Distributed Parameter Estimation Research Articles

Fine-tuning weibull distribution parameters in Morocco’s Tarfaya and Tangier wind farms using two-stage swarm optimization

This study assesses the efficacy of particle swarm optimization (PSO) in estimating scale ( c) and shape ( k) parameters of the Weibull distribution model for wind energy forecasting at two key wind farm sites in Morocco— Tarfaya in the south and Tangier in the north, utilizing real wind data from 2022. Employing a novel square frequency error objective function to enhance parameter accuracy, the study adopts a two-stage training approach involving recursive least-square estimation and PSO fine-tuning. Validation with artificial data underscores PSO’s effectiveness under diverse wind conditions. Parameter sensitivity analysis identifies four optimal PSO configurations, with the PSO-4 model exhibiting superior performance. Comparative analysis against traditional and heuristic optimization methods consistently demonstrates PSO-4’s lowest root-mean-square error (RMSE) and mean absolute error (MAE), high coefficients of determination ( R2), and shortest computation time. The research highlights PSO-4 model as a precise and efficient tool for Weibull distribution parameter estimation in wind energy forecasting, showcasing robust convergence across both wind farm sites.

Estimation method of the Homodyned K-distribution based on the Improved Shuffled Frog Leaping Algorithm for ultrasound tissue characterization

Abstract Aiming at promoting the accuracy of the integral value of the probability distribution function (PDF) of Homodyned K-distribution (HK), a new maximum likelihood estimation method for HK distribution parameters is proposed by using the improved shuffled frog leaping algorithm (ADM-SFLA) and Newton-Raphson iterative algorithm (NR). To improve the accuracy of the global search of the traditional SFLA, two variation factors of Gauss and Cauchy are first used to find the global optimal solution in a convergence state. Secondly, to obtain the integral node with optimal segmentation, the ADM-SFLA is used to perform the non-equidistant adaptive segmentation of the integral interval. Then, the PDF of the HK distribution is calculated between each numerical integration cell based on Simpson integral formula. Subsequently, the integral value of the PDF for HK distribution is obtained by summing the integration values from each numerical integration cell. Finally, the optimal estimation of HK distribution parameters is obtained based on NR algorithm. The performance of the proposed method is evaluated and compared through simulated data as well as the envelope signals obtained from the ultrasonic simulation model with different scattering components. The results show that the ADM-SFLA based method can improve the estimation accuracy of HK distribution parameters effectively.

Comparison Of Some Estimation Methods For The Estimators Of Marshall Olkin Distribution With Simulation

The research comprised multiple simulated tests to determine the relationship between (sample size, distribution parameter value, estimation method, and pollution indivuduales). The experimental findings indicate that the estimator is influenced by sample size, the value of distribution parameter, estimation method, and pollution indivuduales. The results of the mean square error analysis indicate that (robust estimation method) produces the best results with the lowest mean square error, and the best estimation method was (191) of (243) simulation experiments. Additional statistical distributions with additional factors can be performed to demonstrate additional results.

Revisiting Maximum Log-Likelihood Parameter Estimation for Two-Parameter Weibull Distributions: Theory and Applications

In this article, we reexamine properties of maximum log-likelihood parameter estimation for two-parameter Weibull distributions which have been applied in many different sciences. Finding reasons for this popularity is a key question. Our main contribution is a thorough existence and uniqueness proof for a global maximizer with respect to the parameter space. We first provide existence and uniqueness of local maximizers by Schauder’s first fixed point theorem, monotony arguments and local concavity of its Hessian matrix. Thus, we can prove our main result of existence and uniqueness of a global maximizer by considering all limiting cases with respect to the parameter space. We finally strengthen our theoretical findings on four data sets. On the one hand, two synthetic data sets underline our need for our data assumptions while, on the other hand, we choose two data sets from wind engineering and reliability engineering to demonstrate usefulness in real-world applications.

The Maxwell-Boltzmann-Exponential distribution with regression model

Abstract This paper proposes a new probability model called as Maxwell-Boltzmann-Exponential (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-skewed and bimodal. Two real data sets are used to demonstrate the applicability of the proposed models against the existing models.

