Classical Estimation Methods Research Articles

Neutrosophic robust ratio type estimator for estimating finite population mean

Various authors have put their sincere efforts into proposing ratio estimators for estimating the population's mean and variance under different situations and sampling methods. But the problem arises when data is unstable, imprecise, ambiguous, incomplete and vague. In such situations, classical methods of estimation do not yield precise results, as these methods are not meant for such problems. Given this difficulty, Neutrosophic statistics are the only alternative as it deals with indeterminacy. So in this study, we have proposed a generalized Neutrosophic robust ratio type estimator which can be used to provide good results in such situations, as well as in the case of the presence of outliers. For the evaluation point of view, we have made use of real data set and simulation study to check the efficacy of our suggested estimators over the mentioned existed estimators.

Probabilistic modeling of COVID-19 events: Exploring new alpha generated family for enhanced analysis capabilities

This study explores a new family of distributions to enhance the analysis capabilities of COVID-19 events, providing valuable insights for informed decision-making and effective public health management. Accurate understanding and prediction of COVID-19 transmission patterns and their impacts are crucial in reducing the mortality rate, especially in proactive control and mitigation efforts. The proposed approach focuses on a best-fit probabilistic model that incorporates a comprehensive assessment of various statistical measures. Additionally, seven well-recognized classical point estimation methods are employed to identify the most suitable approach for assisting epidemiologists in their analysis. The study analyzes COVID-19 data from multiple countries, including the Netherlands, Mexico, the United Kingdom, China, Canada, Saudi Arabia, and Italy, considering different aspects such as mortality rates and the number of deaths. By evaluating the performance of the new alpha generated family of distributions in modeling COVID-19 events. This research contributes to the advancement of our understanding of the disease's probabilistic nature. The findings have practical implications, guiding the development of public health policies, resource allocation strategies, and intervention plans, ultimately facilitating more effective control and mitigation of COVID-19 outbreaks.

Estimating the survival function Maximum Likelihood and Cramér-Von Mises Method use of amixture distribution weibull and ailamujia with apractical application

Tow failure distributions were mixed ,weibull distribution and ailamujia distribution it's called weibull –ailamujia distribution which consists of four features, the two distributions were mixed by adding a mixing parameter ,the mixture of two distributions would be more efficient ,and representative of the data than the single distributions. A group of statistical properties of the mixture distribution were studied , such as the probability function ,the survival function and the failure rate function .classical estimation method were used to estimate the parameters of the mixture distribution, which are maximum likelihood of method ,the cramer –von mises method ,The method were compared using monte carlo simulations real data were taken regarding drug –resistant tuberculosis (TB) Multi Drug Resistance(MDR) methods were compared using the MSE statistical criterion ,and the result should a preference for the method cramer-von mises for having the lowest MSE

Human Pose Estimation Based on Efficient and Lightweight High-Resolution Network (EL-HRNet).

As an important direction in computer vision, human pose estimation has received extensive attention in recent years. A High-Resolution Network (HRNet) can achieve effective estimation results as a classical human pose estimation method. However, the complex structure of the model is not conducive to deployment under limited computer resources. Therefore, an improved Efficient and Lightweight HRNet (EL-HRNet) model is proposed. In detail, point-wise and grouped convolutions were used to construct a lightweight residual module, replacing the original 3 × 3 module to reduce the parameters. To compensate for the information loss caused by the network's lightweight nature, the Convolutional Block Attention Module (CBAM) is introduced after the new lightweight residual module to construct the Lightweight Attention Basicblock (LA-Basicblock) module to achieve high-precision human pose estimation. To verify the effectiveness of the proposed EL-HRNet, experiments were carried out using the COCO2017 and MPII datasets. The experimental results show that the EL-HRNet model requires only 5 million parameters and 2.0 GFlops calculations and achieves an AP score of 67.1% on the COCO2017 validation set. In addition, PCKh@0.5mean is 87.7% on the MPII validation set, and EL-HRNet shows a good balance between model complexity and human pose estimation accuracy.

