and the probability of a false alarm (PFA). The proposed detector aims to raise the ship detection probability and alleviate interference from complex environments such as multi-target areas, shores, and breakwaters. It estimates clutter-truncated thresholds based on clutter intensity statistics (CIS). Firstly, three statistical parameters, including the mean, standard deviation, and maximum intensity of background clutter contaminated by outliers, are calculated; secondly, these parameters are utilized to estimate the clutter-truncated threshold using the novel CIS; and finally, the pixel under test is determined according to the CIS detection rule. Compared with CFAR-based algorithms, CIS obtains a high probability of detection in complex environments. As for other aspects, the CIS detector is insensitive to the structure of the detection window, as well as the size. It is also computationally efficient due to its simple calculations. The superiority of the CIS detector is validated on scene-differed SAR images from the DSSDD dataset.

The effect of water temperature changes on biological water quality assessment

Increasing temperatures caused by anthropogenic climate change are leading to changes in the composition of local communities across biomes. This has implications for ecological assessment methods that rely on macroinvertebrates as bioindicators of water quality. To investigate the influence of changing water temperature on these assessment methods, we analysed macroinvertebrate data from Swiss national monitoring programs. We used a species distribution model to simulate temperature change effects on macroinvertebrate communities and estimated the resulting changes on three biological indices commonly used in Switzerland, namely the species richness of Ephemeroptera, Plecoptera and Trichoptera (EPT), the Swiss biological (IBCH) index along with its components, as well as the species at risk pesticides (SPEARpesticides) index. While results vary by temperature scenario and index, our model results for the most realistic water temperature increase scenario of + 2 °C across most sites in Switzerland suggest no, or only a minor, influence of temperature (not accounting for other hydrological changes). Our model projection predicted only a small increase in the probability of occurrence for 70 % of the studied families. The sensitivity to temperature as captured in our model is generally not very high and varies among the biological indices: on average across all sites, a + 2 °C increase in temperature resulted in a 7 % increase in EPT species richness, a 4 % increase in the IBCH index, and a less than 1 % increase in the SPEARpesticides index. Our study suggests the robustness of these biological indices to moderate warming and points towards the usefulness of these biological indices for the next few decades as tools for water quality assessment. Despite some limitations of statistical species distribution models (e.g., not accounting for dispersal limitation or biotic interactions, predictive performance varying by taxon), the study provides valuable insights into the complex relationships between environmental factors and macroinvertebrate communities, and the potential impacts of future temperature change. These findings can inform conservation and management efforts for these important ecological systems.

Statistical distributions of free surface elevation and wave height for out-of-equilibrium sea-states provoked by strong depth variations

As unidirectional irregular wave trains propagate over a steep shoal, the sea-state becomes out-of-equilibrium and is continuously affected by the non-equilibrium dynamics (NED) over dozens of characteristic wavelengths. Using the set of accurate numerical simulations of Zhang et al. (2022), the NED effects on the probability distributions of free surface elevation and wave height, the statistical moments and maximum wave statistics are investigated, in both near-field and far-field regions after the water depth transition. The primary contribution of this work is to assess the applicability and limitations of several popular statistical distribution models in describing non-equilibrium statistics. In addition, a new distribution of the free surface elevation in a lognormal shape is proposed, which predicts the non-equilibrium free surface statistics with satisfactory performance and characterizes well the skewness–kurtosis relationship in the short scale. It is shown that the statistics in the far-field region are significantly influenced by the near-field wave-wave interaction, and beyond the capability of all statistical models considered here. Despite this complexity, the sea-state in the far-field region exhibits lower freak wave probability than a Gaussian sea-state. Implications of these findings for engineering practices are discussed.

ТЕХНОЛОГИЯ ВОССТАНОВЛЕНИЯ БЛОКОВ ЦИЛИНДРОВ С ДЕФЕКТОМ КРЫШКИ КОРЕННОЙ ОПОРЫ И ОЦЕНКА КАЧЕСТВА ИХ РЕМОНТА С ПОМОЩЬЮ СТАТИСТИЧЕСКОЙ МОДЕЛИ НАДЕЖНОСТИ

Currently, the reconditioning of engine blocks featuring ‘split joint’ main bearing caps is challenging since there is no basic technology for the rebuilding process. The paper introduces a method for restoring engine blocks with and without the described design feature and discusses the possibility of using a mathematical distribution of the engine life to assess the repair quality. Methods of the mathematical planning theory were used to assess the quality of an overhauled engine. A multifactorial experiment was conducted to obtain experimental data. The overhaul quality properties were analysed to identify indicators and parameters which are critical for assessing the quality of engine repairs. The study established indices of the engine life, namely, the mean life, for assessing the quality of an overhauled engine. For determining the engine reliability, the distribution law of indices for sampling the engine lifetime data was established. Currently, engine blocks featuring ‘split joint’ main bearing caps are not repaired. The technological solution to reconditioning the described engine blocks involves milling the contact surface of the main bearing cap and working it up to exclude lateral displacement during operation. Computations used the reliability index, the mean life between overhauls for assessing the quality of an overhauled engine. The authors came up with a statistical model of the engine life distribution with a confidence coefficient of 91 %.

