Parameter Estimations of Rayleigh Distribution

设随机变量X服从Rayleigh分布，其密度函数为p(x;β)=2x/βe-x^2/β，x＞0,β＞0为参数，对变换群G={gc;gc(x)=c^2x,c＞0}，本文分别在平方损失和熵损失下研究了β在G上的最优同变估计；当β有先验信息时，给出了β的Bayes估计。

Active learning accelerated Monte-Carlo simulation based on the modified K-nearest neighbors algorithm and its application to reliability estimations

This paper proposes an active learning accelerated Monte-Carlo simulation method based on the modified K-nearest neighbors algorithm.The core idea of the proposed method is to judge whether or not the output of a random input point can be postulated through a classifier implemented through the modified K-nearest neighbors algorithm.Compared to other active learning methods resorting to experimental designs,the proposed method is characterized by employing Monte-Carlo simulation for sampling inputs and saving a large portion of the actual evaluations of outputs through an accurate classification,which is applicable for most structural reliability estimation problems.Moreover,the validity,efficiency,and accuracy of the proposed method are demonstrated numerically.In addition,the optimal value of K that maximizes the computational efficiency is studied.Finally,the proposed method is applied to the reliability estimation of the carbon fiber reinforced silicon carbide composite specimens subjected to random displacements,which further validates its practicability.

ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION

The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.

<i>L_p</i>-Estimations of Vector Fields in Unbounded Domains

Some new estimations of scalar products of vector fields in unbounded domains are investigated. Lp-estimations for the vector fields were proved in special weighted functional spaces. The paper generalizes our earlier results for bounded domains. Estimations for scalar products make it possible to investigate wide classes of mathematical physics problems in physically inhomogeneous domains. Such estimations allow studying issues of correctness for problems with non-smooth coefficients. The paper analyses solvability of stationary set of Maxwell equations in inhomogeneous unbounded domains based on the proved Lp-estimations.

The simultaneity in human capital estimations： The case of China

Existing papers on human capital and growth in China has been using single equation estimations. This might cause a simultaneity bias if a two-way causality between the two variables exists. In this paper, the author performs vector autoregressive estimations using panel data on the number of graduates at each level of education as a proxy for human capital in China during 1991-2005. The results show that investment in human capital increases output per worker at all three levels of education. Regarding the effects of output per worker on the accumulation of human capital, the author finds mixed results with the primary-school graduates＇ benefits the most from increases in per capita output.

Modelling Stand Dynamics after Selective Logging： Implications for REDD and Carbon Pools Estimations from Forest Degradation

Forest degradation and biomass damage resulting from logging is currently difficult to evaluate with satellite images, but contributes substantially to carbon emissions in the tropics. To address this situation, we modelled how changes in the minimum felling diameter affect stem density, basal area and the related carbon biomass at the end of the felling cycle （30 years） in a semi-deciduous natural forest in Cameroon. With new MFDs estimates, at 7% logging damage rate, we found that the stem density of initially harvestable trees reduces from 12.3 （50.4 MgC·ha^-1） to 6.7 （32.5 MgC·ha^-1） trees per ha and the number of initial residual trees increases from 80 （18.9MgC·ha^-1） to 85.7 （36.8 MgC·ha^-1） trees per ha. This corresponds to an avoided damage estimated at 17.9 MgC·ha^-1. We also found that increasing mortality and damage intensity also increases the damage on carbon biomass estimated to be 8.9 MgC·ha^-1 at 10% or to be 17.4 MgC.hal at 15% logging damage. Overall, our study shows that proper determination of MFD of logged species taking into consideration their capacity of reconstitution and the Reduced Impact Logging can avoid the loss of up to 35 MgC·ha^-1.

Estimations of Precipitable Water and Its Characteristics during the HUBEX/IOP 1998

GMS-5 satellite data at channels of infrared split windows and water vapor are analyzed to retrieve the precipitable water (PW) distributions under cloud-free conditions. Radiosonde data and surface station data are applied to estimate the PW distributions under cloudy conditions. These two methods are then merged to obtain the PW distributions under all-weather conditions during the Huaihe River Basin Energy and Water Cycle Experiment (HUBEX). The results of the all-weather PW distributions from these methods demonstrate that this new merging technique may be applied to derive large-scale or global maps of PW. It is revealed that the atmospheric water vapor over the Yangtze-Huaihe River Basins came mainly from the southwest during the 1998 prevailing period of Meiyu. Sufficient atmospheric PW is a necessary condition for ground rainfall. Under certain dynamic conditions, it can be partially transformed into surface precipitation. Several types of rain are displayed and their PW conditions and characteristics, as well as atmospheric dynamic conditions, are analyzed. It is demonstrated that surface precipitation centers usually appear not at the high PW centers but on their downwind sides.

