Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.

Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.

Probability estimation based on grey system theory for simulation evaluation

In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.

Robust Interval State Estimation for Distribution Systems Considering Pseudo-measurement Interval Prediction

Interval state estimation(ISE)can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements,thereby analyzing the impact of uncertain pseudo-measurements on states.However,predicted pseudo-measurements have prediction errors,and their confidence intervals do not necessarily contain the truth values,leading to estimation biases of the ISE.To solve this problem,this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression(GPR)model,thereby improving the prediction accuracy of pseudo-measurement confidence intervals.Besides,a weight assignment strategy for improving the robustness of weighted least squares(WLS)ISE is proposed.This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudo-measurement intervals with larger deviations,thereby improving the estimation accuracy and robustness of the ISE.This paper adopts the data from the supervisory control and data acquisition(SCADA)system of the New York Independent System Operator(NYISO).It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods.In addition,this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case.Finally,the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.

Immune Clone Maximum Likelihood Estimation of Improved Non-homogeneous Poisson Process Model Parameters

Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.

Combination of structural reliability and interval analysis

In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

杀虫剂毒力测定中试验数据生成模型和毒力指标估计(英文)

This paper gives the mathematical reason that the probit analysis method of toxicity measurement is reasonable, and proposes a new approach to compute the interval estimation of median lethal dose and 95% lethal dose. Based on the dose-response function of pesticides, this study firstly establishes a model of the data generating progress in toxicity test and proves that when the linear models of the logarithm of probability value and dose have been estimated, the weighted linear regression should be used, it is the reason why there is the heteroscedasticity of random disturbance term in the regression model, and the weight is right the reciprocal of the variance for random disturbance term. Secondly, based on the numerical simulation method, this paper gives a new approach for the interval estimation of median lethal dose and 95% lethal dose.

Determination of Electrical Conductivity of Cadaver Skeletal Muscle: A Promising Method for the Estimation of Late Postmortem Interval

The electrical conductivity(EC)of extracted muscle fluid has been extensively used to evaluate meat freshness and shelf life in the field of food sanitation for decades.The opposite of freshness is the corruption that increases with time.Based on the freshness/corruption principle,we investigated the relationship between long postmortem intervals(PMIs)and EC in cadaver skeletal muscle.EC values of extracted fluid from rat muscles were measured at different PMIs for 10 days.The results indicate that there was a significant correlation between PMI and EC,and the data fit well to the cubic polynomial regression equation y=‑0.01x3+0.264x2‑13.657x+1769.148(R2=0.925).In addition,the EC of different dilutions of these muscle extracts showed strict quadratic correlation(R2=1)with the dilution ratios,suggesting that EC can be measured with very small quantities of muscle sample.Our study suggests that determination of the EC of cadaver skeletal muscle extracts may be a useful method for estimating long PMIs.

Statistical Inference of Stress-Strength Model for Exponentiated Pareto Model with Censored Data

The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme.Different interval estimations are proposed.The interval estimations obtained are exact,approximate and bootstrap confidence intervals.Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations.Simulation results show that the confidence intervals(CIs)of exact and approximate methods are really better than those of the bootstrap method.

The Confidence Distribution Method to the Behrens-Fisher Problem

We use the methods of “The Welch-Satterthwaite test”, “The Cochran-Cox test”, “The Generalized p-value test”, “Computational Approach test” to structure different Confidence Distributions, and use the Confidence Distributions to give an new solution the confidence interval of the difference between two population means where the populations are assumed to be normal with unknown and unequal variances. Finally, we find the most effective solution through the numerical simulation.

The Combining Confidence Distribution Method to the Behrens-Fisher Problem

Based on the Confidence Distribution method to the Behrens-Fisher problem, we consider two approaches of combining Confidence Distributions: P Combination and AN Combination to solve the Behrens-Fisher problem. Firstly, we provide some Confidence Distributions to the Behrens-Fisher problem, and then we give the Confidence Distribution method to the Behrens-Fisher problem. Finally, we compare the “combination” and the “single” through the numerical simulation.

Inference for Gompertz distribution under records

The parameter estimation is considered for the Gompertz distribution under frequensitst and Bayes approaches when records are available.Maximum likelihood estimators,exact and approximate confidence intervals are developed for the model parameters,and Bayes estimators of reliability performances are obtained under different losses based on a mixture of continuous and discrete priors.To investigate the performance of the proposed estimators,a record simulation algorithm is provided and a numerical study is presented by using Monte-Carlo simulation.

