A class of symmetric bivariate uniform distributions

A class of symmetric bivariate uniform distributions is proposed for use in statistical modeling. The distributions may be constructed to be absolutely continuous with correlations as close to±1 as desired. Expressions for the correlations, regressions and copulas are found. An extension to three dimensions is proposed.     

The residual effect of a growth-decay mechanism and the distributions of covariance structures

The product of two independent or dependent scalar normal variables, sums of products, sample covariances, and general bilinear forms are considered. Their distributions are shown to belong to a class called generalized Laplacian. A growth-decay mechanism is also shown to produce such a generalized Laplacian. Sets of necessary and sufficient conditions are derived for bilinear forms to belong to this class. As a generalization, the distributions of rectangular matrices associated with multivariate normal random vectors are also discussed.     

A Sociology of the Periphery Versus a Peripheral Sociology: Rural Sociology and the Dimension of Space1

Abstract Rural sociology is intrinsically concerned with the spatial dimensions of social life. However, this underlying research tradition, particularly the use of space as a research strategy, has been insufficiently addressed and its contributions to general sociology are little recognized. I outline how concern with space, uneven development, and the social relationships of peripheral settings have provided substantive boundary and conceptual meaning to rural sociology, propelled its evolution, and left it with a legacy of strengths, weaknesses, and challenges. A willingness to tackle the dimension of space and the thorny problems it raises often sets rural sociologists apart from other sociologists. This research tradition contrasted with general sociology's concern with developing generalization, aspatial covering laws, and proto-typical relationships of modern or Fordist development settings. Conceptual openings have left sociologists questioning their past agenda. Coupled with the “creative marginality” inherent in the questions and contexts addressed by rural sociologists, this makes the subfield central to contemporary sociology.     

Politics and Scientific Expertise: Scientists, Risk Perception, and Nuclear Waste Policy

To study the homogeneity and influences on scientists'perspectives of environmental risks, we have examined similarities and differences in risk perceptions, particularly regarding nuclear wastes, and policy preferences among 1011 scientists and engineers. We found significant differences ( p 0.05)in the patterns of beliefs among scientists from different fields of research. In contrast to physicists, chemists, and engineers, life scientists tend to: (a)perceive the greatest risks from nuclear energy and nuclear waste management; (b)perceive higher levels of overall environmental risk; (c)strongly oppose imposing risks on unconsenting individuals; and (d)prefer stronger requirements for environmental management. On some issues related to priorities among public problems and calls for government action, there are significant variations among life scientists or physical scientists. We also found that–independently of field of research–perceptions of risk and its correlates are significantly associated with the type of institution in which the scientist is employed. Scientists in universities or state and local governments tend to see the risks of nuclear energy and wastes as greater than scientists who work as business consultants, for federal organizations, or for private research laboratories. Significant differences also are found in priority given to environmental risks, the perceived proximity of environmental disaster, willingness to impose risks on an unconsenting population, and the necessity of accepting risks and sacrifices.     

The identification of logistic regression models with errors in the variables

The simple logistic regression model with normal measurement error and normal regressor is shown to be identifiable without any extra information about the measurement error. The multiple logistic regression model with more than one regressor variable measured with error is not identifiable. If the covariance matrix of the measurement error is known up to a scalar factor, the model is identified. Further we discuss why in spite of the identifiability the models cannot be estimated in a reasonable way without extra information about the measurement error.     

On the run length of a Shewhart chart for correlated data

We consider an extension of the classical Shewhart control chart to correlated data which was introduced by Vasilopoulos/Stamboulis (1978). Inequalities for the moments of the run length are given under weak conditions. It is proved analytically that the average run length (ARL) in the in-control state of the correlated process is larger than that in the case of independent variables. The exact ARL is calculated for exchangeable normal variables and autoregressive processes (AR). Moreover, we compare this chart with residual charts. Especially, in the case of an AR(1)—process with positive coefficient, it turns out that the out-of-control ARL of the modified Shewhart chart is smaller than that of the Shewhart chart for the residuals.     

Useful relationship between the log-survival function and truncated moments,with applications

We present a new characterization technique extracted from a well known idea in statistical inference. We use the partial derivative of the logarithm of the survival function in connection with truncated moments to characterize several probability distributions. Our methods introduce a unified technique to obtain several well known results in a unified way.