Random Variable Model Research Articles

The Vasicek distribution autoregressive time-series model for aggregated data of default and delinquency rates

Abstract Is it possible to analyse time series of aggregated data of default and delinquency rates with a simple model that includes both cross-sectional and serial dependence? To address this question, this paper proposes an autoregressive time-series model for Vasicek-distributed random variables. A direct result from the proposed model is that it leads to a novel out-of-time validation test for aggregated default and delinquency rates. The motivation for the model comes from an analysis of a time series of aggregated US credit card delinquencies, for which the Poisson or binomial distribution cannot be used. The proposed model can also be employed to analyse a time series of the average default probability of a portfolio.

Polynomial chaos expansion vs. Monte Carlo simulation in a stochastic analysis of wave propagation

The paper deals with the propagation of a stochastic wave in an elastic medium using the example of a seismic wave in a ground medium. Identification of subsoil parameters is never exact or complete which justifies the use of random field models or random variable models for input data; thus, the response of the subsoil is also random. In this paper and in the context of random variables, the focus is on a sensitivity analysis addressing the question of how the uncertainty of the input data (subgrade parameters) influences the obtained results (displacements). Two different methods of stochastic analysis are presented—the intrusive polynomial chaos approach supported by the Galerkin projection and Monte Carlo simulation—and compared by using an example of wave propagation in the elastic half-plane. Consistency in the results of both approaches has been achieved; however, the calculation efficiencies differ. The advantages and disadvantages of both approaches are discussed. The upper subsoil layer influences the variances of the random solutions much more than does the lower layer.

A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method

The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case.

Tampered Random Variable Analysis in Step-Stress Testing: Modeling, Inference, and Applications

This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method’s validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis.

Population pharmacokinetics of cyclosporine A in pediatric patients with thalassemia undergoing allogeneic hematopoietic stem cell transplantation.

To establish the population pharmacokinetics (PPK) model of cyclosporine A(CsA) in pediatric patients with thalassemia undergoing allogeneic hematopoietic stem cell transplantation (HSCT), aiming at providing a reference for clinical dose individualization of CsA. Children with thalassemia who underwent allogeneic HSCT were enrolled retrospectively. The PPK structural model and the random variable model of CsA were established on NONMEN. And goodness of fit plots (GOFs), visual predictive check (VPC), and bootstrap and normalized prediction distribution errors (NPDE) were used to evaluate the final model. A one-compartment model with first-order absorption was employed to fit the base model. A total of 74 pediatric patients and 600 observations of whole blood concentration were included. The final model included weight (WT) in clearance (CL), alongside post-operative day (POD), fluconazole (FLUC), voriconazole (VORI), posaconazole (POSA), and red blood cell count (RBC) significantly. All the model evaluations were passed. In the PPK model based on the pediatric cohort on CsA with thalassemia undergoing allogeneic HSCT, WT, POD, FLUC, VORI, POSA, and RBC were found to be the significant factors influencing CL of CsA. The reliability and robustness of the final model were excellent. It is expected that the PPK model can assist in individualizing dosing strategy clinically.

Quantized iterative learning control of communication-constrained systems with encoding and decoding mechanism

In practical applications, due to the limited communication bandwidth, the network control systems (NCSs) are prone to data dropouts when the load is high. In this paper, the problem of quantized iterative learning control (ILC) based on encoding and decoding mechanism for such communication-constrained systems is studied. By combining the encoding and decoding mechanism with the uniform quantizer, the network burden and the impact of quantization error on the tracking performance of the systems are significantly mitigated. Meanwhile, data dropouts are represented as the Bernoulli random variable model, and an ILC law based on gradient is designed. When data dropouts occur, the signals maintain the value of the previous trial, otherwise the signals are updated. For this kind of learning framework, the asymptotic zero-error tracking performance has been rigorously proven for the uniform quantizer. To validate the proposed design, a joint motion of an industrial robot in the horizontal plane is simulated as an example.

Multi-beam line observation optimization strategy based on random variable unitary iterative model

Multibeam system has many advantages such as large measurement range, fast speed, high accuracy, etc., which can be applied in many fields such as marine topographic survey. In this paper, the relationship between coverage width and other variables is obtained by analyzing the geometric relationship between each parameter, and a multibeam sounding model based on geometric relationship is established. And based on the intelligent optimization algorithm, an iterative optimization model with random variable singularization is designed independently. And the actual terrain data were visualized and simplified into various parameters in line with the model. With the help of the definition of the coverage rate, the relationship between the coverage width and other variables, and the one-to-one correspondence between the translation distance of the slope and the coverage rate, the complex measurement problem can be transformed into a simple linear programming problem, and the relationship model between the coverage rate and other variables is established. In the end, the model can be used to derive the optimal wiring scheme to realize high-precision and full-coverage sweeping of the seabed terrain in the given sea area without omission, provided that the ship speed, beam opening angle and other factors are reasonable.

