Parameter Estimation Techniques Research Articles

Advances in medical data modeling: A new logarithmic beta generated family of distributions with theory and inference

This paper introduces a novel logarithmic beta generated family of distributions, designed specifically for the nuanced analysis of medical data. Through meticulous development, we have establish a comprehensive suite of distributional properties, including quantiles, moments, and hazard rate functions. Central to our contributions is the exploration of the power function distribution, a pivotal sub-model within this innovative family, demonstrating unparalleled flexibility across a broad spectrum of data types. Our investigation delves into seven prominent parameter estimation techniques, rigorously assessing their efficacy through both simulation studies and real-life medical datasets. This comparative analysis highlights the superior performance of the proposed model against existing standards, particularly through improved goodness-of-fit measures across four distinct medical science lifetime datasets. The findings highlight the new model's dominance in capturing complex data patterns, attributable to its adaptable density and hazard rate functions. These attributes significantly enhance modeling capabilities, paving the way for more precise and reliable medical research outcomes. The study concludes by emphasizing the model's potential in advancing statistical methodologies for medical science, backed by theoretical and empirical validations of its superior performance and versatility.

A Kepler optimization algorithm improved using a novel Lévy-Normal mechanism for optimal parameters selection of proton exchange membrane fuel cells: A comparative study

Proton exchange membrane fuel cells (PEMFCs) are considered a promising renewable energy source and have sparked a lot of interest over the last few years due to their robust efficiency, low operating temperature, and longevity. The PEMFC's electrochemical model has seven unknown parameters, which are not given in the manufacturer's datasheets and need to be accurately estimated to present a more accurate model, leading to improved efficiency and performance of the PEMFC systems. The estimation of those unknown parameters has been dealt with as a complex and non-linear optimization problem that needs a powerful optimization algorithm to solve it. The existing optimization algorithms still have some disadvantages, such as falling into local minima and low convergence speed, which make them ineligible to solve this complicated problem with acceptable accuracy and low computational cost. Therefore, this study presents a new parameter estimation technique for estimating the unknown parameters of the PEMFC model more accurately, thereby achieving precise modeling of PEMFCs. This technique called IKOA is based on integrating the Kepler optimization algorithm (KOA) with a novel Lévy-Normal (LN) mechanism to strengthen its exploration and exploitation capabilities against this multimodal optimization problem. The Lévy flight in this mechanism aims to improve the KOA's exploitation operator to accelerate the convergence speed toward the near-optimal solution, thus minimizing the computational cost; meanwhile, the normal distribution is used to strengthen its exploration operator, thereby aiding in the escape of local minima. The proposed IKOA and KOA are herein evaluated against several rival algorithms using six well-known commercial PEMFC stacks to highlight their efficiency and effectiveness. Key performance metrics such as computational cost, fitness measures, and statistical validation through the Wilcoxon rank-sum test are herein used to highlight IKOA's effective performance in enhancing the predictive accuracy and operational efficiency of PEMFCs. The numerical findings show the high superiority of IKOA against all rival optimizers on all solved benchmarks.

A statistical model for estimating size and productivity ratio in SDLC

During a software development life cycle, one has to estimate the effort and schedule required to produce a software unit. Estimates for The effort and schedule are derived from other measurements such as size and productivity Ratio. Size may be estimated using methods such as Function Point, WBS, LOC, etc., and the Productivity Ratio is expressed as Size / Time to complete the Unit of Software. Such estimates are static and do not consider real-time Parameters which cause variations from the estimate. In this paper, a statistical model for Size and Productivity Ratios is derived using Historical values after considering several factors influencing the size and the productivity ratio of produced software. Typically, an estimate of the effort and schedule is required to complete. A software work product an enhancement request or a software fix. We use Function Points or WBS to estimate the size of the software in consideration. We use baseline values for estimating productivity Ratios. Real-time values however differ from Baseline values as they are influenced by several factors. Here are some factors which would influence the Actual Size of the software Later on we will use Statistical techniques of Multivariable Parameter estimation and logistic Regression to derive run time equations of Size and Productivity Ratio.

