General laws of large numbers under sublinear expectations

ABSTRACT

In this paper, under some weaker conditions, we give three laws of large numbers (LLNs) under sublinear expectations (capacities), which extend the LLN under sublinear expectations in Peng (2008b Peng, S. (2008b). A new central limit theorem under sublinear expectations. arXiv:0803.2656v1 [math.PR], 18 Mar 2008. [Google Scholar]) and the strong LLN for capacities in Chen (2010 Chen, Z. (2010). Strong laws of large numbers for capacities. arXiv:1006.0749v1 [math.PR], 3 Jun 2010. [Google Scholar]). It turns out that these theorems are natural extensions of the classical strong (weak) LLNs to the case where probability measures are no longer additive.     

A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains

ABSTRACT

In this article, we study a class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains. First, the definition of mth-order asymptotic circular Markov chain is introduced, then by applying the known results of the limit theorem for mth-order non homogeneous Markov chain, the small deviation theorem on the frequencies of occurrence of states for mth-order asymptotic circular Markov chains is established. Next, the strong law of large numbers and asymptotic equipartition property for this Markov chains are obtained. Finally, some results of mth-order nonhomogeneous Markov chains are given.     

水书、周易、九星的数据对比研究

中国数文化,以河图洛书为典型代表。中国易数,有中合双奇、中合双偶、中合奇偶。河图洛书之数,中合奇偶。中合双偶、中合双奇已经失传,目前发现水书有中宫双偶合数图记。易经之数,五十有五,二元十运。九星之数,四十有五,三元九运。水书之数,七十有八,四元十二运。水书数图西北戌位起步,四入中宫,巧妙将盈满的"十"数也隐藏于中宫。水书数图中轴线三宫总数二十八,中宫为双偶的十、四之数合成内静。上九下五,合成外动,两侧对角及平角线对应的合数均为九。实现内外纯阴纯阳理想和谐格局。为此,始信"神秘水书"之说。     

Inferences from logistic regression models in the presence of small samples,rare events,nonlinearity, and multicollinearity with observational data

The logistic regression model has been widely used in the social and natural sciences and results from studies using this model can have significant policy impacts. Thus, confidence in the reliability of inferences drawn from these models is essential. The robustness of such inferences is dependent on sample size. The purpose of this article is to examine the impact of alternative data sets on the mean estimated bias and efficiency of parameter estimation and inference for the logistic regression model with observational data. A number of simulations are conducted examining the impact of sample size, nonlinear predictors, and multicollinearity on substantive inferences (e.g. odds ratios, marginal effects) when using logistic regression models. Findings suggest that small sample size can negatively affect the quality of parameter estimates and inferences in the presence of rare events, multicollinearity, and nonlinear predictor functions, but marginal effects estimates are relatively more robust to sample size.     

基于“奖优罚劣”线性变换算子的区间数多目标灰色局势决策方法

针对多目标决策值为区间数的规范化问题,提出一种具有奖优罚劣特性的[-1,1]线性变换算子,规范化处理原始决策信息,将其运用到目标权重确定,且属性值为区间数的多目标灰色局势决策中,给出了基于"奖优罚劣"算子的区间数多目标灰色局势决策方法,并以空舰导弹设计方案的选择作为应用案例,结果表明该方法操作方便、计算简单、易于实现,可以为一些具有区间值的不确定决策问题提供一种有效、科学、实用的方法。     

论厉鹗的诗

厉鹗是雍乾间以诗而名的学人。他的诗歌喜用典故,尤喜用宋人笔记中之偏事僻典,遣词造句也刻意生涩炫博。厉鹗资书以为诗,其诗显得生、僻、怪、碎,与清代学人诗本经史,引学术入诗的诗学风范有点不同。他后面的诗人惩于厉鹗的堆砌琐碎,于是偏向于以专门之学入诗,特别是以乾嘉学人擅长的金石考据入诗,翁方纲等人的诗歌代表着厉鹗以后乾嘉诗坛学问化的主要衍变方向。     

The q-Bernstein basis as a q-binomial distribution

The q-Bernstein basis, used in the definition of the q-Bernstein polynomials, is shown to be the probability mass function of a q-binomial distribution. This distribution is defined on a sequence of zero–one Bernoulli trials with probability of failure at any trial increasing geometrically with the number of previous failures. A modification of this model, with the probability of failure at any trial decreasing geometrically with the number of previous failures, leads to a second q-binomial distribution that is also connected to the q-Bernstein polynomials. The q-factorial moments as well as the usual factorial moments of these distributions are derived. Further, the q-Bernstein polynomial B_n(f(t),q;x) is expressed as the expected value of the function f([X_n]_q/[n]_q) of the random variable X_n obeying the q-binomial distribution. Also, using the expression of the q-moments of X_n, an explicit expression of the q-Bernstein polynomial B_n(f_r(t),q;x), for f_r(t) a polynomial, is obtained.     

Weak and strong laws of large numbers for sub-linear expectation

Abstract

In this paper, we derive a new form of weak laws of large numbers for sub-linear expectation and establish the equivalence relation among this new form and the other two forms of weak laws of large numbers for sub-linear expectation. Moreover, we obtain the strong laws of large numbers for sub-linear expectation under a general moment condition by applying our new weak laws of large numbers.     

航空制造企业知识管理能力评价案例研究

针对航空制造企业的知识管理能力评价案例,分析了航空制造企业中的知识资源构成,以企业对其内部主要知识资源的管理情况为评价指标,建立了对航空制造企业知识管理能力进行评价的多层次综合评价指标体系。将三角模糊数理论和模糊层次分析法结合起来,提出了一种基于三角模糊数的模糊层次分析方法,并将其应用到航空制造企业知识管理能力评价问题中。这种评价方法适用于被评价对象的性能无法具体量化、指标权重不易判断的多层次指标综合评价问题。最后以某航空制造企业知识管理能力评价结果给出了该方法的应用。