Service life prediction of timber-concrete composite floors

Timber-concrete composite (TCC) systems have application for new floors and for upgrading and enhancing of existing timber floors in residential and office buildings. In order to develop the optimal maintenance programs of structures, it is essential to predict the performance of structures over their life-cycle. The long-term behavior of timber-concrete composite floors is influenced by a combination of various factors, including material properties, load distribution, moisture effects, temperature effects and durability considerations. Timber and concrete material in the composite system, exhibit different behaviors over time due to their inherent characteristics. Deterioration prediction models are used to estimate the future degradation and condition of various types of structures. The aim of this paper is to present two probabilistic models, random variable deterioration rate model and stochastic gamma process model, that will capture uncertainty and variability associated with the deterioration of TCC floor under the service load and to estimate its service life.

Method for determining estimates of random variable models for describing phase equilibrium in rectification processes

The phase equilibrium modeling for multi-component systems is essential in process systems engineering. In particular, phase stability analysis, Gibbs free energy minimization and estimation of parameters in thermodynamic models are challenging global optimization problems involved in phase equilibrium calculations and modeling for both reactive and non-reactive systems. To date, many significant works have been performed in the area of global optimization, and several algorithms and computational contributions of global optimization have been used for solving these problems; global optimization methods used include both deterministic and stochastic algorithms. To the best of our knowledge, there is no review in the literature that focuses on the global optimization methods and their applications to phase equilibrium modeling and calculations. In this paper, we briefly describe the deterministic and stochastic optimization algorithms selected for our rectification process, and then consider their use for phase stability analysis, Gibbs free energy minimization, and parameter estimation in phase equilibrium models. In short, we present an overview of global optimization for modeling and computing the phase behavior of systems with and without chemical reactions, including the prediction of azeotropes and critical points.

Step‐stress life‐testing under tampered random variable modeling for Weibull distribution in presence of competing risk data

AbstractIn this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also.

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently, reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering. However, for deep foundation pit, evaluating the system safety of retaining structures and finding cost-effective design points are main challenges. To address this, this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou, China. The proposed method included two parts: system reliability model and robust design method. Back Propagation Neural Network (BPNN) is used to fit limit state functions and conduct efficient reliability analysis. The common source random variable (CSRV) model are used to evaluate correlation between failure modes and determine the system reliability. Furthermore, based on the system reliability model, a robust design method is developed. This method aims to find cost-effective design points. To solve this problem, the third generation non-dominated genetic algorithm (NSGA-III) is adopted. The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm. The proposed method has a good performance in locating the balanced design point between safety and construction cost. Moreover, the proposed method can provide design points with reasonable stiffness distribution.

Stability Study of Event Dynamic Systems Based on Discrete Mathematical Random Variable Modeling

This project intends to consider the stability of a nonlinear control system with unknown dynamics. The system is controlled systematically by using the reverse step method based on Lyapunov's stability principle. This paper also gives the conclusion that when the control law is in a steady state, the output signal in this state will reach uniform boundedness or asymptotic convergence. Finally, a numerical simulation is carried out through an example, and the results show that the algorithm is effective.

Deep reinforcement learning based model-free optimization for unit commitment against wind power uncertainty

Solving the unit commitment (UC) problem in a computationally efficient manner has become increasingly crucial, especially in the context of high renewable energy penetration. This paper tackles this challenge by employing the offline training of a model-free deep reinforcement learning (DRL) framework, thereby enhancing the optimization efficiency of the UC problem. The complex modeling of random variables is avoided by reformulating the UC problem as a Markov decision process, where the DRL-based method extracts knowledge regarding wind output forecasting errors from historical data. Finally, a discrete proximal policy optimization (PPO-D) algorithm is developed to generate UC solutions under the discrete action spaces necessitated by unit start-up/shut-down variables. Simulation results on the 5-unit system demonstrate that the proposed DRL-based UC model can yield an optimal solution with higher computational efficiency compared to the conventional mathematical optimization methods, while hedging against the wind power uncertainty. In addition, the case study on the IEEE 118-bus system involving 31 testing days further validates the generalization ability of the proposed DRL-based UC model.

Performance of [18F]FDG PET/CT versus FAPI PET/CT for lung cancer assessment: a systematic review and meta-analysis.

