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Interval-valued functional data, a new type of data in symbolic data analysis, depicts the characteristics of a variety of big data and has drawn the attention of many researchers. Mean regression is one of the important methods for analyzing interval-valued functional data. However, this method is sensitive to outliers and may lead to unreliable results. As an important complement to mean regression, this paper proposes an interval-valued scalar-on-function linear quantile regression model. Specifically, we constructed two linear quantile regression models for the interval-valued response and interval-valued functional regressors based on the bivariate center and radius method. The proposed model is more robust and efficient than mean regression methods when the data contain outliers as well as the error does not follow the normal distribution. Numerical simulations and real data analysis of a climate dataset demonstrate the effectiveness and superiority of the proposed method over the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider estimating the parameters of univariate α-stable distributions and their mixtures. First, using a Gaussian kernel density distribution estimator, we propose an estimation method based on the characteristic function. The optimal bandwidth parameter was selected using a plug-in method. We highlight another estimation procedure for the Maximum Likelihood framework based on the False position algorithm to find a numerical root of the log-likelihood through the score functions. For mixtures of α-stable distributions, the EM algorithm and the Bayesian estimation method have been modified to propose an efficient and valuable tool for parameter estimation. The proposed methods can be generalised to multiple mixtures, although we have limited the mixture study to two components. A simulation study is carried out to evaluate the performance of our methods, which are then applied to real data. Our results appear to accurately estimate mixtures of α-stable distributions. Applications concern the estimation of the number of replicates in the Mayotte COVID-19 dataset and the distribution of the N-acetyltransferase activity of the Bechtel et al. data for a urinary caffeine metabolite implicated in carcinogens. We compare the proposed methods, together with a detailed discussion. We conclude with the limitations of this study, together with other forthcoming work and a future implementation of an R package or Python library for the proposed methods in data modelling. [ABSTRACT FROM AUTHOR]

Remote sensing observations of far-ultraviolet (FUV) emissions have been used to estimate 3D neutral hydrogen (H) density models of the terrestrial exosphere under solar minimum (2008) and solar maximum (2013 and 2015) conditions. Specifically, we used Lyman-alpha (Lyman-α, FUV at 121.6 nm) radiance data acquired by the Lyman-alpha detectors (LADs) onboard NASA's TWINS satellites, collected over several days for each of the 3 years to provide sufficient coverage of the exospheric region. The datasets included Lyman-α measurements taken only above Earth radii (Re) of 3.75, assumed to be the optically thin region of the exosphere, where the measured Lyman-α intensity along a line of sight (LOS) is linearly proportional to the atomic hydrogen column density. Based on the calibration using multiple UV-bright stars, a significant decrease in TWINS1 LAD1/2 sensitivities was found for 2013 (LAD2 ∼1/2, LAD ∼1/3) and 2015 (LAD2 ∼1/3, LAD ∼1/7) compared to 2008. The calibration uncertainty was derived to be, on average, 5%. We estimated the 3D global hydrogen density distributions from these radiance data using two different tomographic inversion methods: first, a parametric fitting method based on a spherical harmonic function of order 3 and second, a high degree-of-freedom retrieval approach to validate our retrievals of H density. Both inversion methods consistently incorporate the effects of Lyman-α absorption within the exosphere and Lyman-α re-emission from Earth's albedo. Our results reveal that H densities during solar maximum conditions are, on average, 30%-40% higher than those during solar minimum. All models showed a high concentration of atomic H on the dayside and nightside near the Sun-Earth line, which determines a nose/geotail structure consistent with theoretical effects from the solar radiation pressure. Furthermore, we identified that H-density enhancements during solar maximum with respect to solar minimum conditions occur at mid-to-high latitudes, particularly on the dusk side, while no significant enhancement seems to occur near the dayside nose. [ABSTRACT FROM AUTHOR]

One of the most important hyper-parameters in duration-dependent Markov-switching (DDMS) models is the duration of the hidden states. Because there is currently no procedure for estimating this duration or testing whether a given duration is appropriate for a given data set, an ad hoc duration choice must be heuristically justified. In this paper, we propose and examine a methodology that mitigates the choice of duration in DDMS models when forecasting is the goal. The novelty of this paper is the use of the asymmetric Aranda-Ordaz parametric link function to model transition probabilities in DDMS models, instead of the commonly applied logit link. The idea behind this approach is that any incorrect duration choice is compensated for by the parameter in the link, increasing model flexibility. Two Monte Carlo simulations, based on classical applications of DDMS models, are employed to evaluate the methodology. In addition, an empirical investigation is carried out to forecast the volatility of the S&P500, which showcases the capabilities of the proposed model. [ABSTRACT FROM AUTHOR]

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift, which lies in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permits to identify the parameters of the model. Under this assumption, we prove consistency results and derive a rate of convergence for the estimator. Finally, we show that the identifiability assumption is satisfied in the case of a family of fractional Ornstein–Uhlenbeck processes and illustrate our results with some numerical experiments. [ABSTRACT FROM AUTHOR]