Modelling of Pre-Sex Selection: An Effective Method for Family Planning and Control of Overpopulation

Every couple would want to have balanced sex of babies and a given number of children. But in reality, most couples do not achieve it. Some end up bearing particular sex of baby, this has caused a lot of pressure and untold hardship for couples. In Nigeria, the preference for a son is so strong that any family that does not have a son does not belong. The reason for the preference is mainly for economic and continuation of family lineage. Inability to bear the desired sex of a baby makes couples bear more children than they could cater for. This has caused poverty, overpopulation and reduces life expectancy for many families in Nigeria. In this paper, we have developed a model that will help couples select the desired sex of their babies and avoid unwanted pregnancies. The method is easy to apply whether educated or not. The application of the method will help to reduce family-based violence due to imbalanced sex of babies.

Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.

Confident Estimation for Density of a Biological Population Based on Line Transect Sampling

Line transect sampling is a very useful method in survey of wildlife population. Confident interval estimation for density D of a biological population is proposed based on a sequential design. The survey area is occupied by the population whose size is unknown. A stopping rule is proposed by a kernel-based estimator of density function of the perpendicular data at a distance. With this stopping rule, we construct several confidence intervals for D by difference procedures. Some bias reduction techniques are used to modify the confidence intervals. These intervals provide the desired coverage probability as the bandwidth in the stopping rule approaches zero. A simulation study is also given to illustrate the performance of this proposed sequential kernel procedure.

Cyber-attack Detection Strategy Based on Distribution System State Estimation

Cyber-attacks that tamper with measurement information threaten the security of state estimation for the current distribution system.This paper proposes a cyber-attack detection strategy based on distribution system state estimation(DSSE).The uncertainty of the distribution network is represented by the interval of each state variable.A three-phase interval DSSE model is proposed to construct the interval of each state variable.An improved iterative algorithm(IIA)is developed to solve the interval DSSE model and to obtain the lower and upper bounds of the interval.A cyber-attack is detected when the value of the state variable estimated by the traditional DSSE is out of the corresponding interval determined by the interval DSSE.To validate the proposed cyber-attack detection strategy,the basic principle of the cyber-attack is studied,and its general model is formulated.The proposed cyber-attack model and detection strategy are conducted on the IEEE 33-bus and 123-bus systems.Comparative experiments of the proposed IIA,Monte Carlo simulation algorithm,and interval Gauss elimination algorithm prove the validation of the proposed method.

Mitochondrial and Nuclear DNA-based Identification of Some Forensically Important Calliphoridae(Diptera)in Luoyang of China

Introduction:Calliphoridae plays a key role in forensic entomology research,which is one of the first insects to decompose animal carcasses.The mitochondrial cytochrome c oxidase subunit I and the ribosomal internal transcribed spacer 2(ITS2)are among the most widely used molecular markers for insect taxonomic characterization.Aim:The aim of the study was to test the suitability of two genetic markers based on conducting the molecular identification of six necrophagous Calliphorid flies.Materials and Methods:Fourteen Calliphoridae flies were collected and classified with traditional morphological characteristics.The DNA of flies was extracted and the fragments of COI and ITS2 were amplified and sequenced.All the sequences were aligned and analyzed by MEGA 7 software for NCBI BLAST,nucleotide composition,intra-and inter-specific divergence calculation,and phylogenetic tree inference successively.Results:The results indicated that COI and ITS2 genes were robust in the identification of Calliphoridae at the species level and ITS2 gene sequence possessed a strong resolution power as it showed higher variation values between Lucilia sericata and Lucilia cuprina,Calliphora vomitoria and Triceratopyga calliphoroides,C.vomitoria andAldrichina grahami,but inferior to COI fbrT.calliphoroides and A.grahami.Conclusions:Our results showed that combination of COI+ITS2 genes yields more accurate identification and diagnoses and better agreement with morphological data than the mitochondrial barcodes alone.As a supplementary method for morphological identification,we advocated for the combination of nuclear and mitochondrial gene approaches to address the taxonomy and phylogeny of forensic relevant flies,especially of closely related species and populations.