The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables

In this paper, we show that a hypergeometric random variable can be represented as a sum of independent Bernoulli random variables that are, except in degenerate cases, not identically distributed. In the proof, we use the factorial moment generating function. An asymptotic result on the probabilities of the Bernoulli random variables in the sum is also presented. Numerical examples are used to illustrate the results.     

Social Sources of Community Solidarity in U.S. Congregations

Community solidarity, or a collective sense of belonging, plays a vital role in the health and survival of many organizations. Consequently, identifying the elements that contribute to a strong sense of solidarity within communities has long been a topic of inquiry for scholars. In this study, we draw upon prior theorizing to develop and test four hypotheses regarding the organizational characteristics associated with community solidarity in religious congregations. Multivariate models are estimated using national data on religious congregations from the 2001 U.S. Congregational Life Survey (n?=?357). Organizations with greater community solidarity tend to feature higher levels of social capital (operationalized with measures of friendship networks and participation in organizational activities), higher levels of official membership within the organization, and inspiring congregational leadership. Higher levels of commitment are associated with greater community solidarity, but the effect is wholly mediated by social capital. Congregations that engender higher levels of community solidarity share certain organizational features, including higher levels of social capital, higher rates of membership, and inspiring leaders.     

如何有效地扩大医疗保险覆盖面——拉美国家的经验教训及启示

本文以拉美国家的经验及启示为视角，就如何有效地扩大医疗保险覆盖面问题展开论述。     

Changes in At-Risk American Men's Crime and Substance Use Trajectories Following Fatherhood

Fatherhood can be a turning point in development and in men's crime and substance use trajectories. At-risk boys (N = 206) were assessed annually from ages 12 to 31 years. Crime, arrest, and tobacco, alcohol, and marijuana use trajectories were examined. Marriage was associated with lower levels of crime and less frequent substance use. Following the birth of a first biological child, men's crime trajectories showed slope decreases, and tobacco and alcohol use trajectories showed level decreases. The older men were when they became fathers, the greater the level decreases were in crime and alcohol use and the less the slope decreases were in tobacco and marijuana use. Patterns are consistent with theories of social control and social timetables.     

A Critical Look at Some Analyses of Major League Baseball Salaries

At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at building parsimonious, understandable models that fit the data well. We also find that common data displays, when applied carefully, are often sufficient for even complex analyses such as this.     

Jensen's Inequality for General Location Parameter

A wide class of location parameters is shown to satisfy Jensen's inequality. When the expectation EX exists and l is a convex function, Jensen's inequality states that El(x) ≥ l(EX). It is shown that for μ, a properly defined location parameter, μ(l(x)) μ l(μ(x)).     

Density estimation using asymmetric kernels and Bayes bandwidths with censored data

We propose a modification to the regular kernel density estimation method that use asymmetric kernels to circumvent the spill over problem for densities with positive support. First a pivoting method is introduced for placement of the data relative to the kernel function. This yields a strongly consistent density estimator that integrates to one for each fixed bandwidth in contrast to most density estimators based on asymmetric kernels proposed in the literature. Then a data-driven Bayesian local bandwidth selection method is presented and lognormal, gamma, Weibull and inverse Gaussian kernels are discussed as useful special cases. Simulation results and a real-data example illustrate the advantages of the new methodology.