This study introduces the design of a state-feedback controller for Linear Parameter Varying (LPV) systems in scenarios where exogenous parameters are not directly accessible, and the state vector is to be estimated. Instead of considering a static feedback gain, it proposes a method for estimating these parameters and synthesizing a parameter-dependent state-feedback gain that is robust against uncertainties in parameter estimation. The state vector used by the state-feedback controller, and some quantities required by the estimation law, are both obtained by a robust filter synthesized by LMI (Linear Matrix Inequalities). This paper outlines the estimation, filtering, and control laws, detailing the conditions necessary for ensuring convergence and stability. A numerical experiment and a 2 DoF torsional system application show the enhanced dynamic performance of the method when applied to uncertain dynamic systems. The findings highlight the effectiveness of the proposed approach in maintaining system stability and improving performance despite the inherent uncertainties in parameter estimation, offering a significant contribution to the field of robust control for LPV systems. [ABSTRACT FROM AUTHOR]

In this note we develop a new technique for parameter estimation of univariate time series by means of a parametric copula approach. The proposed methodology is based on a relationship between a process' covariance decay and parametric bivariate copulas associated to lagged variables. This relationship provides a way for estimating parameters that are identifiable through the process' covariance decay, such as in long range dependent processes. We provide a rigorous asymptotic theory for the proposed estimator. We also present a Monte Carlo simulation study to asses the finite sample performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

The object of this study is the process of estimation and control of an IT project. During the study, the problem of increasing the accuracy of estimating the efforts of an IT project to build an information system (IS) was solved. Research in this area is aimed at simplifying the original assessment methods or at applying elements of artificial intelligence to these methods. The task of the impact of the features of IS development methodology on effort assessment remains unexplored. During the study, the method of functional point analysis was modified. The proposed modification makes it possible to increase the accuracy of estimating efforts to build an IS under the conditions of re-using its individual functions. These conditions allow the construction of new system functions by reusing a previously developed function of the same system. The developed method was tested during the evaluation of efforts of an IT project to form the functional task "Forming and executing an individual plan for a research and teaching staff member of the department." The option of re-using one of the functions of a task during the construction of two other functions of the same task is considered. For this option, the estimate was 72 function points (the estimate using the standard method was 144 function points). The use of the results allows us to increase the accuracy in assessing the efforts of IT projects to construct IS under the conditions of applying the methodology of reuse of previously developed system elements. This, in turn, makes it possible to improve the accuracy of estimating time costs, personnel requirements, and financial costs for the implementation of IT projects for constructing IS. The results obtained are used to solve the task of estimating efforts during the planning of IT projects for developing information systems and their software. [ABSTRACT FROM AUTHOR]

In this study, the frequency and capacitance of piezoelectric materials due to compressive stress were analyzed, and the overall material properties (compliance matrix, piezoelectric charge constant and dielectric constant) of piezoelectric ceramics were optimized using parametric estimation methods. The piezoelectric ceramic used for optimization was KICET-PZT8, and the compressive stress was applied from a stress-free condition up to 50 MPa. As a result, with increasing compressive stress, the values of $s_{11}^E$ s 11 E , $ - s_{12}^E$ − s 12 E and $s_{66}^E$ s 66 E tended to increase, while $ - s_{13}^E$ − s 13 E and $s_{33}^E$ s 33 E increased and then decreased at 20 MPa or higher. $ - {d_{31}}$ − d 31 and ${d_{33}}$ d 33 showed the maximum values at 40 MPa of compressive stress, with the values reaching 147 pC/N and 375 pC/N, respectively. These values were analyzed to have increased by 117% and 115%, respectively, compared to the stress-free condition. Additionally, the dielectric constant ($\varepsilon _{33}^T$ ε 33 T ) was found to increase linearly with the applied compressive stress. The understanding of the changes in piezoelectric properties under various compressive stresses derived from this study is expected to be applicable in various ways for the design and application of piezoelectric devices using compressive stresses, including BLT. [ABSTRACT FROM AUTHOR]

The paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of the unknown parameters we consider the tapered Whittle estimator and the simplified tapered Whittle estimators. We show that under broad regularity conditions on the spectral density of the model these estimators are asymptotically statistically equivalent, in the sense that these estimators possess the same asymptotic properties. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory. [ABSTRACT FROM AUTHOR]

ABSTRACTIn this study, the frequency and capacitance of piezoelectric materials due to compressive stress were analyzed, and the overall material properties (compliance matrix, piezoelectric charge constant and dielectric constant) of piezoelectric ceramics were optimized using parametric estimation methods. The piezoelectric ceramic used for optimization was KICET-PZT8, and the compressive stress was applied from a stress-free condition up to 50 MPa. As a result, with increasing compressive stress, the values of [Formula: see text], [Formula: see text] and [Formula: see text] tended to increase, while [Formula: see text]and [Formula: see text] increased and then decreased at 20 MPa or higher. [Formula: see text] and [Formula: see text] showed the maximum values at 40 MPa of compressive stress, with the values reaching 147 pC/N and 375 pC/N, respectively. These values were analyzed to have increased by 117% and 115%, respectively, compared to the stress-free condition. Additionally, the dielectric constant ([Formula: see text]) was found to increase linearly with the applied compressive stress. The understanding of the changes in piezoelectric properties under various compressive stresses derived from this study is expected to be applicable in various ways for the design and application of piezoelectric devices using compressive stresses, including BLT.

