Monte Carlo Simulation Experiments Research Articles

Solving variables with Monte Carlo simulation experiments: A stochastic root-solving approach.

Solving variables with Monte Carlo simulation experiments: A stochastic root-solving approach.

A Novel Methodology for GB-SAR Estimating Parameters of the Atmospheric Phase Correction Model Based on Maximum Likelihood Estimation and the Gauss-Newton Algorithm.

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.

Modeling insurance loss data using novel approach of moment exponential model: Inference, actuarial measures and application

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution’s shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses.

A better performing algorithm for identification of implausible growth data from longitudinal pediatric medical records

Tracking trajectories of body size in children provides insight into chronic disease risk. One measure of pediatric body size is body mass index (BMI), a function of height and weight. Errors in measuring height or weight may lead to incorrect assessment of BMI. Yet childhood measures of height and weight extracted from electronic medical records often include values which seem biologically implausible in the context of a growth trajectory. Removing biologically implausible values reduces noise in the data, and thus increases the ease of modeling associations between exposures and childhood BMI trajectories, or between childhood BMI trajectories and subsequent health conditions. We developed open-source algorithms (available on github) for detecting and removing biologically implausible values in pediatric trajectories of height and weight. A Monte Carlo simulation experiment compared the sensitivity, specificity and speed of our algorithms to three published algorithms. The comparator algorithms were selected because they used trajectory information, had open-source code, and had published verification studies. Simulation inputs were derived from longitudinal epidemiological cohorts. Our algorithms had higher specificity, with similar sensitivity and speed, when compared to the three published algorithms. The results suggest that our algorithms should be adopted for cleaning longitudinal pediatric growth data.

Ultrasound normalized cumulative residual entropy imaging: Theory, methodology, and application

Background and Objective:Ultrasound information entropy imaging is an emerging quantitative ultrasound technique for characterizing local tissue scatterer concentrations and arrangements. However, the commonly used ultrasound Shannon entropy imaging based on histogram-derived discrete probability estimation suffers from the drawbacks of histogram settings dependence and unknown estimator performance. In this paper, we introduced the information-theoretic cumulative residual entropy (CRE) defined in a continuous distribution of cumulative distribution functions as a new entropy measure of ultrasound backscatter envelope uncertainty or complexity, and proposed ultrasound CRE imaging for tissue characterization. Methods:We theoretically analyzed the CRE for Rayleigh and Nakagami distributions and proposed a normalized CRE for characterizing scatterer distribution patterns. We proposed a method based on an empirical cumulative distribution function estimator and a trapezoidal numerical integration for estimating the normalized CRE from ultrasound backscatter envelope signals. We presented an ultrasound normalized CRE imaging scheme based on the normalized CRE estimator and the parallel computation technique. We also conducted theoretical analysis of the differential entropy which is an extension of the Shannon entropy to a continuous distribution, and introduced a method for ultrasound differential entropy estimation and imaging. Monte-Carlo simulation experiments were performed to evaluate the estimation accuracy of the normalized CRE and differential entropy estimators. Phantom simulation and clinical experiments were conducted to evaluate the performance of the proposed normalized CRE imaging in characterizing scatterer concentrations and hepatic steatosis (n = 204), respectively. Results:The theoretical normalized CRE for the Rayleigh distribution was π/4, corresponding to the case where there were ≥10 randomly distributed scatterers within the resolution cell of an ultrasound transducer. The theoretical normalized CRE for the Nakagami distribution decreased as the Nakagami parameter m increased, corresponding to that the ultrasound backscattered statistics varied from pre-Rayleigh to Rayleigh and to post-Rayleigh distributions. Monte-Carlo simulation experiments showed that the proposed normalized CRE and differential entropy estimators can produce a satisfying estimation accuracy even when the size of the test samples is small. Phantom simulation experiments showed that the proposed normalized CRE and differential entropy imaging can characterize scatterer concentrations. Clinical experiments showed that the proposed ultrasound normalized CRE imaging is capable to quantitatively characterize hepatic steatosis, outperforming ultrasound differential entropy imaging and being comparable to ultrasound Shannon entropy and Nakagami imaging. Conclusion:This study sheds light on the theory and methodology of ultrasound normalized CRE. The proposed ultrasound normalized CRE can serve as a new, flexible quantitative ultrasound envelope statistics parameter. The proposed ultrasound normalized CRE imaging may find applications in quantified characterization of biological tissues. Our code will be made available publicly at https://github.com/zhouzhuhuang.

