Journal articles: 'Generalized modulating functions estimation method'

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Tian, Yang, Yan-Qiao Wei, Da-Yan Liu, and Driss Boutat. "Fast and robust estimation for positions and velocities from noisy accelerations using generalized modulating functions method." Mechanical Systems and Signal Processing 133 (November 2019): 106270. http://dx.doi.org/10.1016/j.ymssp.2019.106270.

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Liu, Da-Yan, and Taous-Meriem Laleg-Kirati. "Robust fractional order differentiators using generalized modulating functions method." Signal Processing 107 (February 2015): 395–406. http://dx.doi.org/10.1016/j.sigpro.2014.05.016.

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Pumaricra Rojas, David, Matti Noack, Johann Reger, and Gustavo Pérez-Zúñiga. "State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions." Sensors 22, no. 13 (July 2, 2022): 5008. http://dx.doi.org/10.3390/s22135008.

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Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.

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Fedele, Giuseppe, and Loredana Coluccio. "A recursive scheme for frequency estimation using the modulating functions method." Applied Mathematics and Computation 216, no. 5 (May 2010): 1393–400. http://dx.doi.org/10.1016/j.amc.2010.02.039.

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He, Shanghong. "PARAMETER ESTIMATION OF LINEAR CONTINUOUS-TIME DYNAMIC SYSTEM USING MODULATING FUNCTIONS METHOD." Chinese Journal of Mechanical Engineering 39, no. 12 (2003): 129. http://dx.doi.org/10.3901/jme.2003.12.129.

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Lu, Jing-Yi, Dong Ye, and Wen-Ping Ma. "Time delay estimation based on variational mode decomposition." Advances in Mechanical Engineering 9, no. 1 (January 2017): 168781401668858. http://dx.doi.org/10.1177/1687814016688587.

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In order to improve the time delay estimation of colored noise signals, this article proposes generalized cross-correlation time delay estimation based on variational mode decomposition. First of all, we put forward the signal energy detection criterion to extract the effective signal from the signal, which can reduce the amount of calculation and improve the real-time performance. Second, the effective signal is decomposed into a number of intrinsic mode functions using variational mode decomposition. The correlation coefficients of each intrinsic mode function and the original signal are calculated. The article reconstructed signal with intrinsic mode functions which extract useful intrinsic mode functions by defaulting the correlation coefficient threshold. Finally, this article uses generalized cross-correlation to estimate time delay of the reconstructed signal. Theoretical analysis and simulation results show that the accurate time delay estimation can be obtained under the condition of color noise by the proposed method. The measurement accuracy of the proposed method is 15 times that of the generalized cross-correlation, and the running time of the proposed method is 4.0601 times faster than that of the generalized cross-correlation algorithm. The proposed method can reduce the computation and the running time of the system and also improve the measurement accuracy.

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Gong, Qin, and Bin Yin. "Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test." PLOS ONE 19, no. 9 (September 30, 2024): e0311129. http://dx.doi.org/10.1371/journal.pone.0311129.

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This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

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Rose, Charles E., Michael L. Clutter, Barry D. Shiver, Daniel B. Hall, and Bruce Borders. "A Generalized Methodology for Developing Whole-Stand Survival Models." Forest Science 50, no. 5 (October 1, 2004): 686–95. http://dx.doi.org/10.1093/forestscience/50.5.686.

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Abstract A large source of variability in yield predictions is due to estimation of future surviving trees per unit area. Previous whole-stand survival modeling efforts have concentrated on modeling the empirical survival curve. Modeling hazard functions, an approach to survival analysis commonly used in fields such as medicine and sociology, can be applicable to plantation survival estimation. We offer a generalized method for deriving whole-stand survival models that are capable of modeling complex underlying hazard functions. We use our knowledge of the empirical hazard function to limit our selection to appropriate functions. Integrating selected functions results in initial condition difference equations that, when fitted to our data, provide biologically reasonable whole-stand survival predictions and adequately represent the underlying hazard function. Our method is relatively easy to implement and can model a whole-stand survival curve with a complex underlying hazard function. FOR. SCI. 50(5):686–695.

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Wang, Liming, Songjun Han, and Fuqiang Tian. "At which timescale does the complementary principle perform best in evaporation estimation?" Hydrology and Earth System Sciences 25, no. 1 (January 21, 2021): 375–86. http://dx.doi.org/10.5194/hess-25-375-2021.

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Abstract. The complementary principle has been widely used to estimate evaporation under different conditions. However, it remains unclear at which timescale the complementary principle performs best. In this study, evaporation estimations were conducted at 88 eddy covariance (EC) monitoring sites at multiple timescales (daily, weekly, monthly, and yearly) by using sigmoid and polynomial generalized complementary functions. The results indicate that the generalized complementary functions exhibit the highest skill in estimating evaporation at the monthly scale. The uncertainty analysis shows that this conclusion is not affected by ecosystem type or energy balance closure method. Through comparisons at multiple timescales, we found that the slight difference between the two generalized complementary functions only exists when the independent variable (x) in the functions approaches 1. The results differ for the two models at daily and weekly scales. However, such differences vanish at monthly and annual timescales, with few high x values occurring. This study demonstrates the applicability of generalized complementary functions across multiple timescales and provides a reference for choosing a suitable time step for evaporation estimations in relevant studies.

