Monotonicity of Rank Statistics in some Non–parametric: Testing Problems

For some non–parametric testing problems (one–sided two–sample problem, k –sample trend problem, testing independence against positive dependence) a partial ordering, denoted by ≥, over the alternatives is defined. This partial ordering expresses the strength of the deviation from the null–hypothesis. All familiar rank tests turn out to become more powerful under "increasing" alternatives; that is, all familiar rank statistics preserve the ordering stochastically in samples whenever it is present between underlying distributions. As a tool, the sample equivalence of ≥ is introduced as a partial ordering over pairs of permutations. Functions, defined on pairs of permutations, which preserve this ordering are studied.     

THE JOINT ARRIVAL AND DEPARTURE PROCESS FOR THE M/M/l QUEUE

We consider the M/M/1-queue and derive an explicit expression for the joint distribution of the number of arrivals and the number of departures in [0, t), given the number of customers initially present. The derivation is almost purely combinatorial, it avoids the use of generating functions, and immediately yields a simple probabilistic interpretation of the result.     

The ARCO decision: Inroads into the per se rule under Section 1 of the Sherman Act

In this study, the author analyzes the 1990 U.S. Supreme Court decision inAtlantic Richfield Company vs. USA Petroleum Company approving Atlantic Richfield’s maximum pricing plan improsed on its distributors (despite the Court’s recognition that theper se rule forbade such schemes). Theper se rule had been one of the last substantial measures of effective antitrust policy administered by enforcement authorities and the courts, perhaps even more fundamental than scrutiny of proposed mergers and predatory practices. That principle has been weakened by the ARCO decision. The author addresses some of the likely consequences of the ascendancy of the Chicago School and the NeoClassical theory generally in antitrust interpretation.     

Abstracts

Quality & Quantity -     

EFFECT OF GROUPING OF DATA ON THE DIVERGENCE BETWEEN LASPEYRES AND PAASCHE FORMS OF QUANTUM INDEXES*

Historical data for the manufacturing industry in the United States and United Kingdom are quoted, showing in most cases divergences between Laspeyres and Paasche forms of the quantum index that are by no means negligible. When the Paasche index for two of the series is recalculated with quantity indicators for industries instead of for products, the divergence is greatly reduced, and when quantity indicators for industry groups are substituted it almost disappears. This raises some questions about the practices of econometricians and statisticians, which are discussed. In a mathematical appendix by E. R. Coleman it is suggested that the grouping effect referred to does not depend on the particular way in which the data are grouped in most quantum indexes.     

Managed competition

People don't like change. That includes materiel managers, administrators, and clinical providers. Managed competition or managed care will work if, and only if, the American professions and the American public recognize the value of highly educated and qualified clinical and nonclinical providers and if the health care industry responds in kind.