Deep learning based Compton backscatter imaging with scattered X-ray spectrum data: A Monte Carlo study

Compton backscatter imaging (CBI) is a non-destructive testing (NDT) technique with the Compton effect. In CBI, the radiation source and detector are positioned on the same side of the object, which means that the imaging is almost not limited by the size of the object. The characteristic of single-sided imaging gives CBI substantial potential for applications in specific scenarios. In field archaeology, CBI can rapidly acquire subsurface images with the millimeter-level resolution, effectively enhancing archaeological excavation efficiency while better protecting artifacts. Therefore, CBI offers substantial potential in archaeological excavation. To address the problem of severe noise in CBI, we employed a scintillation detector to receive backscattered X-rays. Transformers directly reconstruct multi-channel projections to swiftly and accurately obtain precise reconstruction images. Monte Carlo simulation experiments confirm this method’s suitability for detecting a variety of common archaeological materials. Experimental results indicate that compared with count mode, multi-channel projections can effectively improve the reconstruction quality of CBI. Moreover, CBI can clearly image various materials of buried artifacts, proving the method’s versatility and practical value in NDT field.

An Adaptive Radar Target Detection Method Based on Alternate Estimation in Power Heterogeneous Clutter

Multichannel radars generally need to utilize a certain amount of training samples to estimate the covariance matrix of clutter for target detection. Due to factors such as severe terrain fluctuations and complex electromagnetic environments, the training samples usually have different statistical characteristics from the data to be detected. One of the most common scenarios is that all data have the same clutter covariance matrix structure, while different data have different power mismatches, called power heterogeneous characteristics. For detection problems in the power heterogeneous clutter environments, we propose detectors based on alternate estimation, using the generalized likelihood ratio test (GLRT) criterion, Rao criterion, Wald criterion, Gradient criterion, and Durbin criterion. Monte Carlo simulation experiments and real data indicate that the detector based on the Rao criterion has the highest probability of detection (PD). Furthermore, when signal mismatch occurs, the detector based on the GLRT criterion has the best selectivity, while the detector based on the Durbin criterion has the most robust detection performance.

Deriving the new cotangent Fréchet distribution with real data analysis

This study introduces the family of the novel ”cot-generator” distributions based on the cotangent function. The construction of the probability density function based on the cot-generator and its corresponding moments, reliability indicators, and order statistics are derived. Regarding inferential procedures, the maximum likelihood estimation method is implemented to estimate the model parameters in a non-closed form. The novel Cot-Fréchet distribution (NCFD) is then focused on a specific class member, constructed using the Fréchet distribution as the baseline. The estimators’ bias, variance, and mean square error (MSE) efficiency are examined and evaluated through Monte Carlo simulation experiments. The novel model is also applied to some real data sets to assess its efficacy and is compared with other competing distributions.

Bootstrap-based confidence intervals for the standard two-sided power distribution

The two-parameter standard two-sided power family of distributions on (0, 1) is considered in this article. We propose bootstrap standard errors for the maximum likelihood estimators, as well as bootstrap confidence intervals for its parameters, once these important statistical measures of accuracy cannot be computed based on first-order asymptotic theory. We consider Monte Carlo simulation experiments to verify the performance of the bootstrap methods, and the numerical results are quite promising. Applications to real data are also considered to illustrate the proposed methodology in practice.

A note on Farebrother’s estimator: a comparative study

In this article, we begin by providing a theoretical comparison between Farebrother’s estimator and the ridge estimator, in terms of the MSE matrix criterion, under three distinct restrictions when r is random. Additionally, we propose an estimate of parameter k for Farebrother’s estimator. Subsequently, we present a Monte Carlo simulation experiment to compare Farebrother’s estimator with OLS, RLS, and ridge estimators.

Higher-order asymptotic refinements in a multivariate regression model with general parameterization

This paper derives a general Bartlett correction formula to improve the inference based on the likelihood ratio test in a multivariate model under a quite general parameterization, where the mean vector and the variance-covariance matrix can share the same vector of parameters. This approach includes a number of models as special cases such as non-linear regression models, errors-in-variables models, mixed-effects models with non-linear fixed effects, and mixtures of the previous models. We also employ the Skovgaard adjustment to the likelihood ratio statistic in this class of multivariate models and derive a general expression of the correction factor based on Skovgaard approach. Monte Carlo simulation experiments are carried out to verify the performance of the improved tests, and the numerical results confirm that the modified tests are more reliable than the usual likelihood ratio test. Applications to real data are also presented for illustrative purposes.

Parameter estimation of Chen distribution under improved adaptive type-II progressive censoring

ABSTRACT This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset.

Bivariate Random Coefficient Integer-Valued Autoregressive Model Based on a ρ-Thinning Operator

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter ρ and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models.

Inference for Compound Exponential XLindley Model with Applications to Lifetime Data

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.