Chirp Rate Estimation of LFM Signals Based on Second-Order Synchrosqueezing Transform

For the problem of low time-frequency aggregation of the short-time Fourier transform (STFT), which causes the parameter estimation performance degradation of linear frequency modulation (LFM) signals at low signal-to-noise ratio (SNR), second-order synchrosqueezing transform (SSST) is proposed based on the square of STFT amplitude. The time-frequency resolution and energy aggregation are improved by means of squeezing and reassigning the time-frequency spectrum. Meanwhile, in order to decrease the calculation of classical parameter estimation methods, the Hough transform is used for rough estimation, and then the fractional Fourier transform (FRFT) is used for accuracy estimation based on the Renyi entropy. The simulation result shows that higher estimation accuracy is obtained at low SNR, and it has better robustness.

Graph meets probabilistic generation model: A new perspective for graph disentanglement

Different from the existing graph disentanglement neural networks, we interpret the graph entanglement under a probabilistic generation framework in this paper. With this foundation, a Mixed Probabilistic Generation Model induced Graph Disentanglement Network (MPGD) is proposed. Considering the disentangled components corresponding to different factors as obeying specific distributions, a generalized probabilistic aggregation scheme among components is deduced theoretically. As a key part of the mixed probabilistic generative model, we provide a solution for estimating the mixture probabilities using self-attention and an in-depth analysis of its close connection with the classical EM parameter estimation method. Meanwhile, a way of probabilistic aggregation is formulated to obtain the node representation in embedding space. In addition, the prior mixture probabilities are formulated as an auxiliary factor-aware representation to facilitate the twin-branch prediction. A variety of experiments show that MPGD achieves more competitive performance than some existing state-of-the-art methods while having ideal disentangling effects. The code implementation is available in https://github.com/GiorgioPeng/MPGD.

The E-Bayesian and hierarchical Bayesian estimations for the reliability analysis of Kumaraswamy generalized distribution based on upper record values

This paper investigates the E-Bayesian and hierarchical Bayesian estimations of shape parameter and reliability function of Kumaraswamy generalized distribution based on upper record values. The classical estimation method is utilized to deduce the maximum likelihood estimation of unknown parameter and reliability function. Bayesian estimates are derived by using conjugate Gamma prior distributions under quadratic and general entropy loss functions. Furthermore, assuming that hyper-hyperparameters obey three prior distributions, the E-Bayesian estimates of unknown parameters and reliability functions are obtained. The hierarchical Bayesian estimates are obtained by using hierarchical prior distributions. We also explore some characteristics and size relationships of E-Bayesian and hierarchical Bayesian estimations. The performance of E-Bayesian, Hierarchical Bayesian, Bayesian, and maximum likelihood estimations is compared based on the minimum mean square error criterion. Finally, the proposed estimation methods are applied to evaluate the reliability of the specimen under ultrasonic fatigue testing, and the results align with their structures and profiles.

Reliability Estimation of Retraction Mechanism Kinematic Accuracy under Small Sample

Due to intricate operating conditions, including structural clearances and assembly deviations, the acquisition of test data of landing gear retraction mechanism is limited, posing challenges for reliability analysis. To solve the problem, a Bayesian-based reliability analysis method by fusing prior and test data is proposed, focusing on the mechanism kinematic accuracy under small-sample conditions. Firstly, a dynamic simulation model is established to collect prior data, and retraction tests are conducted to obtain test data. Then, based on Bayesian theory, the motion accuracy parameter estimation model integrating prior and test samples is established. To obtain accurate hyper parameters, the prior samples are expanded using neural network. Finally, taking the retraction mechanism as the research object, the kinematic accuracy reliability is quantified, and the impact of uncertainty factors is analyzed in depth. The results show that the proposed method is superior to the classical interval estimation method in stability and effectively mitigates the impact of uncertainty factors.

