The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

Thermomechanical analysis of long-term global modal and local deformation measurements of the Kishwaukee Bridge using the bootstrap

In this paper we present a comparative analysis of global frequency and local deformation data for a large concrete bridge. The asymptotic probability distributions of the central statistics are presented, and compared with empirical bootstrap estimates. Bootstrapped distributions are calculated from reference data obtained during 1999–2000 and used to develop change-point alarm criteria for the structure, using reasonable sensitivity measures developed from FEM simulations and structural analysis. The implications of the frequency data are discussed in conjunction with the strain and displacement measurements in order to discern if the load carrying capacity of the bridge has been affected. The critical need for more advanced temperature compensation models for large structures continually in thermal disequilibrium is discussed.

Estimating canopy closure density and above-ground tree biomass using partial least square methods in Chinese boreal forests

Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression （PLSR） models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM＋ data. The established models were optimized according to the variable importance for projection （VIP） criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test （p〈0.05）. The simplified models without insignificant variables （VIP 〈1） performed as well as the full model but with less computation time. The relative root mean square error （RMSE%） was 29% for canopy closure density, and 58% for above ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above ground biomass.

Applications of Bootstrap in Analyzing General Extreme Value Distributions

The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.

Investigation ofβ—‑decay half‑life and delayed neutron emission with uncertainty analysis

β-decay half-life and β-delayed neutron emission(βn) are of great importance in the development of basic science and industrial applications, such as nuclear physics and nuclear energy, where β--decay plays an important role. Many theoretical models have been proposed to describe β-decay half-lives, whereas the systematic study of βn is still rare. This study aimed to investigate β--decay half-lives and βn probabilities through analytical formulas and by comparing them with experimental data. Analytical formulas for β--decay properties have been proposed by considering prominent factors, that is, decay energy,odevity, and the shell effect. The bootstrap method was used to simultaneously evaluate the total uncertainty on calculations,which was composed of statistic and systematic uncertainties. β--decay half-lives, βn probabilities, and the corresponding uncertainties were evaluated for the neutron-rich region. The experimental half-lives were well reproduced. Additional predictions are also presented with theoretical uncertainties, which helps to better understand the disparity between the experimental and theoretical results.

Bias and Mean Square Error of Reliability Estimators under the One and Two Random Effects Models: The Effect of Non-Normality

The coefficient of reliability is often estimated from a sample that includes few subjects. It is therefore expected that the precision of this estimate would be low. Measures of precision such as bias and variance depend heavily on the assumption of normality, which may not be tenable in practice. Expressions for the bias and variance of the reliability coefficient in the one and two way random effects models using the multivariate Taylor’s expansion have been obtained under the assumption of normality of the score (Atenafu et al. [1]). In the present paper we derive analytic expressions for the bias and variance, hence the mean square error when the measured responses are not normal under the one-way data layout. Similar expressions are derived in the case of the two-way data layout. We assess the effect of departure from normality on the sample size requirements and on the power of Wald’s test on specified hypotheses. We analyze two data sets, and draw comparisons with results obtained via the Bootstrap methods. It was found that the estimated bias and variance based on the bootstrap method are quite close to those obtained by the first order approximation using the Taylor’s expansion. This is an indication that for the given data sets the approximations are quite adequate.

Establishment and Optimization of State Feature System of Diesel Engine Fault Diagnosis

For too many state features are used in the diesel engine state evaluation and fault diagnosis, it is not easy to obtain the rational eigenvalues. In the paper, the cylinder subassembly of diesel engine is used to search for the method of establishing state feature system and optimal approach. The signal of diesel engine has been collected when the piston ring and airtight ring are working at different states, then with the Bootstrap method and Genetic Algorithm (GA), an optimum parameter combination is received. Example shows this method is simple and efficient for establishing diesel engine state feature system, Thus, this method is valuable for the virtual state evaluation of similar complex system.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

China’s Gini Coefficient:Myths and Realities

Using retroactive adjustment approach of history data published by the National Bureau of Statistics （NBS）, this study has adjusted micro-level survey data of China Household Income Project Survey （CHIPS, 2007） and conducted point estimation on household income Gini coefficient using the NBS method. On this basis, the standard error of the point estimation of China＇s Gini coefficient is estimated using bootstrap method, creating a confidence interval of Gini coefficient. Results indicate that among five continuous declines of Gini coefficient between 2008 and 2013, only three declines are statistically significant. It is thus too early to jump at the conclusion that the Gini coefficient of China＇s household income distribution has already entered into a downward channel and at least the argument that China＇s Gini coefficient has been on the decline for five consecutive years is questionable.