This article aims to compare the diagnostic performance of 18-fluorodeoxyglucose ([18F]FDG) PET/CT and fibroblast activating protein inhibitor (FAPI) PET/CT in the assessment of primary tumors, lymph nodes, and distant metastases in lung cancer patients. A systematic search was conducted on the Cochrane Library, Embase, and PubMed/MEDLINE databases from inception until November 1, 2022. Included studies assessed the use of FAPI PET/CT and [18F]FDG PET/CT in patients with lung cancer. The Quality Assessment of Diagnostic Accuracy Studies-2 (QUADAS-2) tool was used to evaluate the risk of bias. A random variable model was used to analyze the diagnostic tests of the two imaging modalities. The sensitivity of FAPI PET/CT in detecting primary lung cancer lesions was 0.98 (95% CI: 0.88-1.00), while the sensitivity of [18F]FDG PET/CT was 0.99 (95% CI: 0.74-1.00). For the detection of metastatic lesions (lymph node metastases and distant metastases), FAPI PET/CT had a sensitivity of 0.99 (95% CI: 0.90-1.00), while the sensitivity of [18F]FDG PET/CT was 0.77 (95% CI: 0.66-0.85). However, the specificity of the two imaging modalities could not be assessed due to the lack of sufficient information on pertinent true negatives. In the diagnosis of metastatic lung cancer lesions, FAPI PET/CT demonstrated a higher sensitivity compared to [18F]FDG PET/CT. Therefore, FAPI PET/CT may be considered an alternative imaging modality for the assessment of primary lung cancer tumors, lymph node metastases, and distant metastases. FAPI may be an alternative to [18F]FDG in the assessment of primary lung cancer tumors, lymph node metastases, and distant metastases, which plays a very important role in treatment. • This article is to compare the performance of [18F]FDG PET/CT withFAPI PET/CT in the assessment of primary tumors, lymph nodes, and distant metastases in lung cancer. • However,FAPI PET/CT has a higher sensitivity for the diagnostic assessment of metastatic lung cancer lesions.

Energy consumption structure model considering urban green and low-carbon transportation

<p class="Abstract">The importance of energy conservation and emission reduction has become the consensus of the international community, and Iraq is also actively improving the urban public transportation system to control carbon emissions. This paper collects panel data of Tikrit city in Iraq in the past 3 years, constructs a random effect variable coefficient model, and studies the impact of the development of urban low-carbon transportation system on the energy consumption structure. The study finds that the government can use public transportation pricing strategies to influence consumers. In order to realize the optimization of energy consumption structure, the impact of electric vehicles on energy consumption structure will decrease with the increase of urban development. The transportation sector can increase the purchase and travel costs of traditional cars by restricting travel, purchases, and charging parking fees, which affects the number of private cars and reduces the obstacles to optimizing the energy consumption structure. The government should increase financial subsidies, improve rail transit and reasonable bus (electric) vehicle operation systems, increase investment in new energy vehicle research and development, and encourage high energy density and low power consumption technologies. development, increase residents’ demand for new energy passenger vehicles, and optimize the energy consumption structure.</p>

Statistical inferences under step stress partially accelerated life testing based on multiple censoring approaches using simulated and real-life engineering data

Evaluating the lifespan distribution of highly reliable commodities under regular use is exceedingly difficult, time consuming, and extremely expensive. As a result of its ability to provide more failure data faster and at a lower experimental cost, accelerated life testing has become increasingly important in life testing studies. In this article, we concentrate on parametric inference for step stress partially life testing utilizing multiple censored data based on the Tampered Random Variable model. Under normal stress circumstances, the lifespan of the experimental units is assumed to follow the Nadarajah–Haghighi distribution, with and being the shape and scale parameters, respectively. Maximum likelihood estimates for model parameters and acceleration factor are developed using multiple censored data. We build asymptotic confidence intervals for the unknown parameters using the observed Fisher information matrix. To demonstrate the applicability of the different methodologies, an actual data set based on the timings of subsequent failures of consecutive air conditioning system failures for each member of a Boeing 720 jet aircraft fleet is investigated. Finally, thorough simulation studies utilizing various censoring strategies are performed to evaluate the estimate procedure performance. Several sample sizes were studied in order to investigate the finite sample features of the considered estimators. According to our numerical findings, the values of mean squared errors and average asymptotic confidence intervals lengths drop as sample size increases. Furthermore, when the censoring level is reduced, the considered estimates of the parameters approach their genuine values.

Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring

In this article, we consider the parametric inference, using Type II censored data, based on the tampered random variable (TRV) model for simple step-stress life testing (SSLT). We have taken the members of the Lehmann family of distributions as the baseline lifetimes of the experimental units under normal stress conditions. Based on Type II censored data and a simple SSLT framework, we obtain the maximum likelihood estimator (MLE) and the Bayes estimators of the model parameters. Further, we obtain asymptotic confidence intervals of the unknown model parameters using the observed Fisher information matrix. Moreover, bootstrap confidence intervals were constructed. The Bayes estimators are computed using the Markov chain Monte Carlo (MCMC) method under the squared error loss function and the LINEX loss function. We also construct the highest posterior density (HPD) credible intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Finally, the proposed methods are illustrated with the analysis of a real data set.