Bayesian and Classical Semi-parametric Estimation of the Balanced Longitudinal Data Model

The primary objective of this study is to employ semi-parametric regression techniques in the balanced longitudinal data model. Where the parametric regression models are plagued by the problem of strict constraints, while non-parametric regression models, despite their flexibility, suffer from the problem of the curse of dimensionality. Consequently, semi-parametric regression presents a suitable solution to address the problems in parametric and non-parametric regression methods. The advantage of this model is that it contains all the positive properties included in the previous two models such as containing strict restrictions in its parametric component, complete flexibility in its non-parametric component, and clarity of the interaction between its parametric and non-parametric components. According to the above, two methods were used to estimate a semi-parametric balanced longitudinal data model. The first is the Bayesian estimating method; the second is the Speckman method, which estimated the unknown nonparametric smoothing function by employing the kernel smoothing Nadaraya & Watson method. The Aim was to make a comparison between the Bayesian estimation method and the classical estimation method. Based on simulation experiments conducted on three different sample sizes (50, 100, and 200), it was concluded that the Bayes method is best at the variance levels (1,5). In contrast, the Profile least square method is best at the variance level (10).

Machine learning based low-complexity channel state information estimation

In 5G communications, the acquisition of accurate channel state information (CSI) is of great importance to the hybrid beamforming of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system. In classical mmWave MIMO channel estimation methods, the exploitation of inherent sparse or low-rank structures has demonstrated to improve the performance. However, most high-accurate CSI estimators incur a high computational complexity and require the prior channel information, which hence present the major challenges in the practical deployment. In this work, we leverage machine learning to design the low-complexity and high-performance channel estimator. To be specific, we first formulate the CSI estimation, in the case of sparse structure, as one classical least absolute shrinkage and selection operator problem. In order to reduce the time complexity of existing compressed sensing (CS) methods, we then approximate the original optimization problem to another one, by imposing the other low-rank constraint that was barely considered by CS. We thus solve this new approximated problem and attain the near-optimal solution of the original problem. One new method excludes any prior channel information, and greatly improves the estimation performance, which only incurs a low time complexity. Simulation results demonstrate the superiority of our proposed method both in the estimation accuracy and time complexity.

Different classical estimation methods using ranked set sampling and data analysis for the inverse power Cauchy distribution

A recent two-parameter distribution that offers additional flexibility in modeling a real lifetime dataset is the inverse power Cauchy distribution (IPCD). The IPCD is user-friendly and analytically attractive, and it can be effectively utilized to analyze actual datasets. On the other hand, ranked set sampling (RSS) is a method of gathering data that first combines simple random sampling (SRS) with the expertise and judgment of the field investigator in determining where to take samples. The RSS is known to be more efficient than the SRS as well as less expensive since fewer sample units need to be procured and evaluated. In this article, various estimation techniques for IPCD are examined. The parameter estimates are determined utilizing the RSS and SRS of seven frequentist approaches, which are the maximum likelihood, Anderson-Darling, least squares, Cramér-von Mises, maximum product spacing, weighted least squares, and right-tail Anderson-Darling approaches. Using accuracy criteria, a simulation analysis is done to assess the efficacy of the provided RSS-based estimates. For further clarification, one real data analysis is provided.

Using Feasible Graphical Lasso Regression Method to Estimate the Parameters of General Linear Regression Model Under High Dimensional Data with Application

The high dimensions problem is one of the important problems that affect the data, and with company of high dimensional data in the general linear regression model, it becomes very difficult to use classical estimation methods such as maximum likelihood method and moments method because these methods lead to biased and inefficient estimates for parameters of the model. The necessity to use new methods to estimate the parameters of the general linear regression model. In this research, two methods were used, the Smooth Integration of Counting Absolute Deviation SICA method, as well as the Feasible Graphical Lasso method FGLasso. Simulation data were used, as well as real data representing the level of pollution in the Tigris River. The results compared using the Mean Square Error MSE and the results showed that the FGLasso estimator is the best

