Generalized densities of order statistics

Let X ₁, ... , X _n be independent identically distributed random variables with distribution F . We derive expressions for generalized joint 'densities' of order statistics of X ₁, ... , X _n , for arbitrary distributions F , in terms of Radon–Nikodym derivatives with respect to product measures based on F . We then give formulae for conditional distributions of order statistics and use them to derive results concerning Markov properties of order statistics, formulae for distributions of trimmed sums, and other useful representations. Our approach leads to simple and natural expressions which appear not to have been given before.     

市场前景F预测

本文综合运用马尔可夫链及 F概率的知识 ,对产品在市场上的销售状况进行 F预测 ,为经营者科学地进行市场前景决策提供可靠的依据     

Econometric Analysis of Managers' Judgements on the Determinants of the Financial Situation in Russia

The paper presents an econometric analysis of the determinants of the financial situation in Russian manufacturing. Official statistics in Russia are not reliable. This is why the analysis is based on business opinion surveys carried out within `The Russian Economic Barometer' long-term research programme for monitoring and investigation of the transition to the market in Russia. The new adaptive approach elaborated by the author of the paper is used to form a correct set of explanatory variables in regression equations. This approach is based on the comparison of the forecast abilities of alternative models with different sets of explanatory variables. Two periods are considered and compared: January 1993 to January 1995 and February 1995 to January 1998. Two variables, the diffusion index of output and the average order-book level, provide the best explanation of the managers' judgement regarding the financial situation in Russia for the first period. It was found that for the second period, the influence of the `output index' diminished. The main factors with which managers related a `good' financial situation in their enterprises were the sample average of order-book level, the stocks of finished goods, the index of order-book level, the index of output prices ratio, and the indebtedness to banks. All relationships are presented in the context of linear probability and logit models.     

购销广告中的数学学问

本文通过对需求市场的分析，得出人们的潜在购买量随广告费的增加而增大。但实际需求量是随机的。为使问题简化，并做出定量分析，本文假定实际需求量服从均匀分布，并用数学方法确定广告费和购进量的最优值。     

经济类院校概率统计课程教学的改革与探索

文章提出概率统计课程教学改革的几点建议：教学内容的选择上，要有针对性、专业性、层次性；教学方法的运用上，要注重多样性、灵活性、创新性；同时注意加强数学实验课；数学建模课的教学。强调教学要理论联系实际，培养学生的应用能力。     

Characteristic properties of multivariate survival functions in terms of residual life distributions

This paper discusses the relationships among some characteristic properties of the multivariate survival function based on the residual life distribution, and provides the conditions for their equivalence. In the meanwhile, the corrected version of Ma (1996, Theorem 1 (ii) and (iii)) is given.     

Adaptation investments and homeownership

This article develops a model where ownership improves the efficiency of the housing market as it enhances the utility of housing consumption for some consumers. The model is based on an extended Hotelling–Lancaster utility approach in which the ideal variant of housing is obtainable only by adapting the home through a supplementary investment. Ownership offers low costs of adaptation, but has high contract costs compared with renting. Consumers simultaneously choose housing demand and tenure, and because of the different cost structure only consumers with strong preferences for individual adaptation of the home choose ownership. This article analyses the consumer’s optimization. The model provides an explanation for the observation that homeowners typically live in larger dwelling units than tenants. It also provides an explanation for a high price of housing services tending to reduce homeownership rates.     

企业并购估值中的威斯通模型扩展研究

威斯通模型是企业并购估值贴现现金流模型中具有代表性的研究。在威斯通固定增长模型的基础上,建立了考虑未来经营失败概率的估值模型;对威斯通超常增长而后无增长模型进行了修正,探讨了企业在超常增长期采取不同投资策略对其价值的影响,建立了一个更为简明的估值模型,并给出隐含超常增长期限的一种计算方法。     

Limit theorems for multivariate discrete distributions

According to the usual law of small numbers a multivariate Poisson distribution is derived by defining an appropriate model for multivariate Binomial distributions and examining their behaviour for large numbers of trials and small probabilities of marginal and simultaneous successes. The weak limit law is a generalization of Poisson's distribution to larger finite dimensions with arbitrary dependence structure. Compounding this multivariate Poisson distribution by a Gamma distribution results in a multivariate Pascal distribution which is again asymptotically multivariate Poisson. These Pascal distributions contain a class of multivariate geometric distributions. Finally the bivariate Binomial distribution is shown to be the limit law of appropriate bivariate hypergeometric distributions. Proving the limit theorems mentioned here as well as understanding the corresponding limit distributions becomes feasible by using probability generating functions.     

De Vetula: a Medieval Manuscript Containing Probability Calculations

De Vetula , a poem that contains probability calculations on the throw of three dice, was written in the mid-thirteenth century. The poem was widely circulated, read and quoted. There is strong evidence that some of the medieval readers clearly understood how the probability calculations were obtained. Based on the discussion given here, it is put forward that an elementary probability calculus was established and known in Europe from about the year 1250. A translation of the relevant section of the poem is given.