Modelling Mixed Traffic Time Headway Distribution Induced by Bus Rapid Transit (BRT) in Cape Town, South Africa

Background: The safety and capacity of roadways are immensely influenced by time headways, a major traffic flow characteristic. Time headways are frequently utilized in various aspects of traffic and transportation engineering studies, including capacity analyses, studies of safety, modelling of lane-changing and car-following behaviour, and level of service assessment. Time headway, measured in seconds, refers to the distance between two subsequent passing cars moving over a single spot on the road. This paper reports the statistical modelling of the time headway distribution of a mixed traffic flow scenario caused by BRT via statistical headway distribution models. The paper posits that the introduction of BRT dedicated lane and its adopted design configuration induces anomalous traffic flows on its adjoining lanes with attendant time headway differentials, irrespective of the type of adopted design configuration for the corridor. The objectives of this study were to fit the BRT-induced time headway distribution to probability distribution models and determine the most appropriate distribution model that fits the data derived using the goodness of fit tests. Consequently, this contribution, therefore, fills the gap in research with respect to determining the precise model that fits the time headway distribution of mixed traffic flow scenarios induced by BRT. Methods: The time headway distribution data collected at four designated road segments on a multilane provincial route R27 caused by BRT dedicated lane in Cape Town, South Africa, were fitted to five probability distribution models viz, Lognormal, Inverse Gaussian, Log-logistic, Generalized Extreme Value (GEV), and Burr using MATLAB software. The fitted headway data were with respect to the traffic flows on the adjoining lanes to BRT or traffic flow ‘without BRT’. Precisely, the empirical data were collected over a three-month period using an Automatic Traffic Counter (ATC). Using ModelRisk software, the goodness of fit of the probability models was assessed by the Akaike Information Criterion (AIC), the Schwartz or Bayesian Information Criterion (SIC or BIC), the Hannan Quinn Information Criterion (HQIC), and the loglikelihood (LLH) model performance criteria respectively. The distribution model with the lowest AIC criterion and largest loglikelihood (LLH) values describe the model that best fits the headway data across the four sites. Results: Results showed that the models fitted the headway data well at each site by visual inspection of the attendant Probability Density Function (PDF) and the Probability plots (P-P). However, the Burr distribution provided the overall best fit based on the AIC and LLH values at 95% confidence and 0.05 significance levels across the four sites. At sites 02, 03, and 04, it ranked first with the lowest AIC values of 4025.99, 2595.56, 3815.36, and corresponding largest LLH values of -2008.98, -1293.76, and -1903.66, respectively, while the lognormal distribution performed best at site 01, with AIC value of 4445.14 and LLH value of -2220.57, closely followed by the Burr distribution with AIC and LLH values of 4453.05 and -2222.51, respectively. The P-values, which ranged between 0.65 and 0.80, showed the likelihood of the occurrence of the data sets under the null hypothesis. Hence the null hypothesis was accepted. Conclusion: The study concluded that the introduction of BRT dedicated lanes affects the adjoining lanes’ mixed traffic time headways’ distribution, and the headways are continuously distributed, hence fitting continuous probability distributions.

THE IMPACT OF HYDROLOGICAL RESEARCH, MUNICIPAL AUTHORITIES, AND RESIDENTS ON RAINWATER MANAGEMENT IN GDAŃSK (POLAND) IN THE PROCESS OF ADAPTING THE CITY TO CLIMATE CHANGE

Aim of the study: The city of Gdańsk faces changing climatic conditions that result in a higher frequency of extreme weather events. In response to the increasingly frequent appearance of flash floods, scientific research was carried out on changes in the probability of the occurrence of maximum daily precipitation in Gdańsk. The purpose of this paper is to show the role of hydrological research (science), decisions of local authorities and the engagement of residents in the process of adapting Gdańsk to climate change. Material and methods: The hydrological analysis was carried out using rainfall observations from the Gdańsk Rębiechowo station (1974-2021). Log-normal distribution was used as a statistical model for the precipitation probability distribution. To show the role of the city authorities’ decisions, the methodology developed and used by Gdańsk Water company for rainwater management was presented. To emphasize the importance of city residents in climate adaptation process, the methods adopted by city authorities to involve citizens in the advisory process are discussed, namely Civic Panels and the Gdańsk Climate Change Forum. Results and conclusions: The probability distributions of maximum precipitation for different periods were developed, showing a substantial increase of precipitation with a probability of p=1%. Consequently, changes were introduced in the rainwater management practices by the company Gdańsk Water. Being aware of rising flood hazard, Gdańsk City Hall has embraced a plan for adapting the city to climatic changes by 2030. The local authorities decided to involve citizens in the decision-making process. To this end, discussion panels were organized, and the Gdańsk Climate Change Forum was initiated.