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Linton, Oliver B. "EFFICIENT ESTIMATION OF GENERALIZED ADDITIVE NONPARAMETRIC REGRESSION MODELS." Econometric Theory 16, no. 4 (August 2000): 502–23. http://dx.doi.org/10.1017/s0266466600164023.

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We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and Härdle (1996, Biometrika 83, 529–540) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.

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Co, Tomas B., and Sridhar Ungarala. "Batch scheme recursive parameter estimation of continuous-time systems using the modulating functions method." Automatica 33, no. 6 (June 1997): 1185–91. http://dx.doi.org/10.1016/s0005-1098(97)00020-4.

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Sueishi, Naoya. "A NOTE ON GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION OF SEMIPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS." Econometric Theory 33, no. 5 (September 19, 2016): 1242–58. http://dx.doi.org/10.1017/s0266466616000360.

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This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of Donald, Imbens, and Newey (2003, Journal of Econometrics 117, 55–93) by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $\sqrt n$-consistent, asymptotically normally distributed, and asymptotically efficient.

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Ren, Haiping, Qin Gong, and Xue Hu. "Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples." Axioms 12, no. 8 (August 10, 2023): 776. http://dx.doi.org/10.3390/axioms12080776.

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This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations.

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Gong, Qin, Rui Chen, Haiping Ren, and Fan Zhang. "Estimation of the Reliability Function of the Generalized Rayleigh Distribution under Progressive First-Failure Censoring Model." Axioms 13, no. 9 (August 26, 2024): 580. http://dx.doi.org/10.3390/axioms13090580.

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This study investigates the statistical inference of the parameters, reliability function, and hazard function of the generalized Rayleigh distribution under progressive first-failure censoring samples, considering factors such as long product lifetime and challenging experimental conditions. Firstly, the progressive first-failure model is introduced, and the maximum likelihood estimation for the parameters, reliability function, and hazard function under this model are discussed. For interval estimation, confidence intervals have been constructed for the parameters, reliability function, and hazard function using the bootstrap method. Next, in Bayesian estimation, considering informative priors and non-information priors, the Bayesian estimation of the parameters, reliability function, and hazard function under symmetric and asymmetric loss functions is obtained using the MCMC method. Finally, Monte Carlo simulation is conducted to compare mean square errors, evaluating the superiority of the maximum likelihood estimation and Bayesian estimation under different loss functions. The performance of the estimation methods used in the study is illustrated through illustrative examples. The results indicate that Bayesian estimation outperforms maximum likelihood estimation.

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Hayati, Zohreh, Mohsen Shafieirad, Iman Zamani, Amir Hossein, Amiri Mehra, and Zohreh Abbasi. "Parameter estimation of MIMO two-dimensional ARMAX model based on IGLS method." Control and Cybernetics 50, no. 3 (September 1, 2021): 303–22. http://dx.doi.org/10.2478/candc-2021-0020.

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Abstract This paper presents an iterative method for the unbiased identification of linear Multiple-Input Multiple-Output (MIMO) discrete two-dimensional (2D) systems. The system discussed here has Auto-Regressive Moving-Average model with exogenous inputs (ARMAX model). The proposed algorithm functions on the basis of the traditional Iterative Generalized Least Squares (IGLS) method. In summary, this paper proposes a two-dimensional Multiple-Input Multiple-Output Iterative Generalized Least Squares (2DMIGLS) algorithm to estimate the unknown parameters of the ARMAX model. Finally, simulation results show the efficiency and accuracy of the presented algorithm in estimating the unknown parameters of the model in the presence of colored noise.

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Asiri, Sharefa, and Taous-Meriem Laleg-Kirati. "Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations." Inverse Problems in Science and Engineering 25, no. 8 (October 20, 2016): 1191–215. http://dx.doi.org/10.1080/17415977.2016.1240793.

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Bariza, Kahloul, and Yahia Djabrane. "The Lindley generalized Pareto distribution: properties, estimation and application to COVID-19 data." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 1 (May 21, 2024): 2063–87. http://dx.doi.org/10.54021/seesv5n1-102.

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In this paper, we introduced a new distribution called Lindley Generalized Pareto distribution (LGP), a novel lifetime model derived by combining the Lindley and the generalized Pareto distributions. The corresponding density and distribution functions are derived and shown. Some of the derived statistical properties of the distribution include survival and hazard functions, moments, cumulants, the quantile function, mean deviations, and Entropy are studied. The parameters of the newly distribution are estimated by using Maximum Likelihood method. The adaptability and validity of the proposed LGP distribution are compared via simulation study with alternative known models. In addition, three real data of COVID-19 mortality rates applications are presented to demonstrate that the LGP distribution fits better than known extensions of the Lindley distribution, including the Lindley, XLindley, Power Lindley, gamma Lindley, PXLindley, A Three Parameters Generalized Lindley, Weibul Lindley, Generalized Lindley and Extended Lindley, through analyses of three real datasets.

