The logistic-additive Weibull distribution with statistical properties and regression modeling for reliability applications

The purpose of this work is to interpret the experimental data (deformation, geoacoustic and earthquake parameters) and to establish their relation with the seismicity of the Transcarpathian region using statistical (regression) analysis. The correlation of geophysical parameters is described, namely: deformation, geoacoustic emission and seismic characteristics of magnitude and energy class.For construction of the statistical (regression) model, geoacoustic and deformation data for the period of 2014, as well as data of the seismological catalog provided by the seismicity department of the Carpathian region (Subbotin Institute of Geophysics of NAS of Ukraine) were used. The statistical model of seismicity is built to analyze various geophysical parameters and to establish their relationship with each other by means of regression analysis.This interconnection will give an opportunity to understand how seismicity influences the change of various environmental parameters of the Transcarpathian region. The deformation and geoacoustic data used in the work were obtained at the mode geophysical station (MGS) "Beregove" and the observation point "Janoshi" (Transcarpathia). The basic regression analysis formulas used to construct a linear statistical model are given. According to the seismic catalog, a graph of dependence between energy class (K) and magnitude (MD) for the period 2002–2016 was constructed, which confirmed their dependence, as well as a histogram of seismic activity for the period 2002–2016, from which it follows that the largest number of events was in 2015. The tables, on which graphs of seismicity dependence on deformation and geoacoustics, are presented. The relationship between the magnitude (MI) and the offset shift (lg DP) in depth (h) is shown. Studies were conducted for different depths: 1) up to 2 km, 2) from 2–5 km, 3)5–10 km and 4) from 10 km or more. The results showed that the greater the depth, the greater the relationship between the magnitude (MI) and the offset shift (lg DP) is. Such studies are needed to identify the effect of seismicity on the change of other environmental parameters, in particular, temperature, characteristics of earthquake foci, which will allow building an existing model of seismicity of the Transcarpathian region.

Abstract: Bridges are critical components of transport for any nation. However they may suffer damages due to several reasons which may lead to collapse, and introduce hazards in transportation. Hence, predicting their safety is crucial for safety in road transport. Many existing bridges around the world, especially in seismic zones, were constructed decades ago and are now aging. These aging structures face increased vulnerability during earthquakes due to material deterioration, outdated design standards, and cumulative stress from environmental and traffic loads. However, human inspection in earthquake stricken areas may take a lot of time increasing the risk of using bridges which are severely damaged thereby risking human life. Hence, quick automated tools are required which can predict bridge damages quickly and based on less number of parameters with relatively high accuracy. The proposed model utilizes a large standard corpus of data pertaining to possibility of collapse of aging bridges under seismic impacts. A statistical regression model is proposed which would map the inputs such as age, seismic impact, distance from epicentre to the possibility of collapse. The proposed approach combines Particle Swarm Optimization (PSO) and Statistical Regression. It is expected that the proposed model would be able to render higher prediction accuracy compared to existing research models in the domain. The data set used is the Stanford Earthquake Dataset (STEAD). It has been shown that the proposed work attains high classification accuracy and low computation complexity making the model effective for quick evaluation of bridges from seismic impacts. Keywords: Transportation Engineering, Seismic Damage Prediction, Probability of Collapse, Statistical Regression, Particle Swarm Optimization (PSO), Mean Squared Error, Classification Accuracy.

In some practical situations, it is not possible to categorize samples into one of two response categories because of the vague nature of the response variable. Statistical logistic regression models are, therefore, not appropriate for modeling such response variables. Moreover, the small sample size in most cases limits the use of statistical logistic regression models. Fuzzy logistic regression models, instead, can overcome these problems. In order to investigate the use of fuzzy logistic regression, the present study is designed and implemented to evaluate the relationship between dietary pattern and a set of risk factors of interest. Since it is not possible to define a healthy dietary pattern precisely, therefore, the possibility of having the healthy diet is reported for each subject as a number between zero and one. The conventional logistic model is not appropriate and fails in dealing with such imprecise data; hence, a possibilistic approach is used to model the available data and to estimate the fuzzy parameters of the model. For evaluating the model, a goodness-of-fit index and an appropriate predictive capability criterion with cross validation technique is developed. The logistic model investigated here is found to be general and inclusive enough to be recommended for modeling vague observations or ambiguous relations in any field of medical sciences.