Refractivity estimations from an angle-of-arrival spectrum

This paper addresses the probability of atmospheric refractivity estimation by using field measurements at an array of radio receivers in terms of angle-of-arrival spectrum. Angle-of-arrival spectrum information is simulated by the ray optics model and refractivity is expressed in the presence of an ideal tri-linear profile. The estimation of the refractivity is organized as an optimization problem and a genetic Mgorithm is used to search for the optimal solution from various trial refractivity profiles. Theoretical analysis demonstrates the feasibility of this method to retrieve the refractivity parameters. Simulation results indicate that this approach has a fair anti-noise ability and its accuracy performance is mainly dependent on the antenna aperture size and its positions.

Parameter Estimations in BurrⅫ Model Using Masked Data

We consider a series system of two independent and non-identical components which have different BurrⅫ distributed lifetime.The maximum likelihood and Bayes estimators of the parameters of the system＇s components are obtained based on masked system life test data.The conclusion is that the Bayes estimates are better than the maximum likelihood estimates in the sense of having smaller mean squared errors.

Parameter Estimations for Some Modifications of the Weibull Distribution

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

A new approach on seismic mortality estimations based on average population density

This study examines a new methodology to predict the final seismic mortality from earthquakes in China. Most studies established the association between mortality estimation and seismic intensity without considering the population density. In China, however, the data are not always available, especially when it comes to the very urgent relief situation in the disaster. And the popu- lation density varies greatly from region to region. This motivates the development of empirical models that use historical death data to provide the path to analyze the death tolls for earthquakes. The present paper employs the average population density to predict the final death tolls in earthquakes using a case-based reasoning model from realistic perspective. To validate the forecasting results, historical data from 18 large-scale earthquakes occurred in China are used to estimate the seismic morality of each case. And a typical earthquake case occurred in the northwest of Sichuan Province is employed to demonstrate the estimation of final death toll. The strength of this paper is that it provides scientific methods with overall forecast errors lower than 20 %, and opens the door for conducting final death forecasts with a qualitative and quantitative approach. Limitations and future research are also analyzed and discussed in the conclusion.

Stochastic Estimations of Fermion Matrix Determinants with Unbiased Subtractions

The Padé-Z_(2) stochastic estimator is used to calculate the fermion matrix determinants and the determinant ratios with an unbiased variational scheme.The results on an 8^(3)×12 lattice with Wilson action show that the determinant ratio with a relatively small number of Z_(2) noises(e.g.,400)can be estimated by using the unbiased subtractions.

Estimations of Weibull-Geometric Distribution under Progressive Type II Censoring Samples

This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown parameters under a squared error loss function. The approximate Bayes estimators will be computed using the idea of Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions. Also the point estimation and confidence intervals based on maximum likelihood and bootstrap technique are also proposed. The approximate Bayes estimators will be obtained under the assumptions of informative and non-informative priors are compared with the maximum likelihood estimators. A numerical example is provided to illustrate the proposed estimation methods here. Maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo Simulation

Parameter Estimations for Generalized RayleighDistribution under Progressively Type-I IntervalCensored Data

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.

Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs

This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the integral form is equivalent, one cannot exist without the other, hence can be used interchangeably. Dimensional model problems consisting of diffusion equation, convection-diffusion equation, and Burgers equation described by self adjoint, non-self adjoint, and nonlinear differential operators are considered to present extensive numerical studies using Galerkin method with weak form (GM/WF) and least squares process (LSP) to determine computed convergence rates of various error norms and present comparisons with the theoretical convergence rates.

A robust triaxial localization method of AE source using refraction path

Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.

Modeling the Dynamics of Tuberculosis with Vaccination,Treatment,and Environmental Impact:Fractional Order Modeling

A mathematical model is designed to investigate Tuberculosis(TB)disease under the vaccination,treatment,andenvironmental impact with real cases.First,we introduce the model formulation in non-integer order derivativeand then,extend the model into fractional order derivative.The fractional system’s existence,uniqueness,andother relevant properties are shown.Then,we study the stability analysis of the equilibrium points.The diseasefree equilibrium(DFE)D_(0)is locally asymptotically stable(LAS)when R_(v)<1.Further,we show the globalasymptotical stability(GAS)of the endemic equilibrium(EE)D*for R_(v)>1 and D_(0)for R_(v)≤1.The existenceof bifurcation analysis in the model is investigated,and it is shown the system possesses the forward bifurcationphenomenon.Sensitivity analysis has been performed to determine the sensitive parameters that impact R_(v).Weconsider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model.The computedbasic reproduction number obtained using the real cases is R0≈3.6615.Various numerical results regardingdisease elimination of the sensitive parameters are shown graphically.