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Abdelhadi, Yaser. "Linear modeling and regression for exponential engineering functions by a generalized ordinary least squares method." International Journal of Engineering & Technology 3, no. 2 (April 20, 2014): 174. http://dx.doi.org/10.14419/ijet.v3i2.2023.

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Linear transformations are performed for selected exponential engineering functions. The Optimum values of parameters of the linear model equation that fits the set of experimental or simulated data points are determined by the linear least squares method. The classical and matrix forms of ordinary least squares are illustrated. Keywords: Exponential Functions; Linear Modeling; Ordinary Least Squares; Parametric Estimation; Regression Steps.

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Cho, Hong-Yeon, Min-Ji Che, and Gi-Seop Lee. "Wave Height Estimation with a Short Return Period." Journal of Korean Society of Coastal and Ocean Engineers 36, no. 5 (October 31, 2024): 167–76. http://dx.doi.org/10.9765/kscoe.2024.36.5.167.

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Bisection and grid search methods are proposed as wave height estimation techniques for short return periods (hereafter RP; reference, one year) using long-term wave monitoring data. The proposed method is compared and evaluated with the estimation results using GP (generalized Pareto) and GEV (generalized extreme value) distribution functions, which are widely used as extreme value analysis methods. The wave height data used for the estimation were KMA Ulleungdo Ocean Buoy’s wave height data observed for 12 years from 2012 to 2023. The estimation results show that the annual frequency wave height is 4.55 m, the 90% confidence interval (±5%) is [4.18, 4.69] (m), and the confidence interval for the RP is [0.58, 1.42] (years). The difference from the GP and GEV estimation results (4.61 m and 4.53 m, respectively) was statistically ‘no significance difference.’ The method proposed in this study can estimate design variables for RPs without assumptions on candidate extreme distribution functions or parameter estimation procedures, so it can be used to estimate wave heights for short RPs of one year or less when observation data of approximately ten years or more are available.

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Adjekukor, A. J., and C. O. Aronu. "Robust Regression Estimation: A Doubly Weighted M-Estimation Approach with Generalized Jackknife Resampling." Asian Journal of Mathematics and Computer Research 32, no. 2 (February 20, 2025): 27–35. https://doi.org/10.56557/ajomcor/2025/v32i29121.

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Robust regression estimation is crucial in addressing the influence of outliers and model misspecification in statistical modelling. This study proposes a Doubly Weighted M-Estimation (DWME) approach, integrating an adaptive weighting scheme with Generalized Jackknife Resampling (GJR) to enhance efficiency and robustness in parameter estimation. The DWME method incorporates case-specific and parameter-specific weighting functions, ensuring resistance against leverage points and heavy-tailed distributions. By leveraging GJR, the proposed estimator achieves reduced bias and variance while maintaining asymptotic efficiency under mild regularity conditions. Empirical analyses demonstrate that DWME outperforms traditional M-estimators, Least Absolute Deviation (LAD), and Huber regression in terms of robustness, efficiency, and predictive accuracy. The proposed methodology offers a reliable alternative for robust estimation in heteroscedastic, non-normal, and contaminated datasets, making it particularly valuable for econometric and high-dimensional applications.

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Tao, Ye. "A New Numerical Algorithm of Three Parameter Generalized Extreme Value Distribution of Wind Speed." E3S Web of Conferences 248 (2021): 01023. http://dx.doi.org/10.1051/e3sconf/202124801023.

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Maximum likelihood estimation method is used to solve the problem of parameter estimation of three-parameter generalized extreme value distribution. Based on the theory of order reducing，a new numerical algorithm is presented to resolve the problem of maximum likelihood estimation of three-parameter generalized extreme value distribution．Firstly，the shape parameter is assumed to be known and ternary likelihood equations can be transferred into binary ones that are solved with the dichotomy．And then，scale and location parameters are the functions of shape parameter. Further，the maximum likelihood function is described as a unitary function of shape parameter. The optimal estimation of shape parameters can be obtained by applying dichotomy again.

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Zhou, Guang-Dong, You-Liang Ding, and Ai-Qun Li. "Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/870420.

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Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD) of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.

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Anghel, Cristian Gabriel, and Cornel Ilinca. "Evaluation of Various Generalized Pareto Probability Distributions for Flood Frequency Analysis." Water 15, no. 8 (April 16, 2023): 1557. http://dx.doi.org/10.3390/w15081557.

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This article analyzes six probability distributions from the Generalized Pareto family, with three, four and five parameters, with the main purpose of identifying other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distribution use are presented, such as the probability density functions, the complementary cumulative distribution functions, the quantile functions, and the exact and approximate relations for estimating parameters, for both methods of parameter estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor River to numerically present the analyzed distributions. The performance of this distribution is evaluated using a linear moments diagram.

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Tsai, Tzong-Ru, Yuhlong Lio, Jyun-You Chiang, and Ya-Wen Chang. "Stress–Strength Inference on the Multicomponent Model Based on Generalized Exponential Distributions under Type-I Hybrid Censoring." Mathematics 11, no. 5 (March 4, 2023): 1249. http://dx.doi.org/10.3390/math11051249.

