Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test

In this article, we propose a novel approach for testing the equality of two log-normal populations using a computational approach test (CAT) that does not require explicit knowledge of the sampling distribution of the test statistic. Simulation studies demonstrate that the proposed approach can perform hypothesis testing with satisfying actual size even at small sample sizes. Overall, it is superior to other existing methods. Also, a CAT is proposed for testing about reliability of two log-normal populations when the means are the same. Simulations show that the actual size of this new approach is close to nominal level and better than the score test. At the end, the proposed methods are illustrated using two examples.     

历史变局、国家兴衰与发展之路——三次千年变局叠加下的中国特色社会主义发展道路

每当先进的发展制度开始取代落后的发展制度时，整个世界格局就会进入重大的转换阶段。在中国五千年的发展历史中，有两次重大的历史变局完全改变了中国历史发展轨迹并深远地影响了当前中国的发展模式。新时代下的中国作为前两次历史变局影响的客体，曾经既是先进发展制度取代落后发展制度的受益者，也经历过作为落后发展制度主体而被先进发展制度冲击的过程。目前世界正处于第三次先进发展制度与落后发展制度交替的历史变局阶段，作为第三次重大历史变局的主体，在三次千年历史变局叠加的背景下，能否有效地认识、适应并改造利用前两次历史变局的经验与教训，构建系统性、科学性、可行性、领先性的中国特色社会主义制度，将决定中国在本次历史变局中能否顺利成为先进发展制度的主体从而实现民族复兴。     

巴渝古崖居的空间分布与景观特征

巴渝古崖居的分布与地理、地质、交通等诸多因素有关，以成渝交通要道、长江干流和支流为线，串起沿途各个点，由线成面，呈现出渝西、渝东北两头集中、整体北多南少的分布特征。巴渝古崖居大多开凿于明清晚期，这一时期巴渝许多地区战乱频繁、匪患猖獗。古崖居的集中分布与这些地区相吻合，从侧面印证了巴渝古崖居的空间分布特征。巴渝古崖居的广泛开凿体现了古人高超的建筑艺术以及社会历史文化的变迁。     

A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

20世纪初中国人对马克思思想解读的再评价

19世纪末20世纪初,马克思的思想就传入了中国,梁启超在传统大同思想与社会主义贯通中对它进行解读;早期国民党人在批判资本主义,建构民生主义中对它进行评价;无政府主义在反传统中认同马克思的共产主义。虽然各有局限性,但又各有自身的意义。以十月革命的经验解读马克思主义,遮蔽了对马克思思想早期传播的研究,研究马克思主义在中国的早期传播,对认识马克思主义中国化有重要意义。     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.     

On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

Analyzing multiple vector autoregressions through matrix-variate normal distribution with two covariance matrices

Abstract

This article proposes a new approach to analyze multiple vector autoregressive (VAR) models that render us a newly constructed matrix autoregressive (MtAR) model based on a matrix-variate normal distribution with two covariance matrices. The MtAR is a generalization of VAR models where the two covariance matrices allow the extension of MtAR to a structural MtAR analysis. The proposed MtAR can also incorporate different lag orders across VAR systems that provide more flexibility to the model. The estimation results from a simulation study and an empirical study on macroeconomic application show favorable performance of our proposed models and method.