The principal issue associated with wind parks (WPs) based on doubly-fed induction generators (DFIGs) is their vulnerability to network faults. This paper presents a novel nonlinear forward power controller design with an adaptive backstepping command using parametric estimation (NFPC_ABC-PE) to enhance fault ride-through (FRT) capacities in WP utilizing DFIGs. The suggested NFPC_ABC-PE manupiles both rotor and network-side power converters (i.e., RSPCs and NSPCs). Specifically, RSPCs are manipulated to maintain the targeted voltage at dc-bus terminals, while NSPCs are manipulated to supply the reactive energy (power) necessary if the network is disturbed. As a result, the NFPC_ABC-PE proposed precisely supplies reactive energy to ensure the smooth execution of FRT ability. The method developed comprehends the dynamics of RSPC, NSPC-side filters, and dc-bus terminal voltage in the form of electrical active and reactive output power. The parameters of the RSPC and NSPC-side filters, including those associated with the dc-bus capacitor, are regarded as entirely unknown. To estimate and regulate these parameters, adaptation algorithms are utilized. The NFPC_ABC-PE employs parameter adaptation algorithms and switching control inputs designed to safeguard the overall stability of WP. The stability analysis of the DFIG-based WPs with the proposed NFPC_ABC-PE involves applying stability in the sense of the Lyapunov function (LF). To validate its efficacy, simulations are carried out on a single 10 MW power generation unit. The results of the simulation highlight a clear enhancement in the stability and FRT capability of WP, contrasting with the nonlinear forward power controller employing the sliding mode command (NFPC-SMC).

In this paper, we consider the neutrosophic generalized Rayleigh distribution (NGRD). Various neutrosophic properties of NGRD are developed and discussed. The developed distribution is specifically more useful to model indeterminate data which are skewed lifetime data. Also, the neutrosophic parameters are estimated using the well-known method of maximum likelihood (ML) estimation based on a neutrosophic environment. A simulation study is carried out to establish the achievement of the estimated neutrosophic parameters. As a final point, the proposed NGRD applications in the real world have been discussed with the help of real data. A comparative studies also carried out with some recent proposed neutrosophic distributions.

This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models. [ABSTRACT FROM AUTHOR]

Purpose: To accelerate radially sampled diffusion weighted spin‐echo (Rad‐DW‐SE) acquisition method for generating high quality ADC maps. Methods: A deep learning method was developed to generate accurate ADC maps from accelerated DWI data acquired with the Rad‐DW‐SE method. The deep learning method integrates convolutional neural networks (CNNs) with vision transformers to generate high quality ADC maps from accelerated DWI data, regularized by a monoexponential ADC model fitting term. A model was trained on DWI data of 147 mice and evaluated on DWI data of 36 mice, with acceleration factors of 4× and 8× compared to the original acquisition parameters. Results: Ablation studies and experimental results have demonstrated that the proposed deep learning model generates higher quality ADC maps from accelerated DWI data than alternative deep learning methods under comparison when their performance is quantified in whole images as well as in regions of interest, including tumors, kidneys, and muscles. Conclusions: The deep learning method with integrated CNNs and transformers provides an effective means to accurately compute ADC maps from accelerated DWI data acquired with the Rad‐DW‐SE method. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study that explores the performance of various meta-heuristics employed for Optimal Signal Design, specifically focusing on estimating parameters in nonlinear systems. The study introduces the Robust Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (rSOESGOPE) methodology, which is originally derived from the well-known Particle Swarm Optimization (PSO) algorithm. Through a real-life case study involving an Autonomous Surface Vessel (ASV) equipped with three Degrees of Freedom (DoFs) and an aerial holonomic propulsion system, the effectiveness of different meta-heuristics is thoroughly evaluated. By conducting an in-depth analysis and comparison of the obtained results from the diverse meta-heuristics, this study offers valuable insights for selecting the most suitable optimization technique for parameter estimation in nonlinear systems. Researchers and experimental tests in the field can benefit from the comprehensive examination of these techniques, aiding them in making informed decisions about the optimal approach for optimizing parameter estimation in nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the neutrosophic generalized Rayleigh distribution (NGRD). Various neutrosophic properties of NGRD are developed and discussed. The developed distribution is specifically more useful to model indeterminate data which are skewed lifetime data. Also, the neutrosophic parameters are estimated using the well-known method of maximum likelihood (ML) estimation based on a neutrosophic environment. A simulation study is carried out to establish the achievement of the estimated neutrosophic parameters. As a final point, the proposed NGRD applications in the real world have been discussed with the help of real data. A comparative studies also carried out with some recent proposed neutrosophic distributions. [ABSTRACT FROM AUTHOR]