Fisher information contained in incomplete observations

The accuracy of statistical estimates of unknown distribution parameters depends not only on the bulk of sampling data but also on the method of data acquisition. The information content of experimental data is one of the basic requirements. Problems of mathematical statistics, in particular parametric estimation based on censored observations, have specific features. Typical representatives of models of incomplete observations on a straight line are models of random censoring, competing risks of (single, multiple) random censoring. The purpose of this study is to show that censoring does not always lead to loss of (Fisher) information. It is shown that if censoring is informative, i.e., the distribution of censoring random variables depends on the same parameter, it is possible to specify a model where information can be preserved due to censoring. On the contrary, if the censoring is not informative, then the loss of information is inevitable. The Cramer – Rao efficiency was taken as a criterion for the quality of the assessment, whereas the Fisher information was taken as the criterion for information about the unknown parameter.

Bias-compensated based diffusion affine projection like maximum correntropy algorithm

A distributed network with highly colored input signal is often located in a scenario where the output signal is subject to impulse noise. Under the above scenario, the performance of the diffusion adaptive algorithms will suffer from performance degradation, which includes distributed parameter estimation accuracy and convergence/tracking rate. To solve these problems, the diffusion affine projection like maximum correntropy (DAPLMC) algorithm is proposed. Moreover, highly colored input signals tend to be mixed with noise, which will lead to biased estimation. To deal with the adverse impact of biased estimation, based on the bias compensation (BC) strategy, the bias-compensated DAPLMC (BC-DAPLMC) algorithm is proposed in this paper. By analyzing the convergence performance of the BC-DAPLMC algorithm, a range of its step size is obtained, and the steady-state error of the BC-DAPLMC algorithm is studied. The superior performance of the BC-DAPLMC algorithm and theoretical steady-state error analysis is validated by simulation results.

Output-Feedback-Based Adaptive Leaderless Consensus for Heterogenous Nonlinear Multiagent Systems With Switching Topologies.

This article investigates the leaderless output consensus control problem for a class of nonlinear multiagent systems with heterogenous system orders and unmatched unknown parameters via output-feedback control. The interaction topology among the agents is undirected and jointly connected. Due to the heterogenous system orders and switching topology among the agents, the classical distributed adaptive backstepping-based control technique cannot be applied to solve the problem considered in this article. To solve this issue, a novel distributed reference system is first proposed for each agent, by using only relative outputs of the neighboring agents. Subsequently, a fully distributed reference system-based adaptive leaderless output consensus control scheme is designed via output-feedback control. A remarkable merit of the proposed control scheme lies in that precisely known nonlinear dynamics, system states, distributed parameter estimates, and the states of virtual reference system are no longer needed to be shared with neighbors. This implies that the communication burden can be effectively alleviated, and even the communication network can be replaced by some perception sensors. Finally, two illustrative examples are provided to verify the effectiveness of the proposed control scheme.

Conway-Maxwell-Poisson profile monitoring with rk-Shewhart control chart: a comparative study

A control chart is an essential tool in Statistical Quality Control for monitoring the production process. It provides a visual means of identifying process irregularities. In this study, we focus on the Shewhart control chart based on the rk-deviance residuals, namely rk-Shewhart control charts to examine the Conway–Maxwell–Poisson (COM-Poisson) profile, which is used to model the count data with varying degrees of dispersion. The primary goal of this study is to identify the biasing parameter that produces the best result among newly presented biasing parameters developed based on existing ones. It provides a short overview of the COM-Poisson distribution, its modeling, and rk parameter estimation in the case of multicollinearity, as well as the construction of the deviance-residual-based Shewhart chart. To evaluate the performance of the rk-Shewhart, we conduct an analysis using a real-life data set, considering various shift sizes. By employing different biasing parameters, we examine the effectiveness of the rk-Shewhart control chart. The performance evaluation outcomes of the rk-Shewhart charts are compared to the ML-deviance-based Shewhart chart and within themselves based on the biasing parameters. The results demonstrate the advantage of the rk-Shewhart charts over the ML-deviance-based control chart in detecting out-of-control signals. Among the considered biasing parameters, the rk-Shewhart chart utilizing the adjusted biasing parameter k_4 shows the best performance based on the ARL metric.

Generalized Moment Estimators Based on Stein Identities

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.

