Learning a population distribution

This paper introduces a dynamic Bayesian game with an unknown population distribution. Players do not know the true population distribution and assess it based on their private observations using Bayes׳ rule. First, we show the existence and characterization of an equilibrium in which each player׳s strategy is a function not only of the player׳s type but also of experience. Second, we show that each player׳s initial belief about the population distribution converges almost surely to a “correct” belief.     

The empirical distribution function as a tail estimator

It is shown that the empirical distribution function performs well in tail estimation. Consistency as well as the relative error are considered. The results hold true without any condition on the theoretical distribution function.     

Transforms for finding probabilities and variate values of a distribution function in tables of a related distribution function

Het verband tussen enige bedkende verdelingen.
In dit artikel worden enkele schema's gegeven voor het verband tussen een aantal van de meest bekende verdelingen. Bovendien wordt een aantal andere relaties besproken. He doel van dit artikel is drieledig. Ten eerste kunnen statistische afdelingen, die in het bezit zijn van een uitgebreide tabellenverzamelign de gegeven transformaties gebruiken om bestaande tabellen uit andere tabellen te vervolledigen ten dienste van bepaalde praktische toepassingen. Ten tweede kunnen statistici, die niet in het bezit van volledige tabellenverzamelingen zijn, ontbreakende tabellen vervanden tussen deze verdelingen leiden tot meer inzicht in bepaalde toetsings-methoden. Dit laatste punt wordt niet uitvoerig uitgewerkt.
Par. 1. geeft een inleiding en overzicht; par. 2 vermeldt de gebruikte symbolen en verwijst naar bekende tabellenverzamelingen; par. 3 en 4 geven schematisch de transformaties weer; par. 5 geeft een schematisch overzicht van de relaties; par. 6 geeft een aantal numerieke voorbeelden; in de appendix worden de wiskundige formules van de verdelingen vermeld.
Afleidingen worden niet gegeven.     

The entropy paradox and the distribution of urban population

This paper presents an empirical application of an information theoretic approach to spatial hypothesis testing. Following the lead of Batty [1] this study employs the concept of expected information to test hypotheses concerning the distribution of urban population and population density in San Antonio for the years 1960 and 1970. Cast for the first time in a longitudinal context, major concerns of this work are the relative advantages, both theoretical and methodological, of certain entropy measures. Specifically, comparisons are made between the Shannon and the Kullback formulations. In this context of comparison, problems closely linked to what has been called the “entropy paradox” are identified and explained, suggesting important qualitative differences between these two measures.     

Minimax invariant estimator of a continuous distribution function under a general loss function

The problem of invariant estimation of a continuous distribution function is considered under a general loss function. Minimaxity of the minimum risk invariant estimator of a continuous distribution function is proved for any sample size n ≥ 2.     

On the distribution of a distance function on the sphere

Summary The distribution of the square of the distance between a random point and a fixed point on ap-dimensional unit sphere when (i) the two points lie on the whole sphere and (ii) the two points lie in the positive quadrant, has been derived, assuming that the random point is distributed proportionally to exp (ky ₁), wherek is a concentration parameter. Then-th order moment in both cases is also obtained.     

Estimating a distribution function in the presence of auxiliary information

For estimating the distribution functionF of a population, the empirical or sample distribution functionF _n has been studied extensively. Qin and Lawless (1994) have proposed an alternative estimator for estimatingF in the presence of auxiliary information under a semiparametric model. They have also proved the point-wise asymptotic normality of . In this paper, we establish the weak convergence of to a Gaussian process and show that the asymptotic variance function of is uniformly smaller than that ofF _n . As an application of , we propose to employ the mean and varianceŜ _n ² of to estimate the population mean and variance in the presence of auxiliary information. A simulation study is presented to assess the finite sample performance of the proposed estimators , andŜ _n ² .     

Minimax invariant estimation of a continuous distribution function under entropy loss

For the invariant decision problem of estimating a continuous distribution function F with two entropy loss functions, it is proved that the best invariant estimators d ₀ exist and are the same as the best invariant estimator of a continuous distribution function under the squared error loss function L (F, d)=∫|F (t) −d (t) |² dF (t). They are minimax for any sample size n≥1.     

Minimax estimation of a cumulative distribution function by converting to a parametric problem

Let X = (X ₁,...,X _n ) be a sample from an unknown cumulative distribution function F defined on the real line . The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute error.     

Kernel estimation of a smooth distribution function based on censored data

The problem of estimating a smooth distribution functionF at a pointτ based on randomly right censored data is treated under certain smoothness conditions onF. The asymptotic performance of a certain class of kernel estimators is compared to that of the Kaplan-Meier estimator ofF(τ). It is shown that the relative deficiency of the Kaplan-Meier estimator ofF(τ) with respect to the appropriately chosen kernel type estimator tends to infinity as the sample sizen increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved. Research Surported in part by NIH grant 1R01GM28405.     

The distribution function of a statistic for testing the equality of scale parameters in two gamma populations

Summary The exact distribution function of the ratio of two sums of gamma variates is derived in this paper. The result applies to ratios of quadratic forms and to a statistic used for testing the equality of scale parameters in two gamma populations.     