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The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation methods of the maximum likelihood and Bayesian are utilized to infer the system reliability. For the Bayesian estimation method, informative and non-informative priors combined with three loss functions are considered. Because the computational difficulty on working posteriors, the Markov chain Monte Carlo method is adopted to obtain the approximation of the reliability estimator posterior. In addition, the bootstrap method and highest probability density interval are used to obtain the reliability confidence intervals. The simulation study shows that the Bayes estimator with informative prior is superior to other competitors. Finally, two real examples are given to illustrate the proposed estimation methods.

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Asiri, Sharefa, and Taous-Meriem Laleg-Kirati. "Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow." IFAC-PapersOnLine 50, no. 1 (July 2017): 7082–88. http://dx.doi.org/10.1016/j.ifacol.2017.08.1356.

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Karimbaev, Tagir Т., Sergey А. Medvedev, and Elena Т. Zakharova. "Using the DIRECT optimization algorithm and piecewise-linear functions for building nonlinear regression model." Journal Of Applied Informatics 19, no. 2 (April 29, 2024): 23–41. http://dx.doi.org/10.37791/2687-0649-2024-19-2-23-41.

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Nonlinear regression models are an important tool in agricultural research, as many biological processes are theoretically and experimentally described by nonlinear functions. In addition to accurately describing experimental data, nonlinear models have the property of physical interpretability of parameters and are more robust outside the domain of the studied sample. Currently, existing methods for calculating model coefficients – such as Ordinary Least Squares, Weighted Least Squares, and Generalized Least Squares – have several drawbacks. The most advanced Generalized Least Squares method relies on a large number of axioms, which are often not adhered to in real examples, and the theoretical proof is not apodictic. This article introduces a flexible, robust, and accurate method for calculating coefficients for arbitrary single-factor regression models based on the maximum likelihood estimation method. The method is theoretically justified with a minimal number of axioms, and examples of results from the software implementation are provided for the logistic function and the Michaelis function using synthetic test data and experimental samples of dry grass mass production depending on the volume of nitrogen fertilizers. The main advantage of the method lies in the simplicity of theoretical proof and the small number of theoretical constraints on the input parameters of the problem. Unlike Generalized Least Squares, the proposed method deterministically converges to the absolute minimum, thanks to the use of the DIRECT algorithm. It can account for heteroscedasticity and does not require manual tuning of optimization parameters to ensure convergence. Considerations for possible extensions of the method to multifactorial regression analysis and potential improvements for heteroscedasticity estimation are also presented.

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Levine, Michael, and Jinguang Li. "LOCAL INSTRUMENTAL VARIABLE METHOD FOR THE GENERALIZED ADDITIVE-INTERACTIVE NONLINEAR VOLATILITY MODEL ESTIMATION." Econometric Theory 28, no. 3 (January 20, 2012): 629–69. http://dx.doi.org/10.1017/s0266466611000363.

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In this article we consider a new separable nonparametric volatility model that includes second-order interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the local instrumental variable estimation method first introduced in Kim and Linton (2004, Econometric Theory 20, 1094–1139). This method is computationally more effective than most other nonparametric estimation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained.

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Gorgoso-Varela, Jose Javier, Segun M. Adedapo, and Friday N. Ogana. "A Comparison of Probability Density Functions Fitted by Moments and Maximum Likelihood Estimation Methods Used for Diameter Distribution Estimation." Forests 15, no. 3 (February 22, 2024): 425. http://dx.doi.org/10.3390/f15030425.

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Modeling diameter distribution is a crucial aspect of forest management, requiring the selection of an appropriate probability density function or cumulative distribution function along with a fitting method. This study compared the suitability of eight probability density functions—A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (two- and three-parameter)—fitted using both derivative methods (Moments) fitted in SAS/STATTM and optimization methods (MLE) fitted with the ‘optim’ function in R for diameter distribution estimation in forest stands. The A Charlier and Gumbel functions were used for the first time in this type of comparison. The data were derived from 167 permanent sample plots in an Atlantic forest (Quercus robur) and 59 temporary sample plots in tropical forests (Tectona grandis). Fit quality was assessed using various indices, including Kolmogorov–Smirnov, Cramér–von Mises, mean absolute error, bias, and mean squared error. The results indicated that Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, three-parameter Weibull, and generalized beta consistently performed well across different fitting methods, while the fits produced by gamma, Gumbel, and two-parameter Weibull were of poor quality.

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Титов and I. Titov. "Application of the Method for Generalised Estimation of the Public Health Factors (Review of Literature)." Journal of New Medical Technologies. eJournal 8, no. 1 (November 5, 2014): 1–10. http://dx.doi.org/10.12737/3439.

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The paper presents the review of various methods for generalized estimation of the public health parameters, which are based on the principle of regulation of deviations from normative factors and are used in the management activities. The different algorithms for generalized evaluation of the health factors are given. The considered techniques suppose the choice of indicators on the basic directions of activity, tasks of the normative values of the selected indicators. This corresponds to the task of achieving the required values of the indicators in the reporting period, the calculation of current (achieved) health factors, the comparison of the current and normative factors of health on the one given in this paper the methods of calculation of the generalized evaluation and the level of achievement of result. The calculation is realized with provision for value chosen for calculation of the factors, including in the manner of functions. Methods of generalized evaluation of health factors can be used in the management activities of the health institutions and territorial public health, as well as on separate directions of their activity. By means of these techniques it is possible to evaluate the activities for improving health indicators. The advanced multivariate analysis based on generalized evaluation of health factors can be carried out, including on the basis of the algebraic models of constructive logic.