Bias-Correction Methods for the Unit Exponential Distribution and Applications

The bias of the maximum likelihood estimator can cause a considerable estimation error if the sample size is small. To reduce the bias of the maximum likelihood estimator under the small sample situation, the maximum likelihood and parametric bootstrap bias-correction methods are proposed in this study to obtain more reliable maximum likelihood estimators of the unit exponential distribution parameters. The procedure to implement the bias-corrected maximum likelihood estimation method is derived analytically, and the steps to obtain the bias-corrected bootstrap estimators are presented. The simulation results show that the proposed maximum likelihood bootstrap bias-correction method can significantly reduce the bias and mean squared error of the maximum likelihood estimators for most of the parameter combinations in the simulation study. A soil moisture data set and a numerical example are used for illustration.

A new extended Pham distribution for modelling cancer data

In this study, a novel extended Pham model is offered and examined. This model can fit positive, negative, and approximately symmetric data. In addition, it features four alternative hazard rate shapes, namely increasing, decreasing, bathtub, and upside-down bathtub shapes. The new model's main properties, such as quantiles, moments, and mean deviations, are derived. To evaluate the estimation of distribution parameters, two approaches are studied. From a classical standpoint, the maximum likelihood technique is used to determine the point and approximate confidence intervals of all unknown parameters. The Bayesian estimation method, on the other hand, is considered via the Markov chain Monte Carlo technique for obtaining Bayes point estimates alongside Bayes credible intervals. We present various Monte Carlo simulation studies to investigate the efficacy of maximum likelihood and Bayes estimation findings for the model's parameters. Numerical investigations showed that the offered Bayes estimates outperformed those derived using the conventional method. We also analyzed two sets of real data taken from the medical sector; the first represents survival rates for cancer patients who received a combination of radiotherapy and chemotherapy, and the second consists of remission times for bladder cancer patients. These clinical scenarios reveal that the new model outperforms other important competing models based on specific statistical criteria. Ultimately, for both clinical data applications, the proposed extended Pham distribution is the best choice compared to the traditional Pham and the other well-known eight lifetime models.

Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer’s Disease Using Biophysical Modeling and Deep Learning

Alzheimer’s disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer’s mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.

Fast parameter estimation of generalized extreme value distribution using neural networks

AbstractThe heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm (pre‐industrial), 700 ppm (future conditions), and 1400 ppm , and compare the results with those obtained using the maximum likelihood approach.

Improvement of the method of time rationing for assembling car groups on one track

Purpose. To improve the method for standardizing the duration of the shunting operation of assembling cars on one track. This can be achieved as a result of solving the following research problems: development of a method for searching the optimal order of assembling cars on one track; distribution parameters estimation of the random value of the duration of shunting operation of assembling cars on one track based on calculation experiments. Methodology. During the research, the methods of theory of railway operation, dynamic programming and mathematical statistics were used. Findings. Research on the assembling process of car group to one track established the distribution parameters of the random variable of time spent for shunting. In the course of the research, the problem of choosing the optimal order of shunting operations during car assembling was formalized and solved as a problem of dynamic programming. The time spent for shunting work was chosen as the optimality criterion. The paper considers the possibility of approximating the data of calculation experiments by analytical dependencies. It was found out that the use of linear polynomials with interaction allows obtaining dependencies describing time standards with a relative accuracy of ±5 %. Originality. The method is improved for developing the time standards for shunting work, which, unlike the existing one, is based on the performance of a series of calculation experiments, each of which solves the optimization problem of finding such an order of assembling cars that ensures minimum time consumption for shunting. Practical value. The methods developed in the work and the dependencies obtained allow improving the quality of decisions made when developing technology and designing railway stations and sidings of industrial enterprises.

Collaborative Parameter Estimation of Multiple Unmanned Surface Vessels: A Robust Distributed Estimator-Based Approach

In this paper, the collaborative parameter estimation of multiple unmanned surface vessels (USVs) with model structure uncertainties is studied. The considered parameter estimation problem is first converted into a distributed state and parameter joint estimation problem. Then, the robust distributed estimator is constructed to handle the inevitable model structure uncertainties, and the upper bounds of prediction and estimation error covariance matrices are derived respectively. Additionally, the upper bound of the estimation error covariance matrix is minimized by designing appropriate estimator gains. Finally, the advantages of the proposed distributed parameter estimation approach from the perspectives of information interaction and consideration of model structure uncertainties are verified via simulations and practical experiments.