Analysis of recent decade rainfall data with new exponential-exponential distribution: Inference and applications

This study introduces the New Exponential-Exponential Distribution (NEED) within the broader New Exponential-Generating (NE-G) family of distributions, targeting enhancements in rainfall data analysis. The significance of this research lies in addressing the need for sophisticated statistical models to accurately capture the complex variability of rainfall patterns, which are critical for effective environmental planning and disaster management. Aiming to refine rainfall data modeling, we employ the NEED model, emphasizing its application across diverse climatic conditions. Our methodology encompasses a comprehensive evaluation of seven distinct parameter estimation techniques, with a particular focus on the Anderson-Darling and maximum product spacing methods. These were selected based on their performance in minimizing bias and mean square error, assessed through a rigorous Monte-Carlo simulation study. Additionally, the study utilizes rainfall data from various geographical regions to validate the model's efficacy. The major conclusion of our investigation is the demonstrable superiority of NEED over traditional models in fitting rainfall data, as evidenced by its enhanced predictive accuracy. This outcome not only contributes to the theoretical advancements in statistical meteorology but also offers practical methodologies for improved weather forecasting. The integration of NEED with contemporary machine learning algorithms further suggests potential for groundbreaking applications in climate science and water resource management.

Optimal Parameter Estimation Techniques for Complex Nonlinear Systems

AbstractAccurate parameter estimation and state identification within nonlinear systems are fundamental challenges addressed by optimization techniques. This paper fills a critical gap in previous research by investigating tailored optimization methods for parameter estimation in nonlinear system modeling, with a particular emphasis on chaotic dynamical systems. We introduce and compare three optimization methods: a gradient-based iterative algorithm, the Levenberg-Marquardt algorithm, and the Nelder-Mead simplex method. These methods are strategically employed to simplify complex nonlinear optimization problems, rendering them more manageable. Through a comprehensive exploration of the performance of these methods in determining parameters across diverse systems, including the van der Pol oscillator, the Rössler system, and pharmacokinetic modeling, our study revealed that the accuracy and reliability of the Nelder-Mead simplex method were consistent. The Nelder-Mead simplex algorithm emerged as a powerful tool, that consistently outperforms alternative methods in terms of root mean squared error (RMSE) and convergence reliability. Visualizations of trajectory comparisons and parameter convergence under various noise levels further emphasize the algorithm’s robustness. These studies suggest that the Nelder-Mead simplex method has potential as a valuable tool for parameter estimation in chaotic dynamical systems. Our study’s implications extend beyond theoretical considerations, offering promising insights for parameter estimation techniques in diverse scientific fields reliant on nonlinear system modeling.

Optimizing Electric Vehicle Performance, Range and Parameter Estimation through NEDC Urban and Suburban Analysis using MATLAB

This research paper focuses on electric vehicle (EV) driving range and parameter estimation, with an emphasis on analyzing the New European Driving Cycle (NEDC) urban and suburban drive cycles. By examining these drive cycles, we obtain critical data on the moments when an electric vehicle transitions between constant velocity, acceleration, and deceleration phases, which significantly affect power consumption and driving range. We investigate various techniques for parameter estimation, including battery capacity, energy consumption rates, and powertrain efficiency, essential for improving EV performance and providing realistic range expectations. Empirical experiments in diverse driving conditions contribute valuable data to refine our understanding of EV driving range and performance in different scenarios. The research underscores the role of predictive modeling, data analytics, and advanced technologies in real-time parameter estimation, offering precise and convenient range predictions to enhance user confidence.