Learning geometric Jensen-Shannon divergence for tiny object detection in remote sensing images.

Tiny objects in remote sensing images only have a few pixels, and the detection difficulty is much higher than that of regular objects. General object detectors lack effective extraction of tiny object features, and are sensitive to the Intersection-over-Union (IoU) calculation and the threshold setting in the prediction stage. Therefore, it is particularly important to design a tiny-object-specific detector that can avoid the above problems. This article proposes the network JSDNet by learning the geometric Jensen-Shannon (JS) divergence representation between Gaussian distributions. First, the Swin Transformer model is integrated into the feature extraction stage as the backbone to improve the feature extraction capability of JSDNet for tiny objects. Second, the anchor box and ground-truth are modeled as two two-dimensional (2D) Gaussian distributions, so that the tiny object is represented as a statistical distribution model. Then, in view of the sensitivity problem faced by the IoU calculation for tiny objects, the JSDM module is designed as a regression sub-network, and the geometric JS divergence between two Gaussian distributions is derived from the perspective of information geometry to guide the regression prediction of anchor boxes. Experiments on the AI-TOD and DOTA datasets show that JSDNet can achieve superior detection performance for tiny objects compared to state-of-the-art general object detectors.

Analysis of heat transfer enhancement of passive methods in tubes with machine learning

This study investigates the efficacy of machine learning techniques and correlation methods for predicting heat transfer performance in a dimpled tube under varying flow conditions, including the presence of nanoparticles. A comprehensive numerical analysis involving 120 cases was conducted to obtain Nusselt numbers and friction factors, considering different dimple depths and velocities for both pure water and water-Al2O3 nanofluid at 1%, 2%, and 3% volume concentrations. Utilizing the data acquired from the numerical simulations, a correlation equation, SVM ANN architectures were developed. The predictive capabilities of the statistical approach, ANN, and SVM models for Nusselt number distribution and friction factor were meticulously assessed through mean average percentage error (MAPE) and correlation coefficients ( R2). The research findings reveal that machine learning techniques offer a highly effective approach for accurately predicting heat transfer performance in a dimpled tube, with results closely aligned with Computational Fluid Dynamics (CFD) simulations. Particularly noteworthy is the superior performance of the ANN model, demonstrating the most precise predictions with an error rate of 2.54% and an impressive R2 value of 0.9978 for Nusselt number prediction. In comparison, the regression model achieved an average error rate of 6.14% with an R2 value of 0.8623, and the SVM model yielded an RMSE value of 2.984% with an R2 value of 0.9154 for Nusselt number prediction. These outcomes underscore the ANN model’s ability to effectively capture complex patterns within the data, resulting in highly accurate predictions. In conclusion, this research showcases the promising potential of machine learning techniques in accurately forecasting heat transfer performance in dimpled tubes. The developed ANN model exhibits notable superiority in predicting Nusselt numbers, making it a valuable tool for enhancing thermal system analyses and engineering design optimization.

Statistical Analysis and Distribution Modeling of Rainfall Data in Flood-Prone Regions of Karnataka State

This research paper presents a comprehensive analysis of southwest monsoon rainfall data in flood-prone regions of Karnataka State, employing suitable statistical techniques and data distribution modeling. The detailed analysis of the dataset helped in understanding rainfall patterns, which is essential in identifying flood risks in Karnataka.The analysis includes the computation of descriptive statistics, exploration of data stationarity and the application of distribution models to characterize rainfall patterns. Maximum likelihood estimator has been used to estimate the parameters involved in the data distribution modelling. Further, hypothesis tests were conducted to assess the goodness-of-fit of these distribution models. These models are found to be suitable for the dataset in comparison with the Gaussian models.

The unpolarized TMD valence quark distributions of light mesons in the statistical covariant parton model approach

We investigate the unpolarized transverse momentum dependent (TMD) structure of light mesons at low Q^2 scales in nonperturbative region of quantum chromodynamics (QCD). To this end, we calculate the unpolarized TMD valence quark distribution functions of pion and kaon based on the covariant parton model in which the flavour dependent covariant momentum distribution of quarks is needed. We apply the statistical model for this momentum distribution, for the first time, and also consider the quarks to be massive. The results of TMD valence distributions of light mesons show convenient general properties. We also obtain the integrated valence quark distributions of pion and kaon and compare our results with those of other models.

