Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.     

Estimation of generalized linear latent variable models

Summary.  Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must be used for inference. This can limit drastically the number of variables in the model and can lead to biased estimators. We propose a new estimator for the parameters of a GLLVM, based on a Laplace approximation to the likelihood function and which can be computed even for models with a large number of variables. The new estimator can be viewed as an M -estimator, leading to readily available asymptotic properties and correct inference. A simulation study shows its excellent finite sample properties, in particular when compared with a well-established approach such as LISREL. A real data example on the measurement of wealth for the computation of multidimensional inequality is analysed to highlight the importance of the methodology.     

TESTING SPHERICITY UNDER A MIXTURE MODEL

The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non-central Wishart density of rank one is derived in terms of Meijer's G-functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model.     

论社会进步及其评价尺度

马克思的唯物史观告诉我们,社会进步是人类社会发展的必然趋势,但是,由于社会发展过程的复杂性,对于具体的历史事件作用,就存在着评价问题。社会进步的评价尺度其实就蕴含在社会进步的内涵当中。由于社会进步可以归结为生产力水平的提高与人的自由与解放,这两项内容就应当成为社会进步的衡量标准。生产力水平的提高与人的自由与解放的统一也就是马克思主义的历史尺度与价值尺度的统一,这是马克思主义在社会进步评价问题上的重要原则。     

A Bayesian Analysis for Accelerated Lifetime Tests Under an Exponential Power Law Model with Threshold Stress

In this paper, we present a Bayesian methodology for modelling accelerated lifetime tests under a stress response relationship with a threshold stress. Both Laplace and MCMC methods are considered. The methodology is described in detail for the case when an exponential distribution is assumed to express the behaviour of lifetimes, and a power law model with a threshold stress is assumed as the stress response relationship. We assume vague but proper priors for the parameters of interest. The methodology is illustrated by a accelerated failure test on an electrical insulation film.     

Testing symmetry under a skew Laplace model

We develop tests of hypothesis about symmetry based on samples from possibly asymmetric Laplace distributions and present exact and limiting distribution of the test statistics. We postulate that the test statistic derived under the Laplace model is a rational choice as a measure of skewness and can be used in testing symmetry for other, quite general classes of skew distributions. Our results are applied to foreign exchange rates for 15 currencies.     

论非实践性真理标准说的历史形态

非实践性真理标准是前马克思真理标准说的共性。它有理性、感觉、经验和实验等四种历史形态 :理性标准表面上肯定真理的客观性 ,实际上否认真理的客观性 ;感觉标准具有主观唯心主义的特点 ;经验标准承认真理的客观性但还停留在认识的领域 ;实验标准预告着科学真理标准即将诞生。实践标准的确立来之不易 ,是一场认识论上的革命     

持有型犯罪立法理念偏差及价值冲突检讨

对于持有型犯罪的基本理论问题的争议一直存在,但是,目前刑法学界局限于研究如何界定“持有”的行为属性,以及持有型犯罪的定义、范围等形式层面,而不重视从立法意图、规范角度等实质层面评价持有型犯罪。为了弥补这一缺陷,检讨了持有型犯罪的立法基准是否妥当、罪刑配置是否均衡、规范设计是否存在缺陷、立法价值取向等问题,指出持有型犯罪目前存在的理念偏差及价值冲突问题,并认为持有型犯罪立法不应扩张。     

谁开创了贝叶斯学派？——对拉普拉斯1774年一篇文章的回顾

1764年,贝叶斯的遗作《机遇理论中一个问题的解》，是当今统计学界贝叶斯学派的开山之作，然而直到20世纪，贝叶斯的文章却并未对后世贝叶斯学派的发展产生重大影响。事实上，真正促使贝叶斯的思想在科学界得到广泛传播的关键人物是大科学家拉普拉斯。1774年，拉普拉斯发表的关于贝叶斯理论的里程碑式的文章，使现代读者充分认识到拉普拉斯对贝叶斯学派发展所起的巨大作用，并从拉普拉斯的思想中获得了有益的新知。