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Łęski, J. M., and N. Henzel. "Generalized ordered linear regression with regularization." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 3 (December 1, 2012): 481–89. http://dx.doi.org/10.2478/v10175-012-0061-2.

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Abstract Linear regression analysis has become a fundamental tool in experimental sciences. We propose a new method for parameter estimation in linear models. The ’Generalized Ordered Linear Regression with Regularization’ (GOLRR) uses various loss functions (including the ǫ-insensitive ones), ordered weighted averaging of the residuals, and regularization. The algorithm consists in solving a sequence of weighted quadratic minimization problems where the weights used for the next iteration depend not only on the values but also on the order of the model residuals obtained for the current iteration. Such regression problem may be transformed into the iterative reweighted least squares scenario. The conjugate gradient algorithm is used to minimize the proposed criterion function. Finally, numerical examples are given to demonstrate the validity of the method proposed.

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Osi, Abdulhameed Ado, Sani Ibrahim Doguwa, Yahaya Abubakar, Yahaya Zakari, and Usman Abubakar. "Development of Exponentiated Cosine Topp-Leone Generalized Family of Distributions and its Applications to Lifetime Data." UMYU Scientifica 3, no. 1 (March 23, 2024): 157–67. http://dx.doi.org/10.56919/usci.2431.017.

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The Topp-Leone distribution is widely used for modeling lifetime data across many disciplines. This paper presents the Exponentiated Cosine Topp-Leone Generalized family (ExCTLG), which is an extension of the Topp-Leone family. The research examines the mathematical properties of the ExCTLG, including the survival and hazard functions, moments, moment-generating functions, and Renyi’s entropy. Parameter estimation is carried out using the maximum likelihood estimation (MLE) techniques, and the estimated parameters consistency is validated using the Monte Carlo simulation method, thereby highlighting the superiority of MLE. The advantages and applicability of the proposed distribution are shown by analyzing two-lifetime datasets.

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Badmus, N. I., Olanrewaju Faweya, and K. A. Adeleke. "Generalized Beta-Exponential Weibull Distribution and its Applications." Journal of Statistics: Advances in Theory and Applications 24, no. 1 (December 10, 2020): 1–33. http://dx.doi.org/10.18642/jsata_7100122158.

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In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

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Klakattawi, Hadeel S., and Aisha A. Khormi. "The effect of exponentiating generalized models." International Journal of ADVANCED AND APPLIED SCIENCES 9, no. 11 (November 2022): 51–63. http://dx.doi.org/10.21833/ijaas.2022.11.006.

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A common practice in statistical distribution theory involves exponentiating existing distribution functions to include some extra parameters that increase the flexibility of the distribution. This paper examines the effect of exponentiating some generalized models by adding three extra parameters to their probability distribution. Particularly, a new generalized distribution that is a member of the inverted Kumaraswamy family of distributions is considered. Afterward, three additional parameters are applied to enhance this generalized distribution, which results in a novel distribution referred to as the new generalized exponentiated generalized inverted Kumaraswamy Gompertz distribution (NGEGIKGD). Some of the statistical and mathematical characteristics of this distribution were derived. Additionally, parametric estimation of the new distribution parameters was considered using the maximum likelihood method. Several Monte Carlo simulation studies were conducted in order to explore the usefulness of the estimation method. The proposed distribution is then compared with its corresponding sub-models in order to assess the effects of the exponentiation. Further evaluation of the distribution is accomplished by comparing it to some relative distributions. Specifically, three real-world datasets were analyzed to demonstrate the potentiality of the suggested new modeling approach in enhancing the goodness of fit of the generalized models. Results indicate that exponentiating a generalized model significantly improves its fit compared to the non-exponentiating distributions.

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Adnan, Adnan, and Adnan Amin. "Neutrosophic Maxwell–Boltzmann Distribution: Properties and Application to Healthcare Data." International Journal of Neutrosophic Science 25, no. 4 (2025): 444–52. https://doi.org/10.54216/ijns.250438.

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In this work, we present and analyze new probability distribution by generalizing the classical Maxwell–Boltzmann model to neutrosophic structure. The generalized structure, known as the neutrosophic Maxwell (NMX) model that is designed to analyze data with imprecise or vague information. Closed-form expressions for cumulative distribution functions, probability density functions, survival functions, hazard functions, and moments, moment generating functions, mode, skewness, and kurtosis are derived as part of its detailed mathematical and statistical characteristics. The parameter estimation of the suggested model is carried out employing the maximum likelihood estimation (MLE) technique, and the statistical properties of the estimators are discussed in uncertain environments. The inverse cumulative distribution method is established to generate random samples from the proposed model and to evaluate the efficiency of the MLE method. Eventually, a real-world healthcare data set is used to show the efficacy of the proposed model. This research provides new knowledge in the field of neutrosophic statistics, laying a foundation for further exploration in this area

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Manjón, Miguel, and Juan Mañez. "Production Function Estimation in Stata Using the Ackerberg–Caves–Frazer Method." Stata Journal: Promoting communications on statistics and Stata 16, no. 4 (December 2016): 900–916. http://dx.doi.org/10.1177/1536867x1601600406.

