Distribution of product statistics from aPareto population

Summary Distributions are derived of the product of sample values, the sample geometric mean, the product of two minimum values from sample of unequal size and product ofk minimum values from sample of equal size from aPareto population. The distributions can be conveniently transformed tox ². Paper presented at the Eastern Regional meeting of the Institute of Mathematical Statistics, Upton, Long Island, New York, April 27–29, 1966. Work done when the author was on the faculty of Western Reserve University, Cleveland, Ohio, U.S.A.     

Distribution of Dixon’s statistics in the case of an exponential population

Summary The distributions of Dixon’s statistics for the case of the sample from an exponential population are found. For some of these statistics the upper 100 α percentage points (α=0,1; 0,05 and 0,01) are tabulated.

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Zusammenfassung Die Verteilungen der Variablen von Dixon werden für den Fall der Stichproben aus einer exponentialen Grundgesamtheit gefunden. Für einige dieser Variablen werden die oberen 100 α Prozentpunkte (α=0,1; 0,05 und 0,01) tabelliert.

     

英国房市为何与经济背道而驰？

英国失业率的迅速升高和信贷持续紧缩并未令楼市跌入低谷,反而渐从疲态中走出,缘由何在？楼市会由出人意料进而演变成反弹吗？     

The long run effects of changes in tax progressivity

This paper compares the steady-state outcomes of revenue-neutral changes to the progressivity of the tax schedule. Our economy features heterogeneous households who differ in their preferences and permanent labor productivities, but it does not have idiosyncratic risk. We find that increases in the progressivity of the tax schedule are associated with long-run distributions with greater aggregate income, wealth, and labor input. Average hours generally declines as the tax schedule becomes more progressive implying that the economy substitutes away from less-productive workers toward more-productive workers. Finally, as progressivity increases, income inequality is reduced and wealth inequality rises. Many of these results are qualitatively different than those found in models with idiosyncratic risk, and therefore suggest closer attention should be paid to modeling the insurance opportunities of households.     

Minimal sufficient statistics for the group divisible partially balanced incomplete block design (GD-PBIBD) with interaction under an Eisenhart Model II

Summary In this paper, an Eisenmhart Model II with interaction for a GD-PBIB design withp replicates per cell is considered. Specifically the Model Y_ijl=µ+_i+_j+()_ij+e_ijl is assumed, wherei=1, 2, ...,b; j=1, 2, ...,t andl=0, 1, 2, ...p s _ij wheres _ij=1, if treatmentj appears in blocki, 0, otherwise.If _i, _j, ()_ij ande _ijl are normally and independently distributed, then a minimal sufficient (Vector-valued) statistic for the class of densities for this model is found, together with the distribution of each component in the minimal sufficient statistic. It is also shown that the minimal sufficient statistic for this class densities is not complete. Hence the solution of the problem of finding minimum variance unbiased estimators of the variance components is not straightforward.     

The homogeneity problem in statistics

The theory of probability is the most abstract mathematical science with unlimited scope of application. However, the essential question of the theory of probability has not been solved: how can we use probabilities in the epistemology of empirical data sets? The answer to this question can be given on the basis of the concept of homogeneous random processes.     

Effective writing in mathematical statistics

Care should be taken in the writing of papers in mathematical statistics for two reasons. First this enhances a paper's chances to be accepted for publication in a top journal. Second the contributions of a paper will reach a wider audience if the main ideas are easily accessible. This paper gives suggestions for improvement in two directions: presentation of mathematics and organization of papers.     

The importance of being earnest in statistics

The principal assumption of statistical theory is that a sample came from a homogeneous population. This assumption is not tested when statistical computations are produced. It creates a gap between statistical theory and statistical practice. This gap is bridged by the new quality philosophy (NQP) in statistics. The NQP defines a homogeneous population in terms of classical probability discrete distributions.     

Some properties of Rho-b statistics

This article asseses the utility of Spearman's rho-b in path analyses. First, the performance of rho-based statistics are tested against Kim's criteria. The method works quite well on monotonic data, and under certain circumstances perfect detection of underlying interval structures is possible. Second, problems of implementing multivariate analyses with Spearman statistics are discussed. The simplest procedure is to recode the variables as ranks and to use Pearson algorithms and tests of significance. These are valid.     

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.     