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

A new one-parameter Chris-Jerry distribution,created by mixing exponential and gamma distributions,is discussed in this article in the presence of incomplete lifetime data.We examine a novel generalized progressively hybrid censoring technique that ensures the experiment ends at a predefined period when the model of the test participants has a Chris-Jerry(CJ)distribution.When the indicated censored data is present,Bayes and likelihood estimations are used to explore the CJ parameter and reliability indices,including the hazard rate and reliability functions.We acquire the estimated asymptotic and credible confidence intervals of each unknown quantity.Additionally,via the squared-error loss,the Bayes’estimators are obtained using gamma prior.The Bayes estimators cannot be expressed theoretically since the likelihood density is created in a complex manner;nonetheless,Markov-chain Monte Carlo techniques can be used to evaluate them.The effectiveness of the investigated estimations is assessed,and some recommendations are given using Monte Carlo results.Ultimately,an analysis of two engineering applications,such as mechanical equipment and ball bearing data sets,shows the applicability of the proposed approaches that may be used in real-world settings.

Body composition and metabolic syndrome in patients with type 1 diabetes

BACKGROUND In recent years,the prevalence of obesity and metabolic syndrome in type 1 diabetes(T1DM)patients has gradually increased.Insulin resistance in T1DM deserves attention.It is necessary to clarify the relationship between body composition,metabolic syndrome and insulin resistance in T1DM to guide clinical treatment and intervention.AIM To assess body composition(BC)in T1DM patients and evaluate the relationship between BC,metabolic syndrome(MS),and insulin resistance in these indi-viduals.METHODS A total of 101 subjects with T1DM,aged 10 years or older,and with a disease duration of over 1 year were included.Bioelectrical impedance analysis using the Tsinghua-Tongfang BC Analyzer BCA-1B was employed to measure various BC parameters.Clinical and laboratory data were collected,and insulin resistance was calculated using the estimated glucose disposal rate(eGDR).RESULTS MS was diagnosed in 16/101 patients(15.84%),overweight in 16/101 patients(15.84%),obesity in 4/101(3.96%),hypertension in 34/101(33.66%%)and dyslip-idemia in 16/101 patients(15.84%).Visceral fat index(VFI)and trunk fat mass were significantly and negatively correlated with eGDR(both P<0.001).Female patients exhibited higher body fat percentage and visceral fat ratio compared to male patients.Binary logistic regression analysis revealed that significant factors for MS included eGDR[P=0.017,odds ratio(OR)=0.109],VFI(P=0.030,OR=3.529),and a family history of diabetes(P=0.004,OR=0.228).Significant factors for hypertension included eGDR(P<0.001,OR=0.488)and skeletal muscle mass(P=0.003,OR=1.111).Significant factors for dyslipidemia included trunk fat mass(P=0.033,OR=1.202)and eGDR(P=0.037,OR=0.708).CONCLUSION Visceral fat was found to be a superior predictor of MS compared to conventional measures such as body mass index and waist-to-hip ratio in Chinese individuals with T1DM.BC analysis,specifically identifying visceral fat(trunk fat),may play an important role in identifying the increased risk of MS in non-obese patients with T1DM.

A comparative study of data-driven battery capacity estimation based on partial charging curves

With its generality and practicality, the combination of partial charging curves and machine learning(ML) for battery capacity estimation has attracted widespread attention. However, a clear classification,fair comparison, and performance rationalization of these methods are lacking, due to the scattered existing studies. To address these issues, we develop 20 capacity estimation methods from three perspectives:charging sequence construction, input forms, and ML models. 22,582 charging curves are generated from 44 cells with different battery chemistry and operating conditions to validate the performance. Through comprehensive and unbiased comparison, the long short-term memory(LSTM) based neural network exhibits the best accuracy and robustness. Across all 6503 tested samples, the mean absolute percentage error(MAPE) for capacity estimation using LSTM is 0.61%, with a maximum error of only 3.94%. Even with the addition of 3 m V voltage noise or the extension of sampling intervals to 60 s, the average MAPE remains below 2%. Furthermore, the charging sequences are provided with physical explanations related to battery degradation to enhance confidence in their application. Recommendations for using other competitive methods are also presented. This work provides valuable insights and guidance for estimating battery capacity based on partial charging curves.