南宁市中心区的功能结构与空间分布研究——基于用地增量的研究

基于对1994年和2004年两个年度南宁市中心区用地的现状资料的统计分析,并考查了10年的时间段南宁市中心区用地增量的功能结构与空间分布,揭示了南宁市中心区土地利用与空间结构演变的特征,对揭示我国中、西部特大城市空间结构的演变规律具有一定的理论意义.     

Design-based distribution function estimation for stigmatized populations

In this paper, we discuss in a general framework the design-based estimation of population parameters when sensitive data are collected by randomized response techniques. We show in close detail the procedure for estimating the distribution function of a sensitive quantitative variable and how to estimate simultaneously the population prevalence of individuals bearing a stigmatizing attribute and the distribution function for the members belonging to the hidden group. The randomized response devices by Greenberg et al. (J Am Stat Assoc 66:243–250, 1971), Franklin (Commun Stat Theory Methods 18:489–505, 1989), and Singh et al. (Aust NZ J Stat 40:291–297 1998) are here considered as data-gathering tools.     

A model of population distribution,traffic congestion,and neighborhood crowding in a circular city

An idealized static equilibrium model of a circularly symmetric city is presented. The model allows one to compute the spatial distribution of residences, given certain simple and plausible assumptions about the “costs” of transport, housing and neighborhood crowding. The model is chosen so as to guarantee that in first approximation, the residential population distribution which would be considered optimal by a perfect planner is identical to the distribution reached in a push-shove, laissez-faire equilibrium. This aspect of the construction is shown to be related in a simple way to the familiar “external diseconomy” situation in which a free resource is allocated among alternative uses by equating average, rather than marginal products. The existence of an infinite class of models in which the associated planner's optimum and laissez-faire equilibria are equivalent follows naturally from the standard theory of the private and social costs of highway congestion. The model leads naturally to exponentially falling population distributions which exhibit an “urban-suburban” dichotomy, to a particular overall city size, and to an optimal allocation of land between transport and residential uses.     

Modelling the spatiotemporal distribution of the incidence of resident foreign population

Many European countries have recently experienced a substantial increase in the proportion of immigrants in their populations. The incidence of resident foreigners calculated at a national level does not provide information on the local spatial and temporal distribution of the phenomenon. This information may be of crucial importance for planning local policies. In this article, we suggest a tool for practitioners to provide spatiotemporal maps representing the local distribution of the incidence of resident foreigners in the territory, and changes in spatial trends over time. We illustrate this with Italian data at a municipal level, for the period 2003–2008. To account for spatiotemporal interactions in the data, we propose using a generalized additive model incorporating a smoother of the time and space dimensions. Specifically, we set up a tensor product smoother combining a cubic regression spline basis for time and a soap film spline basis for space. This approach provides a consistent framework to produce spatiotemporal maps which could be effectively used by policy makers to decide the allocation of economic resources at a local level.     

广州市外来人口空间分布变动分析

利用第三、四、五次人口普查资料,对广州市外来人口的空间分布进行分析,结果表明1980年代以来广州市外来人口在数量急剧增长的同时,其空间分布格局也发生了根本变化,即由原来主要集中于中心区转向主要集中于近郊区,并逐渐向远郊区延伸.根据外来人口的空间变化规律,提出了加强城市人口管理和城市规划建设的若干建议.     

The development of a comprehensive medical-surgical distribution agreement

The selection of a medical-surgical distributor has become one of the most important decisions made by a hospital materiel manager today. It is therefore critical that before a distributor is selected a clearly defined development process and master plan be established. This master plan should contain, at a minimum, (1) a comprehensive strategic plan, (2) a detailed request for proposal, and (3) a detailed project implementation schedule. A well-structured, well-executed plan will help to ensure that the best distributor is selected and that the best possible distribution agreement is designed.     

引导京津冀地区人口合理布局的思路与对策研究

近年来,北京城市人口规模持续高位攀升,造成了交通拥堵、就业紧张、住房困难、水资源紧缺、环境污染等城市问题。从城市发展战略出发,采取引导和疏散人口的有效措施和政策,是首都实现可持续发展的重要环节。本文基于"京津冀一体化"国家战略,探索通过产业发展和功能提升增强首都周边区域对人口的吸引力,引导京津冀区域人口合理分布和有序流动,从而促进京津冀地区人口与经济社会、资源环境全面协调可持续发展。     

湖北省人口收缩城市的空间格局与类型识别

通过对湖北省82个县(市、区)的常住人口变化率和人口净流量进行交互分析,引入城乡建设用地脱钩模型和人口—土地城镇化协调指数,分析了人口收缩区域建设用地结构和城镇化协调类型。结果显示,湖北省存在37个人口持续流出、规模减少的区域,这些区域不仅在总量上表现为人口收缩与建设用地扩张的悖论关系,而且在城镇化方面也多表现为人口城镇化与土地城镇化不协调的状态,而从城乡建设用地结构的角度表现为不同的脱钩类型,其中仅有少数收缩区域是强脱钩的合理利用状态。从不同表现特征可将收缩城市类型分为空间无序扩张型、工业衰退型、资源枯竭型以及中心袭夺型四个类别,并概括为人口资源与土地资源、经济发展等在时空上的不匹配。最后,结合资源禀赋、经济结构变化等特征对人口收缩区域类别进行了归纳,并提出了针对性的城市规划和发展建议。