On functionals of order statistics

Summary Let g_n be real functions,U _ni, 1in, the ordered sample ofn independentU(0,1) distributed random variables, andc _ni(), 1in, 01 be (known) real numbers,n=1, 2, ... The random quantity , 01, is studied. Based on a method proposed byShorack [1972] the main result is the weak convergence of to Gaussian processes, where , 01. The convergence is with respect to theSkorokhod [1956]-topologiesM ₂,M ₁ onD (I) and the -topology onC(I), depending on the conditions imposed on thec _ni().     

Is there a long run demand for currency in China?

The record of Chinese monetary authorities at targeting MO in the late eighties early nineties is rather poor. This paper thus first aims at determining whether the instability of currency demand is responsible for this. By so doing we show, using adequate econometric techniques, that a long-run demand for currency did exist over the 1988–1993 period, with quarterly data.Most previous studies concluded that the income elasticity of currency demand in China is very high. The second objective of the paper is to test for the robustness of this result. We show that this income elasticity is unity when proper account is taken of institutional variables representative of the transition process.Abbreviations ADF Augmented Dickey Fuller - ARCH Auto Regressive Conditional Heteroskedasticity - IMF International Monetary Fund - LDCs Less Developed Countries - M0 currency - M1 narrow money - M2 broad money - PBC People's Bank of China - VAR Vector Auto Regressive Model Comments on an earlier version by my colleagues Christian Bordes and Dominique Lacoue-Labarthe and by an anonymous referee were very useful in improving the present paper. It also benefited from comments by participants at the annual conference of the (UK) Chinese Economic Society in December 1995. However, I remain solely responsible for all remaining errors.     

Do homeowners achieve more household wealth in the long run?

Despite the public’s faith in homeownership as a vehicle for wealth creation, there are surprisingly few empirical studies of the independent impact of homeownership and its duration on household wealth accumulation. This paper provides the first empirical evidence that homeownership, after controlling for other drivers of wealth accumulation, is positively and significantly associated with wealth accumulation over time. Using the Panel Survey of Income Dynamics, it examines the influence of housing tenure choices between 1989 and 2001 on household net wealth levels in 2001 after controlling for initial wealth in 1989, location, income, education, and other family and personal characteristics that might influence the rate of wealth accumulation. Importantly, the models used also control for the tendency of households to accumulate wealth between 1984 and 1989 (five years prior to the studied period). This approach is used to address the possibility that an unobserved variable—the propensity to save or accumulate wealth—may be associated with both the probability and duration of homeownership and the rate of wealth accumulation. All else equal, those who owned homes and owned for longer periods of time had significantly higher household net wealth by 2001. These results are compelling because house price appreciation over the period was near its long-run average while stock gains were above and real rent increases below their long-run averages. Hence, the findings are suggestive of a positive influence of ownership over long periods on net wealth, even during a period when alternative investments produced higher than normal returns and rents grew slowly. This is especially important because the overwhelmingly majority of households do not sell their homes shortly after buying them. In our sample, those who became owners typically owned for 7 years. Furthermore, most households that bought during a period of declining real home values in the early 1990s continued to own their homes for at least eight years and came out well ahead of those who did not own.     

浅谈统计在企业管理中的作用

随着社会经济的日益发展,统计在企业管理中越来越重要,没有科学的统计数据为依据,企业的各项管理就如空中楼阁,虚而不实,管理过程中便不能很好地找到切入点,从政府宏观调控来说,也难很好地找到着力点。     

工业统计在企业经济管理中的作用

文章首先阐述了工业统计在企业经济管理中的重要性,然后对工业统计在当今企业经济管理应用中的现状进行了分析,最后就工业统计如何更好地应用于企业经济管理中提出了建议。     

浅谈会计与统计在医院财务管理上的结合

医院的会计与统计属于医院经济管理信息系统 ,在 2 1世纪的今天 ,医院将面临各种新情况、新问题和新要求 ,医院的各项经济活动、各种经济信息、业绩分析评价、目标落实的措施、内部考核的各种数据等等 ,都与会计与统计有着紧密的联系 ,都要求会计与统计在管理上与之相适应。笔者试从二者的结合上谈谈自己的认识和看法。一、会计与统计在理论上的有机结合了解会计与统计的渊源关系的过程 ,我们可以发现 ,人类起初的统计行为 ,大体上是与会计行为同时产生的。在进入古代文明社会之后 ,统计工作又是“大会计”范畴中的一个组成部分 ,会计、统计…