THE LIMITING DISTRIBUTIONS OF SOME SUBCLASSES OF THE GENERALIZED NON-CENTRAL t-DISTRIBUTION

A general theorem on the limiting distribution of the generalized t-distribution is obtained,many applications of this theorem to some subclasses of elliptically contoured distributions in cluding multivariate normal and multivariate t distributions are discussed.Further,their limiting distributions by density function are derived.

The Series of Reciprocals of Non-central Binomial Coefficients

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.

An Extended Bivariate T-Distribution Type Symmetry Model for Square Contingency Tables

The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.

Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method

So far, Schrodinger equation with central potential has been solved in different methods but solving this equation with non-central potentials is less dealt with. Solving such equations are way more difficult and complicated and a certain and limited number of non-central potentials can be solved. In this paper, we introduce one of the solvable kinds of such potentials and we will use NU method for solving Schrodinger equation and then by using this method we have calculated particular figures of its energy and function.

Zero-inflated non-central negative binomial distribution

In this article, the zero-inflated non-central negative binomial(ZINNB) distribution is introduced. Some of its basic properties are obtained. In addition, we use the maximum likelihood estimation method to estimate the parameters of the ZINNB distribution, and illustrate its application by fitting the actual data sets.

Pricing European Options Based on a Logarithmic Truncated t-Distribution

The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.

An Extension of the Non-central Wishart Distribution with Integer Shape Vector

This research paper deals with an extension of the non-central Wishart introduced in 1944 by Anderson and Girshick,that is the non-central Riesz distribution when the scale parameter is derived from a discrete vector.It is related to the matrix of normal samples with monotonous missing data.We characterize this distribution by means of its Laplace transform and we give an algorithm for generating it.Then we investigate,based on the method of the moment,the estimation of the parameters of the proposed model.The performance of the proposed estimators is evaluated by a numerical study.

A Multi-Strategy-Improved Northern Goshawk Optimization Algorithm for Global Optimization and Engineering Design

Optimization algorithms play a pivotal role in enhancing the performance and efficiency of systems across various scientific and engineering disciplines.To enhance the performance and alleviate the limitations of the Northern Goshawk Optimization(NGO)algorithm,particularly its tendency towards premature convergence and entrapment in local optima during function optimization processes,this study introduces an advanced Improved Northern Goshawk Optimization(INGO)algorithm.This algorithm incorporates a multifaceted enhancement strategy to boost operational efficiency.Initially,a tent chaotic map is employed in the initialization phase to generate a diverse initial population,providing high-quality feasible solutions.Subsequently,after the first phase of the NGO’s iterative process,a whale fall strategy is introduced to prevent premature convergence into local optima.This is followed by the integration of T-distributionmutation strategies and the State Transition Algorithm(STA)after the second phase of the NGO,achieving a balanced synergy between the algorithm’s exploitation and exploration.This research evaluates the performance of INGO using 23 benchmark functions alongside the IEEE CEC 2017 benchmark functions,accompanied by a statistical analysis of the results.The experimental outcomes demonstrate INGO’s superior achievements in function optimization tasks.Furthermore,its applicability in solving engineering design problems was verified through simulations on Unmanned Aerial Vehicle(UAV)trajectory planning issues,establishing INGO’s capability in addressing complex optimization challenges.

应用t-SNE算法探讨实验室检查在自身免疫性疾病诊断上临床意义

应用机器学习算法t-SNE(t-Distributed Stochastic Neighbor Embedding)对自身免疫性疾病患者实验室检查数据进行数据分析,探索其中数据结构、数据之间的关系以及在自身免疫性疾病诊断方面的意义。方法 构建以t-SNE为基础的数据分析模型,以原始实验室检查数据生成的大量高维数据集反复训练模型,确定各种重要参数和实验流程,最终对生成的一系列可视化散点图进行分析,揭示其中包含的信息和知识。结果 本研究建立了可靠性与实用性较强的数据分析模型以及具有临床实践意义的数据分析流程。通过对880例常见自身免疫性疾病病种的数据分析,发现超敏C反应蛋白将所有病例显著地分为两大类;同病种的病例具有明显聚集的数据簇结构,不同病例的数据点有重叠现象;通过比较不同的数据集分析结果,进一步简化了检查项目组合。结论 采用本研究建立的数据分析模型,能够将复杂的临床高维数据集通过计算简化为二维的可视化散点图。通过对散点图上重叠数据点的解析,快速地将疑难病例甄别出来,表明了数据分析模型的可靠性;研究结果表明超敏c反应蛋白可能在自身免疫性疾病的发生发展中具有启动者的作用;简化的检查项目组合也可以取得具有临床诊断价值的结果,在一定程度上节约了医疗资源。

Non-Central Zone 3D Sound Field Reproduction for Multichannel System

The 22.2 multichannel system and its simplified system with 10-channel and 8-channel have been proposed, which brings people 3 D listening experience. But these systems could only accurately reproduce sound field at a central listening point which is called sweetspot. In order to solve this problem, this paper proposes a non-central zone sound field reproduction method PVMDZ（particle velocity matching between different zones） based on the physical property of sound. The proposed method matches the physical property of sound of non-central zone in reconstructed sound field with that of central zone in original sound field, so the reproduced non-central zone would produce the same listening experience as the central zone of the original system does. By experiments, we compare the performances of the proposed method with the traditional one, and the result proves that the sound field error of proposed method is reduced.

Reliability analysis method for slope stability based on sample weight

The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.

ESTIMATING THE NONCENTRALITY PARAMETER OF A t-DISTRIBUTION

Inadmissibility of a traditional class of noncentrality parameter esti-mators under quadratic loss is established.The result is heuristically motivatedby the form of generalized Bayes estimators and is proved via unbiased estimatorsof the risk function and a solution to an integro-differential inequality.