Supraharmonics emitted by power electronic equipment will cause electromagnetic interference. However, there is no uniform standard for the measurement of supraharmonics. Unlike non-parametric methods, such as Fourier transform, the matrix pencil method has attracted the attention of researchers in many fields because of its super-resolution characteristics. In this paper, an attempt is made to apply the matrix pencil method to the high-resolution measurement of supraharmonics. Noting that parametric methods offer a promising alternative strategy for high time-resolution analysis of supraharmonics, the matrix pencil method is introduced for high-resolution measurements and estimating the supraharmonic components in grid voltage and current signals. By deriving and analyzing the Cramér–Rao bound of the method, two excellent properties of the matrix pencil method are found: robustness to time-varying signals in supraharmonics measurements and accuracy in frequency localization of components with large amplitudes. Meanwhile, the effectiveness of the matrix pencil method when applied to the high-resolution estimation and measurement of supraharmonics in grid signals is demonstrated by measuring, estimating, and analyzing grid voltage and current signals containing different typical supraharmonics characteristics. This parametric approach opens up a new avenue that allows more signal information to be obtained while maintaining high accuracy, thus enabling the analysis of supraharmonics with higher time resolution. [ABSTRACT FROM AUTHOR]

ABSTRACTPorous piezoelectric materials have been widely used in hydrophone applications owing to their excellent hydrostatic charge constant (dh) and voltage constant (gh). However, owing to the difficulty in sample manufacturing, the evaluation of the overall piezoelectric properties for reliable device design using simulations is challenging. Herein, a two-step simulation was performed to accurately determine the overall properties of the porous PZT. First, the piezoelectric charge constant was calculated by displacement calculations using the electrostrictive effect. Second, using the calculated piezoelectric charge constant and impedance spectrum obtained from the experiment, the initial value for optimizing the properties was selected, and the overall properties were obtained using the parametric estimation technique. These parametric estimation simulation procedures were performed with the samples of radial and thickness modes based on the IEEE standards. Finally, the piezoelectric properties obtained were compared and verified with the experimental values. Therefore, the overall piezoelectric properties include mechanical, frequency and dielectric properties according to the porosity were obtained with reliable results.

ABSTRACTThe piezoelectric properties of a piezoelectric single crystal are typically determined using a resonance method. However, it is challenging to evaluate these properties in single crystals owing to their high sensitivity and property variations. In this study, to accurately determine the piezoelectric properties, initial values were obtained using two types of samples (TE and TS modes). Impedance spectrum tendency analysis was performed according to the variables to develop a property estimation method. To determine the reliability of this method, the piezoelectric single crystal properties were evaluated and compared using the resonance method. Hence, it was confirmed that high-accuracy piezoelectric properties were obtained in a cost effective and timeous manner.

Parametric identification approaches play a crucial role in the control and monitoring of industrial systems. They facilitate the identification of system variables and enable the prediction of their evolution based on the input-output relationship. In this study, we employ the ARMAX approach to accurately predict the dynamic vibratory behavior of MS5002B gas turbine bearings. By utilizing real input-output data obtained from their operation, this approach effectively captures the vibration characteristics of the bearings. Additionally, the ARMAX technique serves as a valuable diagnostic tool for the bearings, enhancing the quality of identification of turbine variables. This enables continuous monitoring of the bearings and real-time prediction of their behavior. Furthermore, the ARMAX approach facilitates the detection of all potential vibration patterns that may occur in the bearings, with monitoring thresholds established by the methodology. Consequently, this enhances the availability of the bearings and reduces turbine downtime. The efficacy of the proposed ARMAX approach is demonstrated through comprehensive results obtained in this study. Robustness tests are conducted, comparing the real behavior observed through various probes with the reference model, thereby validating the approach. [ABSTRACT FROM AUTHOR]

The piezoelectric properties of a piezoelectric single crystal are typically determined using a resonance method. However, it is challenging to evaluate these properties in single crystals owing to their high sensitivity and property variations. In this study, to accurately determine the piezoelectric properties, initial values were obtained using two types of samples (TE and TS modes). Impedance spectrum tendency analysis was performed according to the variables to develop a property estimation method. To determine the reliability of this method, the piezoelectric single crystal properties were evaluated and compared using the resonance method. Hence, it was confirmed that high-accuracy piezoelectric properties were obtained in a cost effective and timeous manner. [ABSTRACT FROM AUTHOR]

Porous piezoelectric materials have been widely used in hydrophone applications owing to their excellent hydrostatic charge constant (dh) and voltage constant (gh). However, owing to the difficulty in sample manufacturing, the evaluation of the overall piezoelectric properties for reliable device design using simulations is challenging. Herein, a two-step simulation was performed to accurately determine the overall properties of the porous PZT. First, the piezoelectric charge constant was calculated by displacement calculations using the electrostrictive effect. Second, using the calculated piezoelectric charge constant and impedance spectrum obtained from the experiment, the initial value for optimizing the properties was selected, and the overall properties were obtained using the parametric estimation technique. These parametric estimation simulation procedures were performed with the samples of radial and thickness modes based on the IEEE standards. Finally, the piezoelectric properties obtained were compared and verified with the experimental values. Therefore, the overall piezoelectric properties include mechanical, frequency and dielectric properties according to the porosity were obtained with reliable results. [ABSTRACT FROM AUTHOR]

