俄汉数字文化对比与翻译

俄汉两种语言中的数字文化 ,有其独特的民族文化内涵及成因。俄语中数词“虚用”现象的翻译应采取灵活的方法。     

The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree

This article is devoted to the strong law of large numbers and the entropy ergodic theorem for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree, which generalizes the relevant results of tree-indexed nonhomogeneous bifurcating Markov chains. Meanwhile, our proof is quite different from the traditional method.     

Asymptotic estimators of the sample size in a record model

The connection between Stirling numbers of the first kind and records is well-known. Applying this relationship, we derive bounds for the maximum likelihood estimator of the sample size based on the number of observed records. The proof proceeds by a remarkable expression of the mode of the unsigned Stirling numbers of the the first kind due to Hammersley. Moreover, this representation of the mode leads to an accurate approximation of the maximum likelihood estimator.     

On the formulation of uniform laws of large numbers: a truncation approach

The paper develops a general framework for the formulation of generic uniform laws of large numbers. In particular, we introduce a basic generic uniform law of large numbers that contains recent uniform laws of large numbers by Andrews [2] and Hoadley [9] as special cases. We also develop a truncation approach that makes it possible to obtain uniform laws of large numbers for the functions under consideration from uniform laws of large numbers for truncated versions of those functions. The point of the truncation approach is that uniform laws of large numbers for the truncated versions are typically easier to obtain. By combining the basic uniform law of large numbers and the truncation approach we also derive generalizations of recent uniform laws of large numbers introduced in Pötscher and Prucha [15, 16].     

Occupancy distributions for testing marginal homogeneity

In this paper different pairs of urns are considered. We are interested in the number of ways in which N balls can be placed into the urns so that differences and ratios between the number of balls in certain pairs of urns are the same.     

A general robustness property of rank correlations

Rank correlations are shown to be generally robust in the sense that the tests for independence, which they naturally define, have weakly equicontinuous error probabilities. The ordinary sample correlation coefficient is not robust in this respect.     

A test for homogeneity when the sample is a positive lagrangian poisson distribution

In this note, we obtain, based on the sample sum, a statistic to test the homogeneity of a random sample from a positive (zero truncated) Lagrangian Poisson distribution given in Consul and Jain (1973). This test statistic conforms, in a special case, to Singh (1978). A goodness-of-fit test statistic for the Borel-Tanner distribution is obtained as a particular case cf our results.     

On exact strong laws of large numbers for ratios of random variables and their applications

Abstract

We study the almost sure convergence of weighted sums of ratios of independent random variables satisfying some general, mild conditions. The obtained results are applied to exact laws for order statistics. An exact law for independent random variables which are nonidentically distributed is also proved and applied to ratios of adjacent order statistics for a sample of uniformly distributed random variables.     

Usefulness of Asymptotic Distributions in the Classical Occupancy Problem

Approximations to the distribution of a discrete random variable originating from the classical occupancy problem are explored. The random variable X of interest is defined to be how many of N elements selected by or assigned to K individuals when each of the N elements is equally likely to be chosen by or assigned to any of the K individuals. Assuming that N represents the number of cells and each of the K individuals is placed in exactly one of the cells, X can also be defined as the number of cells occupied by the Kindividuals. In the literature, various asymptotic results for the distributions of X and (N ? X) are given; however, no guidelines are specified with respect to their utilization. In this article, these approximations are explored for various values of K and N, and rules of thumb are given for their appropriate use.