Applications of a new loss and cost-based process capability index to electronic industries

In this article, we propose a new process capability index called C pmc ′ which is based on asymmetric loss function (linear exponential) and tolerance cost function for a normal process which provides a tailored way of incorporating the loss and tolerance cost in capability analysis. Next, we estimate the proposed PCI C pmc ′ when the process follows the normal distribution using six classical methods of estimation and we compare the performance of the considered methods of estimation in terms of their mean squared errors through simulation study. Besides, five bootstrap methods are employed for constructing the confidence intervals for the index C pmc ′ . The performance of the bootstrap confidence intervals (BCIs) are compared in terms of average width and coverage probabilities using Monte Carlo simulation. Finally, for illustrating the effectiveness of the proposed index and methods of estimation and BCIs, two real data sets from electronic industries are re-analyzed.

Inverse power Ramos–Louzada distribution with various classical estimation methods and modeling to engineering data

This work uses the inverse-power transformation to create the inverse power Ramos–Louzada distribution (IPRLD), a novel two-parameter version of the Ramos–Louzada distribution. The failure rate of the new distribution can be represented by a reverse bathtub shape, a rising shape, or a decreasing shape, making it appropriate for a range of real data. Asymmetrical and unimodal densities can be produced via the IPRLD. Its mathematical characteristics are computed in some cases. The novel proposed model’s structural characteristics are derived. To estimate the model parameters, several estimating strategies are explored, including ten classical methods. Simulation results with their partial and total ranks are used to evaluate the ranking and behavior of various approaches. Finally, two real-world datasets are used to experimentally show the suggested distribution’s adaptability. The analysis of the data reveals that the introduced distribution offers a better fit than some significant rival distributions, including the inverse Ramos–Louzada, inverse power Burr Hatke, inverse Nakagami-M, inverse log-logistic, inverse weighted Lindley, inverse Lindley, and Ramos–Louzada.

The Comparison of Classical and Bayesian Structural Equation Models Through Ordered Categorical Data: A Case Study of Banking Service Quality

This study aims to compare classical Structural Equation Modeling (SEM) and Bayesian Structural Equation Modeling (BSEM) in terms of ordered categorical data. In order to show the relationship between service dimensions and banks’ customers’ satisfactions, a data were analyzed with classical SEM and BSEM parameter estimation methods. In the Banking Service Quality Scale (SERVQUAL), which consists of sequential categorical data, classical SEM and BSEM were compared to evaluate customer satisfaction. In classical SEM, parameter estimations were made according to the Maximum Likelihood (ML) estimation method. In most of the studies using SERVQUAL in the literature, the results found in previous studies could not be used as prior informative because the service dimensions consisted of different number of factors. For this reason, considering that the results could yield similar results with the ML estimation method due to the high sample size, the use of conjugate prior was preferred instead of the non-informative prior due to the ordinal categorical nature of the data in the BSEM analysis. Since the questionnaire used in the study had a Likert type scale structure, the threshold values were calculated for ordered categorical data and used as prior informative. Thus, by using the threshold values obtained from the data set, a faster convergence of the parameters was achieved. As a result, service dimensions affecting satisfaction according to the ML parameter estimation method were found, Assurance, Physical Appearance, and Accessibility. In addition to these, Reliability as a service dimension was found to be also statistically significant in BSEM.