The human microbiome has been recently shown to be associated with disease risks and has important implications in risk stratification and precision medicine. Due to abundant taxa in the human body, microbiome data are high-dimensional and compositional. Dirichlet distributions and their generalization are used to characterize the dependence structures of microbial data. Another existing method for fitting microbiome data employed Gaussian graphical model using the centered log-transformation (CLR). However, Dirichlet distributions are not able to infer networks or to estimate some extremely rare probabilities. On the other hand, it is hard to interpret the network analysis results using CLR. Furthermore, the data analysis showed that there is a lack of efficient multivariate distributions for fitting microbiome data, which results in inadequate statistical inferences. In this paper, we propose new multivariate distributions for modeling the dependence structures of the high dimensional and compositional microbiome data using inverse gamma distributions and copula techniques. The data analysis in the American gut project shows our proposed methods perform well. [ABSTRACT FROM AUTHOR]

We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of N interacting particles observed over a fixed time horizon in a mean-field regime N → ∞. By implementing the classical theory of Ibragimov and Hasminski, we obtain in particular sharp results for the maximum likelihood estimator that go beyond its simple asymptotic normality thanks to Hájek's convolution theorem and strong controls of the likelihood process that yield asymptotic minimax optimality (up to constants). Our structural results shed some light to the accompanying nonlinear McKean–Vlasov experiment, and enable us to derive simple and explicit criteria to obtain identifiability and non-degeneracy of the Fisher information matrix. These conditions are also of interest for other recent studies on the topic of parametric inference for interacting diffusions. [ABSTRACT FROM AUTHOR]

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Causal mediation analysis is used to decompose the total effect of an exposure on an outcome into an indirect effect, taking the path through an intermediate variable, and a direct effect. To estimate these effects, strong assumptions are made about unconfoundedness of the relationships between the exposure, mediator and outcome. These assumptions are difficult to verify in a given situation and therefore a mediation analysis should be complemented with a sensitivity analysis to assess the possible impact of violations. In this paper we present a method for sensitivity analysis to not only unobserved mediator-outcome confounding, which has largely been the focus of previous literature, but also unobserved confounding involving the exposure. The setting is estimation of natural direct and indirect effects based on parametric regression models. We present results for combinations of binary and continuous mediators and outcomes and extend the sensitivity analysis for mediator-outcome confounding to cases where the continuous outcome variable is censored or truncated. The proposed methods perform well also in the presence of interactions between the exposure, mediator and observed confounders, allowing for modeling flexibility as well as exploration of effect modification. The performance of the method is illustrated through simulations and an empirical example. [ABSTRACT FROM AUTHOR]

In this paper, a promising modeling strategy for data fitting is derived from a new general class of univariate continuous distributions. This class is governed by an original logarithmically-exponential one-parameter transformation which has the ability to enhance some modeling capabilities of any parental distribution. In relation to the current literature, it appears to be a "limit case" of the well-established truncated generalized Fréchet generated class. In addition, it offers a natural alternative to the famous odd inverse exponential generated class. Some special distributions are presented, with particular interest in a novel heavy-tailed three-parameter distribution based on the Lomax distribution. Functional equivalences, modes analysis, stochastic ordering, functional expansions, moment measures, information measures and reliability measures are derived. From generic or real data, our modeling strategy is based on the new class combined with the maximum likelihood approach. We apply this strategy to the introduced modified Lomax model. The efficiency of the three parameter estimates is validated by a simulation study. Subsequently, two referenced real data sets are adjusted according to the rules of the art; the first one containing environmental data and the second one, financial data. In particular, we show that the proposed model is preferable to four concurrents also derived from the Lomax model, including the odd inverse exponential Lomax model.

The paper introduces novel parametric estimators for the mean value function (MVF) and variance function (VF) in geometric processes (GPs) based on a random sample which belongs to a GP. Specifically, it addresses scenarios where the distribution function of the first interarrival time of GP is analytically known, but its parameters, along with the ratio parameter of the GP, are unknown. It establishes a solid theoretical foundation for the estimators proposed and investigates some statistical properties such as strong consistency and asymptotic unbiasedness of the estimators. These results generalize some of the findings acquired in previous studies. To evaluate the performance of the proposed estimators, we conduct a comprehensive Monte Carlo simulation study. This involves using various lifetime distributions, such as gamma, Weibull, and lognormal considering different sample sizes and parameter values. A discussion of an application to software engineering is also provided to illustrate the applicability of the methods developed in this study. [ABSTRACT FROM AUTHOR]

In this article we present a parametric estimation method for certain multiparameter heavy‐tailed Lévy‐driven moving averages. The theory relies on recent multivariate central limit theorems obtained via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to previous papers, which propose to use the marginal empirical characteristic function to estimate the one‐dimensional parameter of the kernel function and the stability index of the driving Lévy motion. We extend their work to allow for a multiparametric framework that in particular includes the important examples of the linear fractional stable motion, the stable Ornstein–Uhlenbeck process, certain CARMA(2, 1) models, and Ornstein–Uhlenbeck processes with a periodic component among other models. We present both the consistency and the associated central limit theorem of the minimal contrast estimator. Furthermore, we demonstrate numerical analysis to uncover the finite sample performance of our method. [ABSTRACT FROM AUTHOR]

This study aims to develop a methodology for parametric estimation of flexible manipulators considering an equivalent underactuated manipulator with passive joints, which should allow better possibilities to control flexible systems when addressing challenging problems to reach a satisfactory tracking motion. Theoretically, this is achieved by a minimum number of internal dynamics variables needed for representing almost all dynamics of the system. The parametric estimation approach is based on the optimal control theory considering a robust, stable method. This methodology requires only measured/computed data that are system output. Validation occurs through a virtual plant of the flexible manipulator observing a numerical perspective. The systems studied have serial and parallel kinematics and are mounted on carts for more diverse applications and general possibilities of the methodology. [ABSTRACT FROM AUTHOR]

The nonlinearity behaviour of magnetorheological fluid (MRF) can be described using a number of established models such as Bingham and Modified Bouc-Wen models. Since these models require the identification of model parameters, there is a need to estimate the parameters’ value carefully. In this paper, an optimization algorithm, i.e., the Particle Swarm Optimization (PSO) algorithm, is utilized to identify the models’ parameters. The PSO algorithm distinctively controls the best fit value by minimizing marginal error through root-mean-square error between the models and the empirical response. The validation of the algorithm is attained by comparing the resulting modified Bouc-Wen model behaviour using PSO against the same model’s behaviour, identified using Genetic Algorithm (GA). The validation results indicate that the application of PSO is better in identifying the model parameters. Results from this estimation can be used to design a controller for various applications such as prosthetic limbs.

This paper describes a novel method to synthesize load and feeder models, by estimating the load composition and the load parameters, using instantaneous voltage and current measurements, obtained at the distribution level, from disturbance events. A novel feeder model structure has been proposed in this work comprising of single-phase loads, three-phase loads, impedance loads, distribution transformers and distribution line segments. The load composition of the proposed feeder models and the motor load parameters are determined using a non-linear least squares algorithm integrated with an electromagnetic transient (EMT) analysis tool PSCAD. The efficacy of the proposed algorithm is examined for feeders at different physical locations and with distinctly varied load characteristics. Using this approach, parameters of the motor loads have been obtained within a fixed set of bounded values for each corresponding parameter. The ability of the proposed feeder and load models to capture severe fault induced delayed voltage recovery events (FIDVR) has also been discussed here.

Autonomous Surface Vessels (ASVs) are reliable and robust vehicles. They perform autonomous missions in lakes, rivers and even open waters. Those are dangerous environments that requires precise and secure navigation. Under these conditions, the knowledge of a robust and accurate mathematical model is a fundamental aspect for adjusting the control system for reaching safety and performance. Moreover, traditional mathematical models disregard assimetries and coupling between the degrees of freedom. While those models work fine for bigger vessels, to ignore these characteristics in small ASVs compromises the model’s quality. In this context, this work presents a new methodology for modeling and identifying the dynamics of ASVs along with the uncertainties arising from disturbances and non-modeled dynamics. As for the uncertainties and disturbances, this work considers the coupling parameters into the mathematical modeling, which synthesizes the divergences between the model and the real application, allowing to incorporate asymmetries and model deficiencies. Regarding the parameter identification, the proposal is based on (i) the design of optimal input excitation signals from a double layer optimization methodology and (ii) a parametric estimation concept in two steps, dividing the original set of parameters into two partially coupled sub-problems. Finally, this work also presents a full discussion and analysis about the importance to manage the trade-off between precision and complexity of mathematical models, its respective solution spaces and the impact over the optimization algorithms. To validate the approach, a real 3 Degree of Freedom ASV with aerial holonomic propulsion system is used. The results show that it is possible to successfully capture the complex set of parameters and identify physical characteristics not considered by the model.

In this research paper, a combinatorial optimization approach is proposed for parameter estimation in single-phase transformers considering voltage and current measurements at the transformer terminals. This problem is represented through a nonlinear programming model (NLP), whose objective is to minimize the root mean square error between the measured voltage and current values and the calculated values from the equivalent model of the single-phase transformer. These values of voltage and current can be determined by applying Kirchhoff's Laws to the model T of the transformer, where its parameters, series resistance and reactance as well as the magnetization resistance and reactance, i.e., R 1 , R 2 ′ , X 1 , X 2 ′ , R c y X m , are provided by the Hurricane Optimization Algorithm (HOA). The numerical results in the 4 kVA, 10 kVA and 15 kVA single-phase test transformers demonstrate the applicability of the proposed method since it allows the reduction of the average error between the measured and calculated electrical variables by 1000% compared to the methods reported in the specialized literature. This ensures that the parameters estimated by the proposed methodology, in each test transformer, are close to the real value with an accuracy error of less than 6%. Additionally, the computation times required by the algorithm to find the optimal solution are less than 1 second, which makes the proposed HOA robust, reliable, and efficient. All simulations were performed in the MATLAB programming environment. [ABSTRACT FROM AUTHOR]

We present a new way to estimate the lifetime distribution of a reparable system consisted of similar (equal) components. We consider as a reparable system, a system where we can replace a failed component by a new one. Assuming that the lifetime distribution of all components (originals and replaced ones) are the same, the position of a single component can be represented as a renewal process. There is a considerable amount of works related to estimation methods for this kind of problem. However, the data has information only about the time of replacement. It was not recorded which component was replaced. That is, the replacement data are available in an aggregate form. Using both Bayesian and a maximum likelihood function approaches, we propose an estimation procedure for the lifetime distribution of components in a repairable system with aggregate data. Based on a latent variables method, our proposed method out-perform the commonly used estimators for this problem. The proposed procedure is generic and can be used with any lifetime probability model. Aside from point estimates, interval estimates are presented for both approaches. The performances of the proposed methods are illustrated through several simulated data, and their efficiency and applicability are shown based on the so-called cylinder problem. The computational implementation is available in the R package srplv. [ABSTRACT FROM AUTHOR]