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We present a new e-class command, acfest, that implements the method of Ackerberg, Caves, and Frazer (2015, Econometrica 83: 2411–2451) to estimate production functions. This method deals with the functional dependence problems that may arise in the methods proposed by Olley and Pakes (1996, Econometrica 64: 1263–1297) and, particularly, Levinsohn and Petrin (2003, Review of Economic Studies 70: 317–341) (implemented in Stata by Yasar, Raciborski, and Poi [2008, Stata Journal 8: 221–231] and Petrin, Poi, and Levinsohn [2004, Stata Journal 4: 113–123], respectively). In particular, the acfest command yields (nonlinear, robust) generalized method of moments estimates using a Mata function and two specification tests (Wald and Sargan–Hansen). After estimation, predict provides the estimated productivity of the firms in the sample.

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Rabie, Abdalla, and Junping Li. "E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data." Symmetry 11, no. 5 (May 3, 2019): 626. http://dx.doi.org/10.3390/sym11050626.

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In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

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Surulere, Samuel A., Micheal Y. Shatalov, Andrew C. P. G. Mkolesia, and Igor Fedotov. "A Modern Approach for the Identification of the Classical and Modified Generalized Morse Potential." Nanoscience & Nanotechnology-Asia 10, no. 2 (February 25, 2020): 142–51. http://dx.doi.org/10.2174/2210681208666181010141842.

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Introduction: This paper proposes an approach for parameter estimation of the Classical and Generalized Morse Potential functions. A new potential which is a modification of the Generalized Morse Potential was proposed as parameter estimates yielded complex conjugate roots using gold atom for simulation. Methods: Existing methods of parameter estimation requires the provision of initial guess values of which convergence to the optimal solution is not always guaranteed. This makes provision of initial guess values that guarantees convergence to the optimum solution more of an art than a science. The proposed objective least squares function method does not require the provision of initial guess values and it involves the minimization of two formulated objective functions using the differential numerical approach and least squares method. The built-in “Minimize” function of Mathematica® is also used to minimize the formulated objective function. Potential energy curves were constructed by fitting estimated parameter values to experimental data sets of the gold atom using values of the proposed approach and Mathematica® for performance evaluation. Errors of each constructed potential energy curves were simulated. Results: It was observed that the errors were very small for both the Classical and Modified Generalized Morse Potential. Conclusion: Hence the approximations of the proposed approach are very good.

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Wall, Melanie M., and Yasuo Amemiya. "Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis." Journal of Educational and Behavioral Statistics 26, no. 1 (March 2001): 1–29. http://dx.doi.org/10.3102/10769986026001001.

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Interest in considering nonlinear structural equation models is well documented in the behavioral and social sciences as well as in the education and marketing literature. This article considers estimation of polynomial structural models. An existing method is shown to have a limitation that the produced estimator is inconsistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estimator is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are discussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Application of the new procedure in a substance abuse prevention study is also reported.

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Zeng, Xinyi, and Wenhao Gui. "Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring." Entropy 23, no. 2 (February 2, 2021): 186. http://dx.doi.org/10.3390/e23020186.

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In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.

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Al-Mofleh, Hazem, Ahmed Z. Afify, and Noor Akma Ibrahim. "A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology." Mathematics 8, no. 9 (September 12, 2020): 1578. http://dx.doi.org/10.3390/math8091578.

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In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

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Vovk, Serhii. "PARAMETER ESTIMATION FOR COMPLICATED NOISE ENVIRONMENT." System technologies 6, no. 125 (December 27, 2019): 15–25. http://dx.doi.org/10.34185/1562-9945-6-125-2019-02.

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For a complicated noise environment the use of M-estimator faces a problem of choosing a cost function yielding the best solution. To solve this problem it is proposed to use a superset of cost functions. The superset capabilities provide constructing a parameter estimation method for complicated noise environment. It consists in tuning the generalized maximum likelihood estimation to the current noise environment by setting values of three free superset parameters related to the scale, the tail heaviness and the form of noise distribution, as well as to the anomaly values that presence in data. In general case, this method requires to solve the optimization problem with a non-unimodal objective function, and it can be mostly implemented by using the zero-order optimization methods. However, if the noise environment has known statistics, the proposed method leads to the optimal estimation. If the noise environment is complicated or does not have a complete statistics, the proposed method leads to the more effective estimates comparing to those of mean, median, myriad and meridian estimators. Numerical simulations confirmed the method performance.

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Daniel-Berhe, S., and H. Unbehauen. "Physical parameters estimation of the nonlinear continuous-time dynamics of a DC motor using Hartley modulating functions method." Journal of the Franklin Institute 336, no. 3 (April 1999): 481–501. http://dx.doi.org/10.1016/s0016-0032(98)00043-x.