Leveraging Google Earth Engine to estimate foliar C: N ratio in an African savannah rangeland using Sentinel 2 data

Rangelands are important fodder for livestock and wildlife, and provide a range of ecosystem services to the environment. Foliar nutrients such as nitrogen, carbon, and plant pigments such as chlorophyll can be used as indicators of rangeland stress, and play a vital role in determining their health and productivity. The C:N ratio is a key factor in regulating nutrient utilization efficiency and productivity in plants. Understanding the C:N ratio in rangelands could therefore help herders understand the nutrient limitations, and herbivores distribution to facilitate strategic grazing plans and management. Therefore, there is a need for spatially accurate and up-to-date information on C:N ratio to understand and monitor rangeland health for proactive rangeland management. Remote sensing approaches are spatially explicit, cost-effective, and efficient in monitoring foliar nutrient ratio in rangelands. Whereas, the new generation and advanced Sentinel 2 multispectral sensor has the potential to monitor vegetation health, the strength of its spectral settings in relation to predicting the C:N ratio in rangelands remains largely unexplored. Advanced and freely available Sentinel 2 multispectral sensor (MSI) with specialized red edge bands offer unprecedented opportunities in mapping and monitoring rangeland nutrients. Hence, this study examined the prospect of combined Sentinel-2 (MSI) spectral bands and vegetation indices, and the random forest algorithm to map the C: N ratio within a rangeland. To determine the C:N ratio distribution, the Random Forest and the Boruta variable selection were employed to assess the performance of the combined Sentinel 2 spectral bands and vegetation indices models. Results show an estimated accuracy R2 of 81 and 74, with RMSE of 2.38 and 2.68 for calibration and validation datasets of the C:N ratio model established by combining the spectral bands and vegetation indices. The random forest variable selection model indicates that the red edge bands, and near-infrared were the most valuable in predicting the C:N ratio. The red edge and near-infrared (Inverted Red-edge Chlorophyll Index) and near-infrared and red band (Enhanced Vegetation Index) vegetation indices were important predictor variables for estimating the C:N ratio. This study demonstrates the prospects and value of mapping the geographic distribution of the C:N ratio in rangelands using high spatial resolution Sentinel 2 MSI. This information will not only help determine nutrient deficiencies in rangelands but will also provide informed recommendation in mitigating landscape degeneration to allow for rangeland regeneration.

Statistical Inference for Gumbel Type-II Distribution Under Simple Step-Stress Life Test Using Type-II Censoring

In this paper, we focus on the parametric inference based on the Tampered Random Variable (TRV) model for simple step-stress life testing (SSLT) using Type-II censored data. The baseline lifetime of the experimental units, under normal stress conditions, follows the Gumbel Type-II distribution with $\alpha$ and $\lambda$ being the shape and scale parameters, respectively. Maximum likelihood estimator (MLE) and Bayes estimator of the model parameters are derived based on Type-II censored samples. We obtain asymptotic intervals of the unknown parameters using the observed Fisher information matrix. Bayes estimators are obtained using Markov Chain Monte Carlo (MCMC) method under squared error loss and LINEX loss functions. We also construct highest posterior density (HPD) intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Three different optimality criteria have been considered to determine the optimal censoring plans. Finally, the methods are illustrated with the analysis of two real data sets.

System approach in optimal management problems for two-stage technological lines

Purpose of work is to research and design process optimization and optimal operational management for a two-stage technological line. Methodology. To achieve the goal, we apply a comprehensive approach, which consists of the formalization and analysis of operational management tasks and technological lines designing.The methods of probability theory are used to determine the optimal level between the maximum bandwidths of the stages of the technological lines and for processing mathematical models of random variables. Research results. The need for a system-wide approach to the management of two-stage technological lines is substantiated, which involves joint consideration of design and operational management tasks. Three optimization problems are considered, which differ in their formulation by initial data, goals and optimization parameters.This is the problem of design optimization when creating equipment, the problem of optimal design of technological schemes and the problem of optimal operational control.These three types of tasks must be considered comprehensively, in mutual connection to achieve a global optimum in terms of the economic criterion.The formalization of such a complex problem for two-stage technological schemes was carried out in a general form and approaches to its solution. The methodology for solving such problems is proposed, based on information about the specific consumption of the resource and the characteristics of the flow of the processed material. Scientific novelty. The formulation of the complex optimization problem for the functioning of two-stage technological lines, including the choice of the equipment and a type of operational management, and a solving approach for the considered problem was provided. Practical significance of work results. The proposed approach makes it possible to find the optimal solution to the problem of management and design of two-stage technological lines from the point of view of the economic criterion.