DSP-TMM:A Robust Cluster Analysis Method Based on Diversity Self-Paced T-Mixture Model

In order to implement the robust cluster analysis,solve the problem that the outliers in the data will have a serious disturbance to the probability density parameter estimation,and therefore affect the accuracy of clustering,a robust cluster analysis method is proposed which is based on the diversity self-paced t-mixture model.This model firstly adopts the t-distribution as the submodel which tail is easily controllable.On this basis,it utilizes the entropy penalty expectation conditional maximal algorithm as a pre-clustering step to estimate the initial parameters.After that,this model introduces l2,1-norm as a self-paced regularization term and developes a new ECM optimization algorithm,in order to select high confidence samples from each component in training.Finally,experimental results on several real-world datasets in different noise environments show that the diversity self-paced t-mixture model outperforms the state-of-the-art clustering methods.It provides significant guidance for the construction of the robust mixture distribution model.

Using Excel to Explore the Effects of Assumption Violations on One-Way Analysis of Variance (ANOVA) Statistical Procedures

To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violations of these assumptions. In our earlier articles (Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and heteroskedastic models showing different realizations of these models and the performance of the techniques for identifying the underlying hidden states using simulated data. The advantage of using Excel is that the simulations are regenerated when the spreadsheet is recalculated allowing the user to observe the performance of the statistical technique under different realizations of the data. In this article we will show how to use Excel to generate data from a one-way ANOVA (Analysis of Variance) model and how the statistical methods behave both when the fundamental assumptions of the model hold and when these assumptions are violated. The purpose of this article is to provide tools for individuals to gain an intuitive understanding of these violations using this readily available program.

Ranking Independent Variables in Linear Models

In this article, the true model of sizep is considered. The importance of the independent variables will be studied. The model by dropping independent variable one at a time is called a reduced model, and the size of the model is p-1. The non-centrality quantity is employed to measure the strength of influence on the true model for the independent variable dropped. The larger influence is defined to be more important in the true model. In this article, the goal is ranking the importance of the independent variables to study the structure of the models. It is important in the practical application. The confidence interval approach is used to rank the degrees of the influence of the independent variables in linear models and achieve the goal. An illustrative example is given, and the modeling procedure is studied to check the assumptions step by step in this example to make sure the assumptions satisfied in the true model. As a result, the proposed method can be used efficiently.

Effective Truncation of a Student’s <i>t</i>-Distribution by Truncation of the Chi Distribution in a Chi-Normal Mixture

A Student’s t-distribution is obtained from a weighted average over the standard deviation of a normal distribution, σ, when 1/σ is distributed as chi. Left truncation at q of the chi distribution in the mixing integral leads to an effectively truncated Student’s t-distribution with tails that decay as exp (-q2t2). The effect of truncation of the chi distribution in a chi-normal mixture is investigated and expressions for the pdf, the variance, and the kurtosis of the t-like distribution that arises from the mixture of a left-truncated chi and a normal distribution are given for selected degrees of freedom 5. This work has value in pricing financial assets, in understanding the Student’s t--distribution, in statistical inference, and in analysis of data.

Implementing an Optimal Energy Management System for a Set of Microgrids Using the Harmony Search Algorithm

A microgrid(MG)refers to a set of loads,generation resources and energy storage systems acting as a controllable load or a generator to supply power and heating to a local area.The MG-generated power management is a central topic for MG design and operation.The existence of dispersed generation(DG)resources has faced MG management with new issues.Depending on the level of exchanges between an MG and the main grid,the MG operation states can be divided into independent or grid-connected ones.Energy management in MGs aims to supply power at the lowest cost for optimal load response.This study examines MG energy management in two operational modes of islanded and grid-connected,and proposes a structure with two control layers(primary and secondary)for energy management.At the principal level of control,the energy management system is determined individually for all MG by taking into consideration the probability constraints and RES uncertainty by the Weibull the probability density function(PDF),generation resources’power as well as the generation surplus and deficit of each MG.Then,the information of the power surplus and deficit of each MG must be sent to the central energy management system.To confirm the proposed structure,a case system with two MGs and a condensive load is simulated by using a multi-time harmony search algorithm.Several scenarios are applied to evaluate the performance of this algorithm.The findings clearly show the effectiveness of the proposed system in the energy management of several MGs,leading to the optimal performance of the resources per MG.Moreover,the proposed control scheme properly controls the MG and grid’s performance in their interactions and offers a high level of robustness,stable behavior under different conditions and high quality of power supply.

Asymptotic distributions of non-central studentized statistics

Let X 1, ..., X n be independent and identically distributed random variables and W n = W n (X 1, ..., X n ) be an estimator of parameter ?. Denote T n = (W n ? ? 0)/s n , where s n 2 is a variance estimator of W n . In this paper a general result on the limiting distributions of the non-central studentized statistic T n is given. Especially, when s n 2 is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted χ 2 distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.

Analysis of the Probability Model of Wind Load on the Offshore Wind Turbine

According to the actual measurement data, probability models of horizontal wind load were obtained based on wind velocity statistic and power spectral density function of fluctuating wind velocity through stochastic sampling and using spectrum analysis method. Through the comparison of two models, probability models of horizontal wind load based on probability models of fluctuating wind velocity were obtained by revising the mean and variance of fluctuating wind velocity. Results show that the variance takes lower value when the power spectral density function of fluctuating wind velocity is used to obtain the probability model of horizontal wind load. The quadratic term of fluctuating wind velocity takes a small contribution value in total wind load with almost no contribution to the model of horizontal wind load. It is convenient for practical engineering to obtain the models of horizontal wind load by using probability models of fluctuating wind velocity.