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Sasaki, Nopparut, and Pattrawut Chansangiam. "Modified Jacobi-Gradient Iterative Method for Generalized Sylvester Matrix Equation." Symmetry 12, no. 11 (November 5, 2020): 1831. http://dx.doi.org/10.3390/sym12111831.

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We propose a new iterative method for solving a generalized Sylvester matrix equation A1XA2+A3XA4=E with given square matrices A1,A2,A3,A4 and an unknown rectangular matrix X. The method aims to construct a sequence of approximated solutions converging to the exact solution, no matter the initial value is. We decompose the coefficient matrices to be the sum of its diagonal part and others. The recursive formula for the iteration is derived from the gradients of quadratic norm-error functions, together with the hierarchical identification principle. We find equivalent conditions on a convergent factor, relied on eigenvalues of the associated iteration matrix, so that the method is applicable as desired. The convergence rate and error estimation of the method are governed by the spectral norm of the related iteration matrix. Furthermore, we illustrate numerical examples of the proposed method to show its capability and efficacy, compared to recent gradient-based iterative methods.

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Panibratov, Roman, and Petro Bidyuk. "Estimation of the parameters of generalized linear models in the analysis of actuarial risks." System research and information technologies, no. 2 (June 30, 2023): 139–48. http://dx.doi.org/10.20535/srit.2308-8893.2023.2.10.

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Methods of estimating the parameters of generalized linear models for the case of paying insurance premiums to clients are considered. The iterative-recursive weighted least squares method, the Adam optimization algorithm, and the Monte Carlo method for Markov chains were implemented. Insurance indicators and the target variable were randomly generated due to the problem of public access to insurance data. For the latter, the normal and exponential law of distribution and the Pareto distribution with the corresponding link functions were used. Based on the quality metrics of model learning, conclusions were made regarding their construction quality.

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Kurniasari, Dian, Warsono Warsono, Nourma Indryani, Mustofa Usman, and Sutopo Hadi. "Simulation of generalized Gamma distribution with maximum likelihood estimation and expectation-maximization algorithm on right censored data type 1." Decision Science Letters 10, no. 3 (2021): 415–24. http://dx.doi.org/10.5267/j.dsl.2021.1.003.

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The Generalized Gamma distribution is very suitable for modeling data with various forms of hazard (risk) functions, which makes the Generalized Gamma distribution useful in survival analysis. Survival analysis aims are to predict chances of survival, disease recurrence, death, and other events over a period of time. One characteristic of survival data is the possibility of sensors. Let X be the life span of the person being studied and the right censorship time of Cr, X is assumed to be independent with the probability density function f(x), the survival function S(x), and the hazard function h(x). A person's X life span will be known if X is less than or equal to Cr. If X is greater than Cr, the individual X survives or is censored right now. Statistical inference, especially parameter estimation is needed in analyzing empirical data. Obviously the estimation results obtained are expected to be a good estimator, namely to meet the nature of unbiased and minimum variance. This paper will discuss the results of the estimation of Generalized Gamma distribution parameters with type 1 right censored data through simulations using the Expectation Maximization method and the Maximum Likelihood Estimation method. The simulation is conducted by generating data with the sample size: 25, 50, 100, 200, 500, 1000, 1500 and 2000 as well as determining censored data of 10%, 20% and 30% by first setting the parameters used which are obtained from the data of patients with gastric cancer namely α = 1.0649, β = 1,072, θ = 59.766. Based on the results obtained from the simulations on the two estimation methods that the parameter estimation using the Maximum Likelihood Estimation method is better than the Expectation Maximization method because it provides a smaller bias and MSE value where the larger the sample size used, the estimated parameter value will get closer to the parameter in fact. In addition, the Expectation Maximization method can also be used as an alternative estimation of generalized gamma distribution parameters with type 1 right censored data because it has a bias value and MSE approaching the MLE method.

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Barroso, Raul H., and Alfonso J. Zozaya Sahad. "Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree." Mathematics 13, no. 2 (January 19, 2025): 315. https://doi.org/10.3390/math13020315.

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The estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing singular value decomposition (SVD) filtering, has emerged as a prominent strategy to carry out a complex natural frequency estimation. However, some modern engineering applications increasingly demand higher accuracy estimation. In this context, some intrinsic properties of Hankel matrices and exponential functions are utilized in this paper in order to develop a modified GPOF method which employs a matrix pencil of degree greater than one. Under conditions of low noise in the transient response, our method significantly enhances accuracy compared to the conventional GPOF approach. This improvement is especially valuable for applications involving closely spaced complex natural frequencies, where a precise estimation is crucial.

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Liu, Weidong, Mingjie Li, Tong Wang, Mengzhe Jin, and Qingyuan Fang. "Research on Time Delay Estimation Method of Partial Discharges Signal with Improved Weighted Function." Electronics 12, no. 20 (October 10, 2023): 4196. http://dx.doi.org/10.3390/electronics12204196.