In engineering practice, due to the high compressibility and very low shear strength of organic soils, it is difficult to construct an embankment on organic subsoil. High variability and significant change in geotechnical parameters cause difficulties in predicting the behavior of organic soils under embankment loading. The aim of the paper was to develop empirical relationships used in the preliminary design for evaluating the settlement and undrained shear strength of organic subsoil loaded by embankment based on data obtained from four test sites. Statistical multiple regression models were developed for evaluating the settlement in time and undrained shear strength in time individually for peat and gyttja. Neural networks to predict the settlement and undrained shear strength in time for peat and gyttja simultaneously as double-layer subsoils as well as a separate neural network for peat and a separate neural network for gyttja as single-layer subsoils were also developed. The vertical stress, thickness, water content, initial undrained shear strength of peat and gyttja, and time were used as the independent variables. Artificial neural networks are characterized by greater prediction accuracy than statistical multiple regression models. Multiple regression models predict dependent variables with maximum relative errors of about 35% to about 60%, and neural networks predict output variables with maximum relative errors of about 25% to about 30%.

Combined with the existing transaction orders of carless carriers, the numerical information and text and information are extracted, and the related factors of line guide price are integrated, and the relationship between relevant factors and line guide price is studied. Using the unified unit and 0-1 text setting method, preprocessing data, eliminating the influence of numerical units, quantifying textual data, so that the data can be put into the relevant equations for testing. According to the characterization relationship between the guiding price and factors, a multivariate linear statistical regression model was established, and the statistical P value was used for testing to verify the availability of the model. The index of price overflow rate and equilibrium degree are put forward as the standard to evaluate whether the transaction price of an order is reasonable. The normal distribution of orders can be verified by looking at the scatter plot of the cumulative percentage of transactions and the price spillover rate of orders. According to the central limit theorem of large sample data with normal distribution, the sample can be sampled in sections and the summation can be taken as the transaction probability. According to the operation mode of the vehicle-free carrier platform, the transaction mode of three quotations is added to re-quote the line. The pricing obtained from multiple linear statistical regression is used as the benchmark, and the dynamic pricing strategy is re-customized according to the principle of the first quotation giving priority to lowering the price, the second quotation giving priority to stabilizing the transaction, and the third quotation giving priority to the success rate. The sensitivity analysis shows that the platform can get a revenue increase of 33%∼48% based on this new pricing strategy, and meanwhile improve the balance and stability of orders. The research report provides a calculation method of a new quotation model with high turnover rate and stable income for the non-truck operating common carrier platform, and has a guiding significance for the construction of the non-truck operating common carrier trading system, especially the rationality of the price formulation and the stability of the transaction order quantity.

Saw marks on bone have been routinely reported in dismemberment cases. When saw blade teeth contact bone and the bone is not completely sawed into two parts, bone fragments are removed forming a channel or kerf. Therefore, kerf width can approximate the thickness of the saw blade. The purpose of this study is to evaluate 100 saw kerf widths in bone produced by ten saw types to determine if a saw can be eliminated based on the kerf width. Five measurements were taken from each of the 100 saw kerfs to establish an average thickness for each kerf mark. Ten cuts were made on 10 sections of bovine bone, five with human-powered saws and five with mechanical-powered saws. The cuts were examined with a stereoscopic microscope utilizing digital camera measuring software. Two statistical cumulative logistic regression models were used to analyze the saw kerf data collected. In order to estimate the prediction error, repeated stratified cross-validation was applied in analyzing the kerf mark data. Based on the two statistical models used, 70–90% of the saws could be eliminated based on kerf width.

Can the summer temperatures reduce COVID-19 cases?