The problem of parametric estimation in photovoltaic (PV) modules considering manufacturer information is addressed in this research from the perspective of combinatorial optimization. With the data sheet provided by the PV manufacturer, a non-linear non-convex optimization problem is formulated that contains information regarding maximum power, open-circuit, and short-circuit points. To estimate the three parameters of the PV model (i.e., the ideality diode factor (a) and the parallel and series resistances (Rp and Rs)), the crow search algorithm (CSA) is employed, which is a metaheuristic optimization technique inspired by the behavior of the crows searching food deposits. The CSA allows the exploration and exploitation of the solution space through a simple evolution rule derived from the classical PSO method. Numerical simulations reveal the effectiveness and robustness of the CSA to estimate these parameters with objective function values lower than 1 × 10-28 and processing times less than 2 s. All the numerical simulations were developed in MATLAB 2020a and compared with the sine-cosine and vortex search algorithms recently reported in the literature. [ABSTRACT FROM AUTHOR]

Parameterizing high-complexity thermal models is a common challenge in bioreactor engineering. This paper rapports the mathematical modeling of thermal interactions in a photobioreactor. Energy balances, physical measurements, and mathematical relations from the literature were used. Two experiments (Tests 1 and 2) were done for model parameterization and to validate their mathematical estimation. The difficulty or impossibility of generating thermophysical properties data led to use the Kalman filter for parameter estimation. A mean absolute percentage error from 0.024 to 0.136% was obtained for parametrized models regarding estimates vs. measured values. A significative correlation was obtained for all paired measured vs. estimated values in Test 1 (r = 0.931, p

This article focuses on the design of model predictive control (MPC) for nonlinear systems with slow time‐dynamic change. To avoid frequent updates of the predictive model and guarantee the state always stays inside of a given feasible region, an event‐triggered parametric estimation mechanism is designed. Firstly, a trigger condition is designed to judge if parameters of the predictive model are out of date and differ a lot from their current true values so that there is no feasible solution to regulate the state within the given bound without predictive model parameter update. This condition also depends on the current state and is deduced from a designed Lyapunov constraint, inputs constraints, and the mismatched predictive model. Then the EMPC is designed based on this condition. If the trigger condition is met, the MPC recursively updates the parameters and imposes the Lyapunov constraint. The Lyapunov constraint is based on the mismatched model and the real state does not need to be convergence. Else, the MPC only optimizes the cost function to derive a good profit. We proved that the proposed EMPC promises that the closed‐loop system state is maintained within a predefined stable region when the model mismatch bound can be estimated accurately. A simulation of a chemical process demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The process of software testing usually involves the correction of a detected bug immediately upon detection. In this article, in contrast, we discuss continuous time testing of a software with periodic debugging in which bugs are corrected, instead of at the instants of their detection, at some pre-specified time points. Under the assumption of renewal distribution for the time between successive occurrence of a bug, maximum-likelihood estimation of the initial number of bugs in the software is considered, when the renewal distribution belongs to any general parametric family or is arbitrary. The asymptotic properties of the estimated model parameters are also discussed. Finally, we investigate the finite sample properties of the estimators, specially that of the number of initial number of bugs, through simulation. [ABSTRACT FROM AUTHOR]

Accurate and reliable machine performance degradation tracking and remaining useful life (RUL) prognosis establish the foundation for predictive maintenance scheduling toward improved safety and productivity of machine operations. In general, machine performance degradation exhibits a nonlinear and nonhomogeneous pattern that arises from time-varying degradation rate and abrupt performance changes. To address this challenge and improve the generalizability of degradation modeling, in this article, we present a stochastic modeling technique based on the Lévy process, which generalizes system variations as the accumulations of successive and jump increments. The developed Lévy process model consists of two terms: a linear Brownian motion term for capturing the gradual degradation with time-varying rates and a nonhomogenous compound Poisson process term for capturing transient performance changes. By calculating the moments of the characteristic function of the Lévy model, explicit expressions for the probability distributions of predicted performance degradation and RUL are derived. To obtain the time-varying parameters in the Lévy model, Markov chain Monte Carlo is investigated. The developed technique is evaluated through simulation and run-to-failure tests of roller and ball bearings, and the good performance of the developed Lévy model is confirmed. [ABSTRACT FROM AUTHOR]