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Positioning systems based on the Time Difference of Arrival (TDOA) often struggle to accurately estimate time delays for partial discharge signals in complex electromagnetic environments. To address this, we introduce an improved joint-weighted generalized cross-correlation (GCC) time delay estimation algorithm. Traditional GCC time delay estimations, when reliant on conventional weighted functions, significantly underperform in situations characterized by low signal–noise ratios (SNRs). Our proposed improved joint weighted function combines the advantages of both phase transform (PHAT) and correlation transform (SCOT) weightings, resulting in a composite function. Compared to the conventional weighted GCC, the improved joint weighted GCC displays a more distinct peak in cross-correlation functions and ensures more robust delay estimations, especially under low SNR conditions. Experimental results indicate that the improved joint-weighted GCC algorithm achieves an error margin below 1 ns in challenging outdoor electromagnetic scenarios, demonstrating its aptitude for detecting and localizing partial discharge signals in practical engineering applications.

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Surulere, Samuel A., Michael Y. Shatalov, Andrew C. P. G. Mkolesia, and Adejimi A. Adeniji. "A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms." Nanoscience & Nanotechnology-Asia 10, no. 3 (June 17, 2020): 356–63. http://dx.doi.org/10.2174/2210681209666190220125249.

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Background: The knowledge of parameter estimation for interatomic potentials is useful in the computation of the vibrational structure of van der Waals molecules. Methods: On the estimation of the Generalized Morse and Classical Lennard-Jones potential energy functions, complex conjugates eigenvalues may be obtained. Different approaches can be used to solve this resulting problem. A method that uses the objective least squares function method to estimate parameters of the interatomic potentials is employed. Results: Numerical simulation of the systems using metal atoms yields complex conjugates eigenvalues at some initial point. Conclusion: Other approaches of solving the complex conjugates eigenvalues problem are discussed comprehensively.

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Wu, Tao, Zhenghong Deng, Yiwen Li, and Yijie Huang. "Two-Dimensional DOA Estimation for Incoherently Distributed Sources with Uniform Rectangular Arrays." Sensors 18, no. 11 (October 23, 2018): 3600. http://dx.doi.org/10.3390/s18113600.

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Aiming at the two-dimensional (2D) incoherently distributed (ID) sources, we explore a direction-of-arrival (DOA) estimation algorithm based on uniform rectangular arrays (URA). By means of Taylor series expansion of steering vector, rotational invariance relations with regard to nominal azimuth and nominal elevation between subarrays are deduced under the assumption of small angular spreads and small sensors distance firstly; then received signal vectors can be described by generalized steering matrices and generalized signal vectors; thus, an estimation of signal parameters via rotational invariance techniques (ESPRIT) like algorithm is proposed to estimate nominal elevation and nominal azimuth respectively using covariance matrices of constructed subarrays. Angle matching method is proposed by virtue of Capon principle lastly. The proposed method can estimate multiple 2D ID sources without spectral searching and without information of angular power distribution function of sources. Investigating different SNR, sources with different angular power density functions, sources in boundary region, distance between sensors and number of sources, simulations are conducted to investigate the effectiveness of the proposed method.

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Stenin, А. A., I. G. Drozdovych, and M. O. Soldatova. "APPLICATION OF SPLINE FUNCTIONS AND WALSH FUNCTIONS IN PROBLEMS OF PARAMETRIC IDENTIFICATION OF LINEAR NONSTATIONARY SYSTEMS." Radio Electronics, Computer Science, Control, no. 2 (July 2, 2023): 166. http://dx.doi.org/10.15588/1607-3274-2023-2-17.

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Context. In this article, a generalized parametric identification procedure for linear nonstationary systems is proposed, which uses spline functions and orthogonal expansion in a series according to the Walsh function system, which makes it possible to find estimates of the desired parameters by minimizing the integral quadratic criterion of discrepancy based on solving a system of linear algebraic equations for a wide class of linear dynamical systems. The accuracy of parameter estimation is ensured by constructing a spline with a given accuracy and choosing the number of terms of the Walsh series expansion when solving systems of linear algebraic equations by the A. N. Tikhonov regularization method. To improve the accuracy of the assessment, an algorithm for adaptive partitioning of the observation interval is proposed. The partitioning criterion is the weighted square of the discrepancy between the state variables of the control object and the state variables of the model. The choice of the number of terms of the expansion into the Walsh series is carried out on the basis of adaptive approximation of non-stationary parameters in the observation interval, based on the specified accuracy of their estimates. The quality of the management of objects with variable parameters is largely determined by the accuracy of the evaluation of their parameters. Hence, obtaining reliable information about the actual nature of parameter changes is undoubtedly an urgent task. Objective. Improving the accuracy of parameter estimation of a wide class of linear dynamical systems through the joint use of spline functions and Walsh functions. Method. A generalized parametric identification procedure for a wide class of linear dynamical systems is proposed. The choice of the number of terms of the expansion into the Walsh series is made on the basis of the proposed algorithm for adaptive partitioning of the observation interval. Results. The results of modeling of specific linear non-stationary systems confirm the effectiveness of using the proposed approaches to estimating non-stationary parameters. Conclusions. The joint use of spline functions and Walsh functions makes it possible, based on the proposed generalized parametric identification procedure, to obtain analytically estimated parameters, which is very convenient for subsequent use in the synthesis of optimal controls of real technical objects. This procedure is applicable to a wide class of linear dynamical systems with concentrated and distributed parameters.

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Journal articles on the topic 'Generalized modulating functions estimation method'

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