古希腊筛法及其推广

由古希腊筛法推广出的XZG筛法引出相关数对,由素殆2相关数对推出完全相关数对.     

Adoptions, 2000–2001

ABSTRACT

The number of domestic adoptions has remained relatively constant over the past 15 years, varying between 121,000 and 127,000, but placements have increasingly been completed by public agencies. Adoption of foreign-born children in the United States has nearly tripled in the past 20 years. Despite the increased national interest in adoption in the past decade and the efforts of many dedicated individuals and agencies, it is still difficult to determine the total number of adoptions in the United States. No one agency is charged with compiling adoption information on all adoptions in the United States, and the agencies that do have access to some types of adoption information have no mandate or incentive to compile that information so that it could be integrated with other sources of adoption information.     

Marcinkiewicz–Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators

Both Marcinkiewicz–Zygmund strong laws of large numbers (MZ-SLLNs) and ordinary strong laws of large numbers (SLLNs) for plug-in estimators of general statistical functionals are derived. It is used that if a statistical functional is ‘sufficiently regular’, then an (MZ-)SLLN for the estimator of the unknown distribution function yields an (MZ-)SLLN for the corresponding plug-in estimator. It is in particular shown that many L-, V- and risk functionals are ‘sufficiently regular’ and that known results on the strong convergence of the empirical process of α-mixing random variables can be improved. The presented approach does not only cover some known results but also provides some new strong laws for plug-in estimators of particular statistical functionals.     

基于公理设计理论的仿真软件评价方法研究

针对仿真软件评价优选问题,提出一种基于公理设计理论的仿真软件评价方法。以公理设计理论为指导建立仿真软件评价模型,通过信息公理以信息量大小为测度来度量仿真软件产品的优劣。考虑到备选方案评价指标信息具有不完全性和模糊性特征,采用信息公理中的经典信息量计算方法存在局限性,对信息公理中的信息量计算方法进行拓展,提出基于单值点、区间数相离度、满意度和模糊信息的信息量计算方法。结合经典的和拓展的信息量计算方法,给出仿真软件评价流程。以某生产制造企业选择仿真软件产品为例,说明所提出方法的可行性和有效性,实验结果也揭示了在仿真软件商业领域竞争中软件质量起到至关重要的作用。     

The absorption distribution and the q-binomial theorem

Approximations for the mean and variance for the absorption distribution are found by means of a transformation of ordinary binomial to Gaussian or q-binomial coefficients.     

Exact Distributions of the Number of r-Records and the r-Record and Inter-r-Record Times

Consider a sequence of independent and identically distributed random variables with an absolutely continuous distribution function. The probability functions of the numbers K_n,r and N_n,r of r-records up to time n of the first and second type, respectively, are obtained in terms of the non central and central signless Stirling numbers of the first kind. Also, the binomial moments of K_n,r and N_n,r are expressed in terms of the non central signless Stirling numbers of the first kind. The probability functions of the times L_k,r and T_k,r of the kth r-record of the first and second type, respectively, are deduced from those of K_n,r and N_n,r. A simple expression for the binomial moments of T_k,r is derived. Finally, the probability functions and binomial moments of the kth inter-r-record times U_k,r = L_k,r ? L_k?1,r and W_k,r = T_k,r ? T_k?1,r are obtained as sums of finite number of terms.     

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.