The Heston model (1993) is validated for MXN/USD options, calculating the difference between the theoretical premium and the one issued by the Mexican Derivatives Market. The parameters were estimated covering a period from 2003 to 2018 and the prices of the European Call and Put options were calculated, considering the exercise prices of November 9, 2018. The results reveal overvaluation of Call OTM and ITM options with a variation of 5.87% and 3.46%, respectively, and for Put OTM options with 11.41%, thus ratifying that the model is reliable, it is also confirmed that it is a hedging instrument for all those investors exposed to the exchange market risk. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parametric estimation in solar cells considering manufacturer datasheet information regarding open-circuit, short-circuit, and maximum power points from the point of view of mathematical optimization. To represent this problem a single-objective function is formulated associated with the minimization of the mean square error of the single-diode model evaluated in the operational points reported by the manufacturer. The solution of this nonlinear non-convex optimization model is addressed with a metaheuristic optimization technique known in specialized literature as a vortex search algorithm (VSA). This metaheuristic optimization method works with Gaussian distribution functions and variable radius to explore and exploit the solution space by generating hyperspheres that move through the solution space as a function of the best current solution. The VSA is implemented in MATLAB environment by using commercial photovoltaic module information, where numerical results demonstrate the efficiency of this optimization method with objective functions lower than 1times10-25 and processing times around 6.13s. [ABSTRACT FROM AUTHOR]

Empirical distributions of top incomes suffer from statistical problems affecting the measurement of inequality and its trend. Researchers and practitioners have been increasingly noting parametric regularities across income distributions and turning to parametric functions to approximate or supplement the observed distributions, both for descriptive purposes and for correcting distributional statistics derived from data. The proliferation of distinct branches of modeling literature has highlighted the need to compare the alternative modeling options, and develop systematic tools to discriminate between them. This paper reviews the state of methodological and empirical knowledge regarding the adoptable parametric functions, and lists references and statistical programs allowing practitioners to apply these models to microdata in household surveys and administrative registers, or grouped‐records data from national accounts statistics. Implications for modeling the distributions of other economic outcomes including consumption and wealth, and incomes below the topmost tail, are drawn. For incomes, a handful of distribution functions hold promise for modeling the top tails based on theoretical and empirical properties—namely the extreme values distributions, the generalized Pareto, the Singh–Maddala and the generalized beta type 2. Understanding these functions in relation to other commonly invoked alternatives is a contribution of this review. [ABSTRACT FROM AUTHOR]

A new weighted exponential distribution is proposed with the feature to use a logarithmic weight function. Among the merits, this distribution shows a remarkable flexibility with respect to the probability density and hazard functions shapes. Mathematical properties are studied, including moments, residual life function, order statistics and record values. A parametric estimation is performed using the maximum likelihood method. Applications are provided using four practical data sets. It is shown that the new distribution works better than a number of classical and recent distributions. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the joint distribution of n independent random variables. Given a loss function and a family of candidate probabilities, that we shall call a model, we aim at designing an estimator with values in our model that possesses good estimation properties not only when the distribution of the data belongs to the model but also when it lies close enough to it. The losses we have in mind are the total variation, Hellinger, Wasserstein and L p -distances to name a few. We show that the risk of our estimator can be bounded by the sum of an approximation term that accounts for the loss between the true distribution and the model and a complexity term that corresponds to the bound we would get if this distribution did belong to the model. Our results hold under mild assumptions on the true distribution of the data and are based on exponential deviation inequalities that are non-asymptotic and involve explicit constants. Interestingly, when the model reduces to two distinct probabilities, our procedure results in a robust test whose errors of first and second kinds only depend on the losses between the true distribution and the two tested probabilities. [ABSTRACT FROM AUTHOR]

A state‐of‐the‐art review on various identification schemes proposed for the Hammerstein, Wiener, and Volterra systems is presented with respect to the special problems arising in the identification of unknown nonlinear systems. Past and recent developments in the field of nonlinear system identification, parameter estimation, and nonlinear control schemes along with the nonlinearity issues are also deeply investigated. A comprehensive analysis on various parameter estimation approaches and nonlinear control laws are made adding credit to the noteworthy contributions, constructive arguments, and remarkable breakthroughs of researchers in various research fields. The application of most popular nonlinear control strategies for many nonlinear systems in the existing literature are presented spotlighting their merits and major shortcomings. The challenges faced in the nonlinear control field and their emergences to future directions are projected. [ABSTRACT FROM AUTHOR]

Soil water retention curve (SWRC) reflects different states of soil moisture and describes quantitative characteristics of the unsaturated parts of the soil. Direct measurement of SWRC is time-consuming, difficult and costly. Therefore, many indirect attempts have been made to estimate SWRC from other soil properties. Using pedotransfer functions is one of the indirect methods for estimating SWRC. The aim of this research was to assess the effect of using soil particles percentage in comparison with the geometric characteristics of soil particles on the accuracy of the pedotransfer equations of SWRC and the critical point of it. Accordingly, 54 soil samples of Isfahan province from seven texture classes were used. The most suitable functions for estimating SWRC, parameters of van Genuchten and Brooks-Corey equations, and the critical point of SWRC were selected based on statistical indices. The results indicated that the pedotransfer equations fitted the SWRC data well and the outputs from them were in a good agreement with the independent (validation) SWRC data. The results revealed that using soil particles percentage (sand and clay), bulk density and organic matter content in the point estimation of SWRC was better than applying geometric properties of the soil particle diameter. On the other hand, in the estimation of parametric and critical point of SWRC, using the geometric properties of soil particle diameters resulted in more satisfactory results, as compared with using the soil particles percentage. The NRMSE values indicated that the accuracy of the pedotransfer equations in the lower matric head was greater than that of the higher matric head.