Robust confidence regions for the index and functional coefficients in the single-index varying coefficients regression model

A single-index varying coefficients regression model is considered, from which robust confidence regions/intervals of the regression parameters are derived. Considering the rank-based estimating equations, empirical likelihood objective functions of the index and functional coefficients objective functions are defined and their asymptotic properties are established under mild regularity conditions. The performance of the proposed approach is demonstrated via extensive Monte Carlo simulation experiments. The simulation results are compared with those obtained from a normal approximation alternative. Also the proposed method is compared with the least squares and least absolute deviations alternatives. Finally, a real data example is given to illustrate the method.

Simulation Method for the Impact of Atmospheric Wind Speed on Optical Signals in Satellite–Ground Laser Communication Links

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems.

Testing distribution for multiplicative distortion measurement errors

. In this article, we study a goodness of fit test for a multiplicative distortion model under a uniformly distributed but unobserved random variable. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. The proposed k-th power test statistic is based on logarithmic transformed observations and a correlation coefficient-based estimator without distortion measurement errors. The proper choice of k is discussed through the empirical coverage probabilities. The asymptotic null distribution of the test statistics are obtained with known asymptotic variances. Next, we proposed the conditional mean calibrated test statistic when a variable is distorted in a multiplicative fashion. We conduct Monte Carlo simulation experiments to examine the performance of the proposed test statistics.

“Wrong” skewness and endogenous regressors in stochastic frontier models: an instrument-free copula approach with an application to estimate firm efficiency in Vietnam

Stochastic frontier models commonly assume positively skewed inefficiency. However, if the data speak against this assumption, sample-failure problems are often cited, but less attention is paid to economic reasons. We consider this phenomenon as a signal of distinctive population characteristics stemming from the inefficiency component, emphasizing its potential impact on evaluating market conditions. Specifically, we argue more generally that “wrong” skewness could indicate a lack of competition in the market. Moreover, endogeneity of model regressors presents another challenge, hindering the identification of causal relationships. To tackle these issues, this paper proposes an instrument-free estimation method based on Gaussian copulas to model the dependence between endogenous regressors and composite errors, while accommodating positively or negatively skewed inefficiency through simultaneous identification. Monte Carlo simulation experiments demonstrate the suitability of our estimator, comparing it with alternative methods. The contributions of this study are twofold. On the one hand, we contribute to the literature on stochastic frontier models by providing a comprehensive method for dealing with “wrong” skewness and endogenous regressors simultaneously. On the other hand, our contribution to an economic understanding of “wrong” skewness expands the comprehension of market behaviors and competition levels. Empirical findings on Vietnamese firm efficiency indicate that endogeneity hinders the detection of “wrong” skewness and suggests a lack of competitive market conditions. The latter underscores the importance of policy interventions to incentivize firms in non-competitive markets.

Data-driven quasi-convex method for hit rate optimization of process product quality in digital twin

Hit rate is an important quantitative criterion for the process product quality prediction of the integrated industrial processes. The hit rate indicates the percentage of product quantities accepted by the downstream process within the controlled range of the product quality. The optimization model of the hit rate criterion is a non-convex intractable problem. In order to improve the hit rate of the predicted product quality, we define a hit rate optimization problem, and propose a data-driven quasi-convex approach, which converts the original problem into a set of convex feasible problems and achieves the optimal hit rate. The proposed approach combines factorial hidden Markov models, multitask elastic net and quasi-convex optimization. In order to illustrate the advantages of the proposed approach, a Monte Carlo simulation experiment is designed to verify the convex optimization property. Another experiment is carried out on two actual steel production datasets for the temperature prediction in molten iron dispatch. The results confirm that the proposed approach not only exhibits superior performance with the controlled hit rate, but also improves the hit rate by at least 41.11 % and 31.01 %, respectively, compared with the classical models on two real datasets.

Bayesian and empirical-Bayesian evaluations of the Topp–Leone lifetime model using lower record statistics

Record statistics are generally used to measure a process’ stochastic behavior at previously unheard-of values, either upper or lower. It can be obtained or calculated using order statistics from a sample whose size is dictated by the values and order of occurrence of observations. Due to its finite support and bathtub-shaped hazard function, the Topp–Leone (TL) distribution is appealing for reliability investigations. In today’s practical applications, estimating unknown parameters and predicting upcoming records is an essential issue. Thus, in this work, the TL distribution’s lower record values are taken into account. Against the symmetric squared-error loss, both Bayes and empirical-Bayes approaches are used to estimate the TL’s parameter and calculate prediction limits for upcoming lower record values. A Monte Carlo simulation experiment is performed to assess the accuracy of the estimation methodologies provided. To demonstrate the operability and usefulness of the various approaches, two useful applications are studied. The numerical evaluations show that the suggested approaches perform effectively and that the provided estimations are adequate in practice.