Accelerated test system strength models based on Birnbaum–Saunders distribution: a complete Bayesian analysis and comparison

Several models for studies related to tensile strength of materials are proposed in the literature where the size or length component has been taken to be an important factor for studying the specimens’ failure behaviour. An important model, developed on the basis of cumulative damage approach, is the three-parameter extension of the Birnbaum–Saunders fatigue model that incorporates size of the specimen as an additional variable. This model is a strong competitor of the commonly used Weibull model and stands better than the traditional models, which do not incorporate the size effect. The paper considers two such cumulative damage models, checks their compatibility with a real dataset, compares them with some of the recent toolkits, and finally recommends a model, which appears an appropriate one. Throughout the study is Bayesian based on Markov chain Monte Carlo simulation.     

Modified genetic algorithm-based clustering for probability density functions

This article modifies two internal validity measures and applies them to evaluate the quality of clustering for probability density functions (pdfs). Based on these measures, we propose a new modified genetic algorithm called GA-CDF to establish the suitable clusters for pdfs. The proposed algorithm is tested by four numerical examples including two synthetic data sets and two real data sets. These examples illustrate the superiority of proposed algorithm over some existing algorithms in evaluating the internal or external validity measures. It demonstrates the feasibility and applicability of the GA-CDF for practical problems in data mining.     

A new Bayesian wavelet thresholding estimator of nonparametric regression

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.     

A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.     

Parameter estimation of a composite production function model based on improved artificial fish swarm algorithm and model application

The traditional Cobb–Douglas production function uses the compact mathematical form to describe the relationship between the production results and production factors in the production technology process. However, in macro-economic production, multi-structured production exists universally. In order to better demonstrate such input–output relation, a composite production function model is proposed in this article. In aspect of model parameter estimation, artificial fish swarm algorithm is applied. The algorithm has satisfactory performance in overcoming local extreme value and acquiring global extreme value. Moreover, realization of the algorithm does not need the gradient value of the objective function. For this reason, it is adaptive to searching space. Through the improved artificial fish swarm algorithm, convergence rate and precision are both considerably improved. In aspect of model application, the composite production function model is mainly used to calculate economic growth factor contribution rate. In this article, a relatively more accurate calculating method is proposed. In the end, empirical analysis on economic growth contribution rate of China is implemented.     

A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

均值绝对偏差资产组合选择模型的算法

对均值绝对偏差模型进行了简化,并利用一种旋转算法求解。这种算法比单纯形算法的计算简便,且计算量更小。利用上海和深圳股市1 072支股票70期周末收盘价所作的实验结果表明,对于资产无上界限制的模型,计算20个不同最优投资组合需要1 274次旋转运算,上界为10%时需要1 570次旋转运算,每 次旋转运算约需1 14171次加法和乘法运算。     

快速遗传算法研究

提出了一种称为广义自适应遗传算法的快速遗传算法,它首先产生均匀分布的初始种群,其次根据种群模式的状况决定是否引入“高品质”移民,最后自适应地进行交换和变异运算。其搜索性和全局收敛性比现有的许多遣传算法都有明显的改善,并通过仿真说明了该改进遣传算法的有效性。     

基于遗传算法的进化支持向量机研究

支持向量机是最近发展起来的一种新的通用的机器学习方法 ,其理论基础是统计学习理论 ,支持向量机无论在模式识别还是在函数拟合方面均显示了其优越性 ,并越来越受到国内外研究者的广泛关注 .但是 ,对支持向量机的推广预测能力具有很大影响的核函数和参数C一直没有一个很好的确定方法 ,针对这一问题 ,将遗传算法和支持向量机结合 ,提出了一种自动选择支持向量机参数的方法 ,结果表明 ,这种方法是科学有效的 .