Probabilistic hierarchical forecasting with deep Poisson mixtures

Hierarchical forecasting problems arise when time series have a natural group structure, and predictions at multiple levels of aggregation and disaggregation across the groups are needed. In such problems, it is often desired to satisfy the aggregation constraints in a given hierarchy, referred to as hierarchical coherence in the literature. Maintaining coherence while producing accurate forecasts can be a challenging problem, especially in the case of probabilistic forecasting. We present a novel method capable of accurate and coherent probabilistic forecasts for time series when reliable hierarchical information is present. We call it the deep Poisson mixture network (DPMN). It relies on the combination of neural networks and a statistical model for the joint distribution of the hierarchical multivariate time-series structure. By construction, the model guarantees hierarchical coherence and provides simple rules for aggregation and disaggregation of the predictive distributions. We perform an extensive empirical evaluation comparing the DPMN to other state-of-the-art methods which produce hierarchically coherent probabilistic forecasts on multiple public datasets. Compared to existing coherent probabilistic models, we obtain a relative improvement in the overall continuous ranked probability score (CRPS) of 11.8% on Australian domestic tourism data, and of 8.1% on the Favorita grocery sales dataset, where time series are grouped with geographical hierarchies or travel-intent hierarchies. For San Francisco Bay Area highway traffic, where the series’ hierarchical structure is randomly assigned and their correlations are less informative, our method does not show significant performance differences over statistical baselines.

Experimental investigation on the impact properties and microstructure of recycled steel fiber and silica fume reinforced recycled aggregate concrete

With the continuous development of the economy and society, the production of solid waste is increasing. Construction and demolition waste (CDW), used tires and silica fume are the main components of solid waste. Recycling these materials will reduce resource pressure, decrease carbon emissions and protect the environment, while bringing certain economic benefits. This study focused on the influence of the synergistic effect of recycled steel fibers (RSF) and silica fume on the mechanical properties and impact resistance of recycled aggregate concrete (RAC). The mathematical statistical model of Weibull distribution was adopted to depict the impact results. In addition, the microstructure of the interfacial transition zone (ITZ) between the cement paste and the aggregate/fiber was researched by scanning electron microscopy (SEM). Results revealed that the synergistic effect of RSF and silica fume significantly improved the impact resistance of RAC. Especially the specimen containing 10% silica fume and 0.75% RSF performed the best properties, the first crack impact and failure impact energy increased by 421.9% and 461.3%, the net-gain in them by the synergistic action of silica fume and RSF with values of 102.7% and 115.3%. The distribution law of the impact life for RSF reinforced RAC can better describe by the two-parameter Weibull distribution function. Impact resistance life was predicted corresponding to reliability levels. SEM investigations revealed that the ITZ between cement and aggregate/RSF significantly improved by mixing silica fume.

Statistical Distribution Model of Charpy Absorbed Energy in Transition Temperature Range for Reactor Pressure Vessel Steel

Abstract A statistical model to estimate the distribution characteristics of Charpy absorbed energy in the transition temperature range was proposed based on the variation in fracture toughness addressed by the Master Curve and the relationship between fracture toughness and Charpy absorbed energy associated with the Charpy Master Curve. Charpy absorbed energy in the transition temperature range can be well approximated by both the Weibull and normal distributions, and the parameters to determine the shape of the distributions (scale and shape parameters of the Weibull distribution, mean and standard deviation of the normal distribution) can be deductively defined as the functions of two independent variables, median of the fracture toughness and the difference between reference temperature and Charpy reference temperature. A series of Charpy impact tests were conducted under the same conditions to obtain the characteristics of the variation in Charpy absorbed energy for a reactor pressure vessel steel SQV2A base metal, and the experimental variation was reasonably predicted by the proposed model.

A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data

Statistical distributions are of great interest for actuaries in modelling and fitting the distribution of various data sets. It can be used to present a description of risk exposure on the investment, where the level of exposure to the risk can be determined by “key risk indicators” that usually are functions of the statistical model. Financial mathematicians and actuarial scientists often use such key risk indicators to determine the degree to which a particular company is subject to certain aspects of risk, which arise from changes in underlying variables such as prices of equity, interest rates fluctuations, or exchange rates. Weibull distribution is one of the most popular statistical distribution models employed by the actuarial and financial risk management problems in fitting and or in modelling the behaviours of financial data or lifetime event data to forecast stock pricing movement or uncertainly prediction. In this study, a Bayesian approach to the Weibull distribution model on the assumption of gamma prior to Weibull distribution parameters has been proposed. A computational study based on the actuarial measures is conducted, proving the proposed distribution of the claim amount. Along this line, in assessing the performance of the proposed method, the results of the simulations study have been conducted to explore the efficiency of the proposed estimators is compared to a maximum likelihood (MLE) and simulated annealing algorithm (SA). Finally, an actuarial real data set is analyzed, proving that the proposed model can be used effectively to model insurance claim data.