Parameter Estimation and Hypothesis Testing on Bivariate Log-Normal Regression Models

This study aims to introduce a bivariate Log-Normal regression model and to develop a technique for parameter estimation and hypothesis testing. We term the model Bivariate Log-Normal Regression (BLNR). The estimation procedure is conducted by the standard Maximum Likelihood Estimation (MLE) employing the Newton-Raphson method. To perform hypothesis testing, we adapt the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing with test statistics which, for large n, follows Chi-Square distribution with degrees of freedom p. In addition, the partial testing is derived from a central limit theorem which results in a Z-test statistic.
 Keywords: parameter estimation, hypothesis testing, bivariate log, normal regression

An efficient data sheet based parameter estimation technique of solar PV

This work develops an efficient parameter estimation technique, based on manufacturer datasheet, to obtain unknown parameter of solar photovoltaic (PV), precisely. Firstly, a nonlinear least square objective function, in terms of variables given in manufacturer datasheet, has been developed. Then, two optimization techniques, namely the Particle Swarn Optimization (PSO) and Harmony Search (HS) are applied on the developed objective function to achieve the optimized result. Further, the correctness of the developed technique is tested by estimating the performance indices, namely percentage maximum power deviation index (%MPDI) and overall model deviation index (OMDI), of two different solar PV, viz., Kyocera KD210GH-2PU (poly-crystalline), and Shell SQ85 (mono-crystalline). It is shown that developed method with PSO outperforms the HS. The developed method with PSO gives the values of %MPDI and OMDI of 0.0214% and 0.213, only. Also, the existing methods, based on hybrid, multi-objective function, numerical method, have been considered for the comparative analysis. It is revealed through the comparative studies that the developed method with PSO has smaller value of MPDI (= 0.0041%) and OMDI (0.005) than the other existing methods. Further, the convergence of the developed method has also been estimated to check the speed of estimation. It is shown that the developed technique converges only in 5 s. In addition, the developed technique avoids the need of extensive data as it is based on manufacturer datasheet.

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

Compensating voltage waveform distortions using a practical topology of series active power filters

Addressing harmonics, voltage sags, voltage swells, and asymmetrical variations is essential to seamlessly integrate renewable energy sources, electric vehicle charging stations, and power electronics devices into electric power grids. These issues can significantly impact the sinusoidal symmetry of voltage waveforms. Series Active Power Filters (APFs) present a promising solution that can dramatically improve power quality (PQ) by effectively addressing voltage distortions. This paper first identifies several topology-related impracticalities in the existing literature on series APFs, such as using nonlinear loads or linear loads with a current source. Secondly, to understand the motivations behind these impracticalities, commonly used reference extraction methods, namely, Instantaneous Reactive Power Theory (IRPT) and Synchronous Reference Frame (SRF), are tested on a practical topology consisting of a distorted voltage source and a linear RL load. Results conducted in the MATLAB/Simulink environment show that IRPT fails to extract the reference signal under the practical topology, and SRF leads to unacceptable THDs surpassing the 5% threshold mandated by relevant standards set forth for such applications. Thirdly, the matrix pencil method (MPM), a model-based parameter estimation technique that exploits a voltage waveform's underlying exponential signal model to extract the series APF's reference voltage, is proposed. Extensive simulations showcase the superior performance of the MPM-based series APF. It successfully reduces voltage total harmonic distortion (THD) to below 1.13% across various scenarios, including situations involving harmonic-polluted voltage sources, incorporating nonlinear loads, sag and swell phenomenon, and capacitor utilization in DC link implementation.

Prospects for Taiji to detect a gravitational-wave background from cosmic strings

Recently, multiple pulsar timing array collaborations have presented compelling evidence for a stochastic signal at nanohertz frequencies, potentially originating from cosmic strings. Cosmic strings are linear topological defects that can arise during phase transitions in the early Universe or as fundamental strings in superstring theory. This paper focuses on investigating the detection capabilities of Taiji, a planned space-based gravitational wave detector, for the gravitational wave background generated by cosmic strings. By analyzing simulated Taiji data and utilizing comprehensive Bayesian parameter estimation techniques, we demonstrate a significant improvement in precision compared to the NANOGrav 15-year data set, surpassing it by an order of magnitude. This highlights the enhanced measurement capabilities of Taiji. Consequently, Taiji can serve as a valuable complementary tool to pulsar timing arrays in validating and exploring the physics of cosmic strings in the early Universe.