A new alpha logarithmic-generated class to model precipitation data with theory and inference

Precipitation, or rainfall, is a central feature of the weather cycle and plays a vital role in sustaining life on Earth. However, existing models such as the Poisson, exponential, normal, log-normal, generalized Pareto, gamma, generalized extreme value, lognormal, beta, Gumbel, Weibull, and Pearson type III distributions used for predicting precipitation are often inadequate for precisely representing the complex pattern of rainfall. This study proposes a novel and innovative approach to address these limitations through the new alpha logarithmic-generated (NAL-G) class of distributions. The study authors thoroughly examine the NAL-G class and a unique model, the NAL-Exponential (NAL-Exp) distribution, with a focus on analyzing mathematical properties such as moments, quantile function, entropy, order statistics, and more. Six recognized classical estimation methods are employed, and extensive simulations are conducted to determine the best one. The NAL-Exp distribution demonstrates its high adaptability and value through its superior performance in modeling four distinct rainfall data sets. The results show that the NAL-Exp distribution outperforms other commonly used distribution models, highlighting its potential as a valuable tool in hydrological modeling and analysis. The increased versatility and flexibility of this new approach hold great potential for enhancing the accuracy and reliability of future rainfall predictions.

Neural Partial Differentiation for Parameter Estimation of Flexible Aircraft Dynamics

Although the parameter estimation methodologies had been successfully applied for the rigid aircraft dynamics, the aircraft with high degree of flexibility poses challenges to determine the appropriate aeroelastic models for inclusion in the parameter estimation algorithms. Application of the neural networks for the aerodynamic modeling and parameter estimation of an aeroelastic aircraft (or flexible aircraft) is addressed in this paper. A neural network with the scaled conjugate gradient learning algorithm is used for modeling lift and pitching moment coefficients. The partial differentiation of the neural network output is carried out for the estimation of equivalent parameters of an aeroelastic aircraft. It is demonstrated that a reasonable model and estimates of the equivalent parameters for the aeroelastic aircraft are possible with the neural partial differential method by using the measured motion and control variables, without any need for postulating the coupled equations of motion or initialization of the parameters to be estimated. The proposed approach reduces the large number of parameters for aeroelastic aircraft dynamics into fewer equivalent parameters, and this methodology does not require the measurements of the elastic deflections or their derivatives. The neural partial differential method is applied to the simulated flight data of an aeroelastic aircraft for the longitudinal dynamics. The performance of the neural partial differential approach is compared with the estimates obtained from the other methods like classical estimation methods, analytical computation, and values given in the literature for rigid body modeling. The performance is also validated by comparing the measured lift force and pitching moment coefficients with the neural predicted and neural reconstructed coefficients using the estimates obtained through the neural partial differential approach.

Semi-Supervised Medical Image Segmentation With Voxel Stability and Reliability Constraints.

Semi-supervised learning is becoming an effective solution in medical image segmentation because annotations are costly and tedious to acquire. Methods based on the teacher-student model use consistency regularization and uncertainty estimation and have shown good potential in dealing with limited annotated data. Nevertheless, the existing teacher-student model is seriously limited by the exponential moving average algorithm, which leads to the optimization trap. Moreover, the classic uncertainty estimation method calculates the global uncertainty for images but does not consider local region-level uncertainty, which is unsuitable for medical images with blurry regions. In this paper, the Voxel Stability and Reliability Constraint (VSRC) model is proposed to address these issues. Specifically, the Voxel Stability Constraint (VSC) strategy is introduced to optimize parameters and exchange effective knowledge between two independent initialized models, which can break through the performance bottleneck and avoid model collapse. Moreover, a new uncertainty estimation strategy, the Voxel Reliability Constraint (VRC), is proposed for use in our semi-supervised model to consider the uncertainty at the local region level. We further extend our model to auxiliary tasks and propose a task-level consistency regularization with uncertainty estimation. Extensive experiments on two 3D medical image datasets demonstrate that our method outperforms other state-of-the-art semi-supervised medical image segmentation methods under limited supervision. The source code and pre-trained models of this method are available at https://github.com/zyvcks/JBHI-VSRC.

Simulation Study of the Bayesian and Non-Bayesian Estimation of a new Lifetime Distribution Parameters with Increasing Hazard Rate

In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.

A New Xgamma–Weibull Model Using Type-II Adaptive Progressive Hybrid Censoring and Its Applications in Engineering and Medicine

This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances.