Statistical and Historical Analyses of Nations Which Deviate From the Size-Density Law

We examine nations which deviate significantly from the ?2/3 sizedensity slope previously observed for the aggregated political subdivisions of 98 modern nations and previously derived from the theory of timeminimization. We correct Stephan’s original list of deviant nations, demonstrate that all slopes more negative than ?2/3 were due to the erroneous inclusion of cities in the original data sets, develop a theory to account for the less negative deviant slopes, and test the theory both through statistical manipulation of current data and through analysis of available historical data.     

Dramas,Metaphors, and Structures*

It is argued that dramaturgical sociology/social psychology must be examined as a continuation of the methods and practices of dramatism. Such an examination will reveal answers to the persistent questions regarding the work of Erving Goffman: Is he using a metaphor, simile, analogy, etc.! Is he a symbolic interactionist! Is his work a form of structuralism! What is the relationship between the sociologist and the drama of human relations! What is the relationship between interactionism and structuralism! The answers to these questions, it appears, are that drama is not used as a simple analogy in the study of human relations and that the separation of structuralism and interactionism is yet another essay in the confrontation between Heraclitus' flux and Zeno's paradox. You cannot step twice into the same river; for fresh waters are ever flowing in upon you. Heraclitus In which case, you cannot step even once into the river: there will in fact be no river. after Parmenides, Zeno etc.     

THE EFFECTS OF MARKET PRACTICES IN OLIGOPOLISTIC MARKETS: AN EXPERIMENTAL EXAMINATION OF THE ETHYL CASE

This study reports on the performance of experimental markets characterized by industrial structure and practices similar to those at issue in the Ethyl case. The central question is whether price competition is affected by the practices of advanced notification of price changes and "most-favored nation" contracts or is determined by industrial organization and concentration alone.     

Non-parametric recursive estimates of a probability density function and its derivatives

Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f^(p)_n of f^(p), the pth order derivatives of f, are exhibited. These estimators are of the form $\text{n}{}^{\mathrm{?1}}\text{∑n}\text{j=1}\text{δ}{}_{\mathrm{jp}}$, where δ_jp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f^(p) have been weakened with a little stronger assumption on the kernel function.     

On the optimality of a class of minimal covering designs

It is shown that the minimal covering designs for v=6t+5 treatments in blocks of size 3 are optimal w.r.t. a large class of optimality criteria. This class of optimality criteria includes the well-known criteria of A-, D- and E-optimality. It is conjectured that these designs are also optimal w.r.t. other criteria suggested by Takeuchi (1961).