Genetic-Fuzzy (GF) approach is used to model color yield in the high temperature (HT) polyester dyeing as a function of dye concentration, temperature, and time. The proposed method is compared with statistical regression model for their prediction powers using the Mean Square Errors (MSE). The results show that the GF model is preferable to the statistical regression model in at least two ways. First, it enjoys a better predictive power regarding to its minimum MSE. Second, the statistical regression model fails to satisfy the standard requirements.

Spatial predictions of the fractions of mud, sand and gravel as continuous response variables for the north-west European continental shelf. Mud, sand and gravel fractions range from 0-1 (i.e. 0-100%). These fractions were generated from two additive log-ratios (ALR), ALRs and ALRm which are independent, unconstrained response variables. These raw predictions as rasters are also included presented in the attached dataset. Predicted fractions have been combined to predict the likely sediment classification based on the EUNIS level 3 sediment classification for broadscale habitats, Folk 5, Folk 7, Folk 11 and Folk 15 classification schemes. These are available as raster tif files with an ArcGIS layer file indicating the appropriate class for each raster value. For all predictions an accompanying map of the spatial distribution of error/accuracy is also included as a separate raster. For the three components of the sediment fraction a smoothed Root-Mean-Squared-Error layer is available. For the classification maps a smoothed local accuracy map is available. Spatial predictions of mud, sand and gravel were generated for the north-west European continental shelf. Based on these fractions sediment classification maps were also generated for the study site. To support the interpretation of these layers maps of the spatial distribution of error/accuracy were also generated. In short, analysis combined the eight continuous predictive layers (Bathymetry, Bathymetric position index at a 50-pixel radii, Bathymetric position index at a 434-pixel radii, Distance from coast, Current speed at the seabed, Wave peak orbital velocity at the seabed, and suspended inorganic particulate matter for summer and winter as two separate variables) with sediment observation data in a statistical regression model to make spatial predictions of the fractions of mud, sand and gravel. Spatial predictions were generated based on two additive log-ratios that could then be back transformed to produce spatial predictions for each fraction. From these spatial predictions any classification scheme based on the percentages of mud, sand and gravel can be applied. Included here are the five classification shemes generated from these maps. The maps of accuracy were also generated to support interpretation. For the maps of the fractions of mud, sand and gravel map error was calculated based on the Root-Mean-Squared-Error of the observed vs predicted fractions from the test samples. A smoothed surface of local RMSE was then generated using the Inverse Distance Weighted (IDW) technique in ArcGIS. Each pixels’ RMSE was determined based on the closest 50 points (up to a maximum distance of 200 km). A weighting power function was applied in the IDW tool (set at 0.3) so nearer points contributed more to the pixel than distant points. For the classified maps spatial accuracy was calculated using a locally constrained confusion matrix. The IDW technique was applied to calculate a local thematic accuracy value. As above, this was applied based on the closest 50 points (maximum distance of 200 km) with a weighting power function of 0.3.

In crop modelling, factor analysis and regression type have direct influence on the accuracy of model, but the application of these methods usually depends on the experience. In this paper, the performance of some common methods of statistical analysis and regression model was compared and verified, in order to avoid the blindness in crop modelling. The monitoring data of growth environment and photosynthesis of tomato, pumpkin and cucumber was obtained by PTM-48A, for the object variable of CO2 exchange rate, selectivity on the main environmental factors by correlation analysis and path analysis were quantify compared, the performance of four kinds of multivariate binomial regression equations was compared in respects of complexity and accuracy, then the effectiveness of modelling was verified with the selected optimized multivariate statistical analysis and regression equation. Results showed that path analysis was more comprehensive than correlation to discrimination the variables, and the pure quadratic was more suitable to crop modelling because of its simple structure and high accuracy. The conclusion of the paper has general applicability, and offers a useful reference and guide for the other crops’ modelling. Keywords-crop model; multivariate statistical analysis; regression; comparison

Plant leaf area is a useful observation in physiological and agronomic research. Statistical regression and correlation models have been used to estimate leaf blade area from leaf blade dimensions such as length and width. The objective of this study was to determine if consistent relationships exist among leaf area (A), length (l), and maximum width (m) of pearl millet [ Pennisetum glaucum (L.) R. Br.] leaves from different plant positions and different stages of maturity. Measurements of length, width, and area were made on leaf blades sampled from different positions on pearl millet plants at the 7‐ and 10‐leaf growth stages. Relationships for the model A = klm were derived by least squares regression for these leaves of each position on the plants (where k is an empirical constant). The results of these analyses justified the use of the model A = klm for pearl millet leaves. However, different coefficients may need to be calculated depending on leaf position and growth stage of the plants. This approach could also be applied for other cereal crops whose leaves have similar morphology and anatomy.