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equationsto compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

On the reliable estimation of sequential Monod kinetic parameters

While dozens of studies have attempted to estimate the Monod kinetic parameters of microbial reductive dechlorination, published values in the literature vary by 2–6 orders of magnitude. This lack of consensus can be attributed in part to limitations of both experimental design and parameter estimation techniques. To address these issues, Hamiltonian Monte Carlo was used to produce more than one million sets of realistic simulated microcosm data under a variety of experimental conditions. These data were then employed in model fitting experiments using a number of parameter estimation algorithms for determining Monod kinetic parameters. Analysis of data from conventional triplicate microcosms yielded parameter estimates characterized by high collinearity, resulting in poor estimation accuracy and precision. Additionally, confidence intervals computed by commonly used classical regression analysis techniques contained true parameter values much less frequently than their nominal confidence levels. Use of an alternative experimental design, requiring the same number of analyses as conventional experiments but comprised of microcosms with varying initial chlorinated ethene concentrations, is shown to result in order-of-magnitude decreases in parameter uncertainty. A Metropolis algorithm which can be run on a typical personal computer is demonstrated to return more reliable parameter interval estimates.

Identifying the Probability Distribution of Exchange Rates in Sri Lanka

The exchange rate is one of the main components that represents the status of a country’s economic condition. This study mainly focuses on identifying an appropriate distribution that can capture the asymmetric behaviour of important currency exchange rates related to Sri Lanka. The true behaviour of the exchange rates of USD, EURO, JPY, AUD, GBP, CHF, SGD and CAD in terms of LKR was determined using flexible distributions of generalised lambda distribution (GLD), Normal Inverse Gaussian and Skew-Normal. The parameter estimation was carried out by maximum likelihood estimation (MLE), while for GLD, few more parameter estimation techniques were applied. To understand how well the fitted distributions identify the real behaviour of data, we conducted the goodness-of-fit (GOF) tests. The results from Cramer–Von Mises (CvM) and Anderson–Darling (AD) GOF tests pointed out that the exchange rates data follow a GLD with the parameter estimation of maximum product of spacings (MPS). Further, plots of histograms with theoretical densities, cumulative distribution functions (CDFs) with empirical CDF and Quantile–Quantile plots illustrated the same idea. This study presented the findings based on different suitable parameter estimation techniques and this study is the first investigation on the distribution identification of exchange rates in Sri Lanka. JEL Codes: C12,C13,G10

A Systematic Technique for Kinetic Parameter Estimation in Heterogeneous Solid Catalytic Reaction Networks with Applications

A Systematic Technique for Kinetic Parameter Estimation in Heterogeneous Solid Catalytic Reaction Networks with Applications

A Model for Membrane Degradation Using a Gelatin Invadopodia Assay.

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

Novel hybrid kepler optimization algorithm for parameter estimation of photovoltaic modules

The parameter identification problem of photovoltaic (PV) models is classified as a complex nonlinear optimization problem that cannot be accurately solved by traditional techniques. Therefore, metaheuristic algorithms have been recently used to solve this problem due to their potential to approximate the optimal solution for several complicated optimization problems. Despite that, the existing metaheuristic algorithms still suffer from sluggish convergence rates and stagnation in local optima when applied to tackle this problem. Therefore, this study presents a new parameter estimation technique, namely HKOA, based on integrating the recently published Kepler optimization algorithm (KOA) with the ranking-based update and exploitation improvement mechanisms to accurately estimate the unknown parameters of the third-, single-, and double-diode models. The former mechanism aims at promoting the KOA’s exploration operator to diminish getting stuck in local optima, while the latter mechanism is used to strengthen its exploitation operator to faster converge to the approximate solution. Both KOA and HKOA are validated using the RTC France solar cell and five PV modules, including Photowatt-PWP201, Ultra 85-P, Ultra 85-P, STP6-120/36, and STM6-40/36, to show their efficiency and stability. In addition, they are extensively compared to several optimization techniques to show their effectiveness. According to the experimental findings, HKOA is a strong alternative method for estimating the unknown parameters of PV models because it can yield substantially different and superior findings for the third-, single-, and double-diode models.

Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis

The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.

Parameter estimation and random number generation for student Lévy processes

To address the challenges in estimating parameters of the widely applied Student-Lévy process, the study introduces two distinct methods: a likelihood-based approach and a data-driven approach. A two-step quasi-likelihood-based method is initially proposed, countering the non-closed nature of the Student-Lévy process's distribution function under convolution. This method utilizes the limiting properties observed in high-frequency data, offering estimations via a quasi-likelihood function characterized by asymptotic normality. Additionally, a novel neural-network-based parameter estimation technique is advanced, independent of high-frequency observation assumptions. Utilizing a CNN-LSTM framework, this method effectively processes sparse, local jump-related data, extracts deep features, and maps these to the parameter space using a fully connected neural network. This innovative approach ensures minimal assumption reliance, end-to-end processing, and high scalability, marking a significant advancement in parameter estimation techniques. The efficacy of both methods is substantiated through comprehensive numerical experiments, demonstrating their robust performance in diverse scenarios.

Improved Hybrid Approach for Enhancing Protein Coding Regions Identification in DNA Sequences

Introduction: Identifying and predicting protein-coding regions within DNA sequences play a pivotal role in genomic research. This paper introduces an approach for identifying proteincoding regions in DNA sequences, employing a hybrid methodology that combines a digital bandpass filter with wavelet transforms and various spectral estimation techniques to enhance exon prediction. Specifically, the Haar and Daubechies wavelet transforms are applied to improve the accuracy of protein-coding region (exon) prediction, enabling the extraction of intricate details that may be obscured in the original DNA sequences. background: The identification and prediction of protein-coding regions within DNA sequences play a pivotal role in genomic research. Methods: This research showcases the utility of Haar and Daubechies wavelet transforms, both nonparametric and parametric spectral estimation methods, and the deployment of a digital band pass filter for detecting peaks in exon regions. Additionally, the application of the Electron-Ion Interaction Potential (EIIP) method for converting symbolic DNA sequences into numerical values and the utilization of sum-of-sinusoids (SoS) mathematical models with optimized parameters further enrich the toolbox for DNA sequence analysis, ensuring the success of this proposed method in modeling DNA sequences optimally and accurately identifying genes. objective: Enhanced Protein-Coding Region Identification in DNA Sequences Using Wavelet Transforms Results: The outcomes of this approach showcase a substantial enhancement in identification accuracy for protein-coding regions. In terms of peak location detection, the application of Haar and Daubechies wavelet transforms enhances the accuracy of peak localization by approximately (0.01, 3-5 dB). When employing non-parametric and parametric spectral estimation techniques, there is an improvement in peak location by approximately (0.01, 4 dB) compared to the original signal. The proposed approach also achieves higher accuracy when compared with existing methods. method: hybrid methodology that combines a digital band-pass filter with wavelet transforms and various spectral estimation techniques to enhance exon prediction. Conclusion: These findings not only bridge gaps in DNA sequence analysis but also offer a promising pathway for advancing exonic region prediction and gene identification in genomics research. The hybrid methodology presented stands as a robust contribution to the evolving landscape of genomic analysis techniques. result: The results obtained through this proposed method demonstrate significantly improved identification accuracy. These findings offer a promising avenue for DNA sequence analysis, exonic region prediction, and gene identification.