L1-Tightness and the law of large numbers in D(IR)

This article presents laws of large numbers for random elements of D(IR). The proofs bring forth the similarities between processes restricted to compact sets of D (IR) and processes with increasing trajectories. The results appear to generalize existing results and cover the independent identically distributed case studied by Ranga Rao.     

Banach空间混合列强大数定律的收敛定理

文献［１］讨论了Ｂａｎａｃｈ空间中随机变元列｛Ｘｉ｝满足一定条件时的完全收敛性。文中将进一步讨论Ｂａｎａｃｈ空间中独立非同分布随机变元列的收敛速度，得到了满意的结果     

The case of the random telephone numbers

An unusual pattern of telephone numbers recorded on suspect credit-card purchases led to the development of a generalized multinomial distribution. One usage of credit cards included 26 telephone numbers with a pattern of 7 unique numbers: 16 of one kind, 4 of another, 2 of another, and 4 different ones. With the assumption that the probability of any digit appearing in a telephone number is 1/10, the pattern of the 26 telephone numbers is found to have a probability of occurrence on the order of 1/10⁶⁵. That is, the chance of such a pattern occurring at random is roughly equivalent to winning nine times in a row the popular ottery, LOTO 6/49.     

沉淀法提取混合稀土的工艺条件试验

本文对草酸—碳铵混合物(H_2C_2O_4·2H_2O—NH_4HCO_3)作沉淀剂处理离子型稀土矿水的工艺条件作了系统的试验,找出了提取稀土的最佳工艺条件,很有希望降低提取成本和提高效益。     

The primary-goods indexation problem in Rawls's theory of justice

Rawls's Difference Principle holds that basic social institutions are just if they maximize the worst-off individual's potential welfare, which depends on the vector of amounts of primary goods. As Rawls recognized, the multiplicity of primary goods poses an index number problem. This paper uses the machinery of social choice to characterize the class of procedures for aggregating quantities of several primary goods into a composite ordinal index that are consistent with Rawls's analysis. Only very simple and unattractive aggregation methods in which the various primary goods play roles of radically different magnitudes are compatible with Rawls's argument.     

网络时代下外来生僻人名的汉译策略——以《公共外交》为例

外来人名的汉译国内虽有《世界人名翻译大辞典》可以参考,但对既定文本中出现的不少人名却依然无能为力。在讨论人名翻译的对等原则和罗曼语系人名汉译的特点基础上,以《公共外交》中繁杂的外来人名汉译为例,提出网络检索、官网核查、邮件交流三种策略来解决文本中生僻人名的翻译问题,认为译者在汉译外来人名时,必须要在参考权威辞典的基础之上,充分利用网络带来的便利条件多方求证,力图做到人名汉译的对等与可信,以期为新时代的外译汉研究提供借鉴和思考。     

Standards of Probability Sampling for Legal Evidence

Brief recognition is given to bicentennials of the death of James Stirling (1692–1770) and birth of Ferdinand Rudolph Hassler (1770–1843); to sesquicentennials of the publication of the 3rd definitive edition of Laplace's Théorie analytique des probabilités, and of the births of William Chauvenet (1820–1870) and Isaac Todhunter (1820–1884); to centennials of the births of Louis Bachelier (1870–1946) and Jean Perrin (1870–1942); and to the semicentennial of the initial publication (1920) of Metron, an International Review of Statistics.     

General strong convergence for negatively associated random variables

For negatively associated (NA) random variables, we obtain two general strong laws of large numbers (SLLN) in which the coefficient of sum and the weight are both general functions. As corollaries, we obtain Marcinkiewicz-type SLLN, the logarithmic SLLN and Marcinkiewicz SLLN for NA random variables.     

A Note on Collinearity Diagnostics and Centering

The usual approach for diagnosing collinearity proceeds by centering and standardizing the regressors. The sample correlation matrix of the predictors is then the basic tool for describing approximate linear combinations that may distort the conclusions of a standard least-square analysis. However, as indicated by several authors, centering may eventually fail to detect the sources of ill-conditioning. In spite of this earlier claim, there does not seem to be in the literature a fully clear explanation of the reasons for this bad potential behavior of the traditional strategy for analyzing collinearity. This note studies this issue in some detail. Results derived are motivated by the analysis of a well-known real dataset. Practical conclusions are illustrated with several examples.     

Estimation of a rare sensitive attribute for two-stage randomized response model in probability proportional to size sampling using Poisson probability distribution

This paper addresses the estimation of the mean number of individuals in the population who possess a rare sensitive attribute using Poisson distribution for the situations of (i) clustered population and (ii) stratified population with clusters are strata units. Properties of the proposed estimation procedures have been discussed when the proportion of a rare unrelated non-sensitive attribute is assumed to be known as well as unknown. Empirical studies are carried out to support the theoretical results which showed dominance over Lee et al. [Estimation of a rare sensitive attribute in probability proportional to size measures using Poisson distribution. Statistics (Ber). 2014;48(3):685–709] estimation procedures.