Over the past few years, we have implemented many models for inferential control. These models have been developed from historical data using statistical regression or neural network models. In addition, techniques for online biasing and robust model implementations have been developed. The methodology has been encapsulated in a novel software program. This software allows easy creation of models for inferential control.

A Monod kinetic model, logistic equation model, and statistical regression model were developed for a Chinese hamster ovary cell bioprocess operated under three different modes of operation (batch, bolus fed-batch, and continuous fed-batch) and grown on two different bioreactor scales (3 L bench-top and 15 L pilot-scale). The Monod kinetic model was developed for all modes of operation under study and predicted cell density, glucose glutamine, lactate, and ammonia concentrations well for the bioprocess. However, it was computationally demanding due to the large number of parameters necessary to produce a good model fit. The transferability of the Monod kinetic model structure and parameter set across bioreactor scales and modes of operation was investigated and a parameter sensitivity analysis performed. The experimentally determined parameters had the greatest influence on model performance. They changed with scale and mode of operation, but were easily calculated. The remaining parameters, which were fitted using a differential evolutionary algorithm, were not as crucial. Logistic equation and statistical regression models were investigated as alternatives to the Monod kinetic model. They were less computationally intensive to develop due to the absence of a large parameter set. However, modeling of the nutrient and metabolite concentrations proved to be troublesome due to the logistic equation model structure and the inability of both models to incorporate a feed. The complexity, computational load, and effort required for model development has to be balanced with the necessary level of model sophistication when choosing which model type to develop for a particular application.

The aim of this manuscript is to provide the mathematical and statistical foundations of actuarial learning. This is key to most actuarial tasks like insurance pricing, product development, claims reserving and risk management. The basic approach to these tasks is regression modeling. This manuscript describes the exponential dispersion family which is the most commonly used family of distributions in actuarial modeling. It discusses model fitting and parameter estimation using classical tools from mathematical statistics. It then introduces the crucial tools for prediction and forecast evaluation. Based on these statistical concepts various regression models are studied such as generalized linear models, mixture models and neural network regression models. We explore these modeling approaches from a theoretical and a practical viewpoint on publicly available data and we discuss their applications to insurance modeling. This involves model fitting using Fisher's scoring method, gradient descent algorithms or the expectation-maximization algorithm, model selection, parameter selection, regularization, etc.

Ramadan fasting is an obligatory duty for Muslims. Unique physiologic and metabolic changes occur during fasting which requires adjustments of diabetes medications. Although challenging, successful fasting can be accomplished if pre-Ramadan extensive education is provided to the patients. Current research was conducted to study effective Ramadan fasting with different OHAs/insulins without significant risk of hypoglycemia in terms of HbA1c reductions after Ramadan. ANOVA model was used to assess HbA1c levels among different education statuses. Serum creatinine was used to measure renal functions. Pre-Ramadan diabetes education with alteration of therapy and dosage adjustments for OHAs/insulin was done. Regression models for HbA1c before Ramadan with FBS before sunset were also synthesized as a tool to prevent hypoglycemia and successful Ramadan fasting in future. Out of 1046 patients, 998 patients fasted successfully without any episodes of hypoglycemia. 48 patients (4.58%) experienced hypoglycemia. Χ(2) Test for CRD/CKD with hypoglycemia was also significant (p-value < 0.001). Significant associations and linear regression were found for HbA1c and sunset FBS; RBS post-dawn with RBS mid-day and FBS at sunset. The proposed regression models of this study can be used as a guide in future for Ramadan diabetes management. Some relevant patents are also outlined in this paper.