Application of dynamic image analysis to the optical characterisation of fibrous bulk material

Dynamic image analysis provides an automated evaluation method to determine the size and shape of multiple particles. This method represents a common application for ordinary bulk material. The latest draft of ISO 13322–2:2021 describes the state of the art, but lacks instructions for handling fibrous bulk material. Interlocking fibres complicate the measurement conditions and require a disentanglement of fibrous samples during a pre-dispersion step. A further error source includes the fibre orientation inside the measurement zone of the device. If the thresholding algorithm fails to differentiate between the fibre projection area and the background, a subsequent image optimisation solves the problem. This article addresses the mentioned problems by analysing cotton cellulose and polyacrylonitrile fibres. Besides the execution of a pre-dispersion step, the experiments compare the discrepancies between dry and wet dispersion. Here, the software packages PAQXOS and ImageJ perform the image evaluation. In this case, the wet dispersion setup with a subsequent image evaluation by ImageJ provides comprehensible results.

Gray bootstrap method for estimating frequency-varying random vibration signals with small samples

During environment testing, the estimation of random vibration signals （RVS） is an important technique for the airborne platform safety and reliability. However, the available meth- ods including extreme value envelope method （EVEM）, statistical tolerances method （STM） and improved statistical tolerance method （ISTM） require large samples and typical probability distri- bution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method （GBM） is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated inter- val, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method （BM） and gray method （GM） in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.

Estimation Methods for the Generalized Inverted Exponential Distribution Under Type II Progressively Hybrid Censoring with Application to Spreading of Micro-Drops Data

In this article,we consider the statistical inferences of the unknown parameters of a generalized inverted exponential distribution based on the Type II progressively hybrid censored sample.By applying the expectation–maximization(EM)algorithm,the maximum likelihood estimators are developed for estimating the unknown parameters.The observed Fisher information matrix is obtained using the missing information principle,and it can be used for constructing asymptotic con-fidence intervals.By applying the bootstrapping technique,the confidence intervals for the parameters are also derived.Bayesian estimates of the unknown parameters are obtained using the Lindley’s approximation.Monte Carlo simulations are imple-mented and observations are given.Finally,a real data set representing the spread factor of micro-drops is analyzed to illustrative purposes.

Bootstrap Estimation from Simulation Outputs

This paper discusses a new nonparametric statistical method and applies it to simulation output analysis. This can be used to overcome the limitations of the traditional methods. The steps of making bootstrap interval estimation are given. The simulation results for the examples show that the bootstrap method can produce the valid confidence intervals and improve the simulation precision.

Exact Inference for Joint Type-I Hybrid Censoring Model with Exponential Competing Risks Data

Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates （MLEs） of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function （MGF）. Confidence intervals （CIs） of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.

Estimate of the rate of unreported COVID-19 cases during the first outbreak in Rio de Janeiro

In this work we fit an epidemiological model SEIAQR(Susceptible-Exposed-Infectious-Asymptomatic-Quarantined-Removed)to the data of the first COVID-19 outbreak in Rio de Janeiro,Brazil.Particular emphasis is given to the unreported rate,that is,the proportion of infected individuals that is not detected by the health system.The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines.The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters’estimation.We use the Bootstrap method to quantify the uncertainty of the estimates.For the outbreak of MarcheJuly 2020 in Rio de Janeiro,we estimate about 90%of unreported cases,with a 95%confidence interval(85%,93%).

A New Method of Portfolio Optimization Under Cumulative Prospect Theory

In this paper, the portfolio selection problem under Cumulative Prospect Theory （CPT） is investigated and a model of portfolio optimization is presented. This model is solved by coupling scenario generation techniques with a genetic algorithm. Moreover, an Adaptive Real-Coded Genetic Algorithm （ARCGA） is developed to find the optimal solution for the proposed model. Computational results show that the proposed method solves the portfolio selection model and that ARCGA is an effective and stable algorithm. We compare the portfolio choices of CPT investors based on various bootstrap techniques for scenario generation and empirically examine the effect of reference points on investment behavior.

Statistical analysis of dependent competing risks model in constant stress accelerated life testing with progressive censoring based on copula function

In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.