The two-sample -test with a known ratio of variances

We consider the two-sample t-test where error variances are unknown but with known relationships between them. This situation arises, for example, when two measuring instruments average different number of replicates to report the response. In particular we compare our procedure with the usual Satterthwaite approximation in the two sample t-test with variances unequal. Our procedure uses the knowledge of a known ratio of variances while the Satterthwaite approximation assumes only that the two variances are unequal. Simulations show that our procedure has both better size and better power than the Satterthwaite approximation. Finally, we consider an extension of our results to the General Linear Model.     

Estimating the Lyapunov exponent from chaotic time series with dynamic noise

In this paper, we propose an estimator of the Lyapunov exponent of the skeleton for chaotic time series with dynamic noise and prove the consistency of the estimator under some assumptions.     

梅曾亮与晚清岭西文坛

通过献疑,证明朱琦、龙启瑞、王拯、彭昱尧等人并非通过吕璜得以结识梅曾亮,梅曾亮不曾到过岭西。梅曾亮通过与朱琦等人的宴饮、通信等社交活动对岭西文人进行文学熏陶,他与朱琦等人的文学切劘,提高了朱琦等人的桐城文法水平,使岭西文坛之名在晚清渐起。梅曾亮对岭西文坛的主要影响包括:培养了一批尊崇桐城文法的岭西才士,促进桐城义法在岭西的开衍;促成了《涵通楼师友文钞》的编撰;奠定"岭西五大家"称号形成的基础。     

马克思主义生产力价值论和当代西方经济学

马克思恩格斯的价值论,并非"劳动价值论一元论",而是"效用/劳动价值论",或曰"生产力(率)价值论",它体现并贯彻了生产力决定性;被长期误认为马克思主义价值理论"正宗"的"劳动价值论一元论",源于考茨基在"批修"时对马克思的错解,应予否定;西方经济学的宏观要素价值论及微观效用价值论与马恩有相通之处,我们应批判借鉴。     

Lower bounds of the wrap-around -discrepancy and relationships between MLHD and uniform design with a large size

The wrap-around (WD) L₂-discrepancy has been commonly used in experimental designs. In this paper, some lower bounds of the WD L₂-discrepancy for asymmetrical U-type designs are given and the expectation and variance of midpoint Latin hypercube designs (LHD) are also obtained. Relationships between midpoint LHD and uniform designs for symmetrical and asymmetrical cases are discussed in the sense of comparing the lower bound and the expectation of squared wrap-around L₂-discrepancy of U-type designs. Some comparisons between simple random sampling and the lower bounds of U-type designs are given.     

债法外观法理研究——以债务人对债权准占有人清偿为中心

债务人对债权准占有人清偿,即债务人对债权文书持有人清偿,其清偿若符合善意且无过失的要求,该清偿行为发生债消灭的效力,效力依据对债务人来说在于对债权准占有人受领权外观的合理信赖,对债权人来说是其引致该受领权外观所应承担的权利表见责任,二者构成债法外观法理的核心。债法外观法理同样是债务人对于除债权准占有人以外的其他表见债权人清偿有效的法理基础。     

期权定价方法综述

介绍了期权定价理论的产生和发展; 然后对期权定价方法及其实证研究进行了较详细的 分类综述, 突出综述了既适用于完全金融市场, 又适用于非完全的金融市场的确定性套利定价 方法、区间定价方法和E2套利定价方法; 最后, 对各种方法的条件和特点进行了讨论和评价.     

我国风险资本市场发展制约因素分析

风险资本市场是资本市场中一种创新的市场形态,它的运作有其内在的特殊规律性,其产生和发展需要与之相适应的环境。本文从八个方面详细分析了制约我国风险资本市场的制约因素。     

Reliabilities for (n,f, k (i,j)) and ⟨n,f, k (i,j)⟩ Systems

The (n,f,k(i,j)):F(? n,f,k(i,j)?:F) system consists of n components ordered in a line or circle, while the system fails if, and only if, there exist at least f failed components OR (AND) at least k consecutive failed components among components i,i + 1,…,j ? 1,j. In this article, we present the system reliability formulae for these systems with product of matrices by means of a two-stage finite Markov chain imbedding approach, a technique first used by Cui et al. (2002 Cui , L. R. , Kuo , W. , Xie , M. ( 2002 ). On (f,g)-out-of-((i,j),n) systems and its reliability . In: Third International Conference on Mathematical Methods in Reliability Methodology and Practice , June 17–20 , Norway , Trondheim , pp. 173 – 176 . [Google Scholar]). In addition, their dual systems, denoted by (n,f,k(i,j)):G and ? n,f,k(i,j)?:G, are also introduced. Two numerical examples are given to illustrate the results.     

Some Utilizations of Lambert W Function in Distribution Theory

We introduce a new class of positive infinitely divisible probability laws calling them 𝔏_γ distributions. Their cumulant-generating functions (cgf) are expressed in terms of the principal branch of the Lambert W function. The probability density functions (pdfs) of 𝔏_γ laws are bounded resembling pdf of a Lévy stable distribution. The exponential dispersion model constructed starting from an 𝔏_γ distribution admits the inverse Gaussian approximation. The natural exponential family constructed starting from an 𝔏_γ distribution constitutes the reciprocal of the natural exponential family generated by a spectrally negative stable law with α = 1. We derive new results on 𝔏_γ laws and the related exponential dispersion models, including their convolution and scaling closure properties. We generate another exponential dispersion model starting from an exponentially compounded 𝔏_γ law. This distribution emerges in the Poisson mixture representation of a generalized Poisson law. We extend the Poisson approximation for the scaled Neyman type A exponential dispersion model. We derive saddlepoint-type approximations for some of these exponential dispersion models. The role of the Lambert W function is emphasized.