Fast and High-Performance Learned Image Compression With Improved Checkerboard Context Model, Deformable Residual Module, and Knowledge Distillation.

Deep learning-based image compression has made great progresses recently. However, some leading schemes use serial context-adaptive entropy model to improve the rate-distortion (R-D) performance, which is very slow. In addition, the complexities of the encoding and decoding networks are quite high and not suitable for many practical applications. In this paper, we propose four techniques to balance the trade-off between the complexity and performance. We first introduce the deformable residual module to remove more redundancies in the input image, thereby enhancing compression performance. Second, we design an improved checkerboard context model with two separate distribution parameter estimation networks and different probability models, which enables parallel decoding without sacrificing the performance compared to the sequential context-adaptive model. Third, we develop a three-pass knowledge distillation scheme to retrain the decoder and entropy coding, and reduce the complexity of the core decoder network, which transfers both the final and intermediate results of the teacher network to the student network to improve its performance. Fourth, we introduce L1 regularization to make the numerical values of the latent representation more sparse, and we only encode non-zero channels in the encoding and decoding process to reduce the bit rate. This also reduces the encoding and decoding time. Experiments show that compared to the state-of-the-art learned image coding scheme, our method can be about 20 times faster in encoding and 70-90 times faster in decoding, and our R-D performance is also 2.3% higher. Our method achieves better rate-distortion performance than classical image codecs including H.266/VVC-intra (4:4:4) and some recent learned methods, as measured by both PSNR and MS-SSIM metrics on the Kodak and Tecnick-40 datasets.

Exponentiated extended extreme value distribution: Properties, estimation, and applications in applied fields

<abstract><p>The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramér-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance.</p></abstract>

Linear Convergence of distributed estimation with constraints and communication delays

Motivated by the multi-sensor estimation problem, we consider a distributed constraint parameter estimation problem on a directed graph. Our goal is to design a fast distributed algorithm to handle constraint parameter estimation problems, especially considering the communication delays when sensors interact on a directed graph. Based on the gradient-tracking algorithm and indirect projection method, the Projected Distributed Parameter Estimation Algorithm (PDPEA) is proposed, which can deal with the closed convex set constraint and use the historical information stored by the sensors to achieve fast and accurate mean gradient estimation. The analysis shows that the PDPEA converges to a global and consensual minimizer even under the influence of measurement noise, arbitrarily bounded communication delays, and directed information topologies. Under the assumption that the local cost function is strongly convex and smooth, we show that the algorithm converges at a linear rate for an appropriate choice of stepsize. Lastly, we demonstrate the effectiveness of the proposed algorithm by setting up a multi-sensor parameter estimation network.

A versatile model for lifetime of a component under stress

In this study, a versatile model, called alpha-monotone inverse Weibull distribution (alphaIW), for lifetime of a component under stress is introduced by using the alpha-monotone concept. The alphaIW distribution is also expressed as a scale-mixture between the inverse Weibull distribution and uniform distribution on (0, 1). The alphaIW distribution includes alpha-monotone inverse exponential and alpha-monotone inverse Rayleigh distributions as submodels and converenges to the inverse Weibull, inverse exponential, and inverse Rayleigh distributions as limiting cases. Also, slash Weibull, slash Rayleigh, and slash exponential distribuitons can be obtained under certain variable transformation and parameter settings. The alphaIW distribution is characterized by its hazard rate function and characterizing conditions are provided as well. Maximum likelihood, maximum product of spacing, and least squares methods are used to estimate distribution parameters. A Monte-Carlo simulation study is conducted to compare the efficiencies of the considered estimation methods. In the application part, two practical data sets, Kevlar 49/epoxy and Kevlar 373/epoxy, are modeled via the alphaIW distribution. Modeling performance of the alphaIW distribution is compared with its rivals by means of some well-known goodness-of-fit statistics and results show that alphaIW distribution performs better modeling than them. Results of comparison also indicate that obtaining the alphaIW distribution by using the alpha-monotone concept is cost effective since the new shape parameter added to the distribution by using the alpha-monotone concept significantly increases the modeling capability of the IW distribution. As a result of this study, it is shown that the alphaIW distribution can be an alternative to the well-known and recently-introduced distributions for modeling purposes.