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.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

Henry George and Europe

A bstract . In the eyes of European scholars, publicists and politicians who studied Henry George's work, he, as a social philosopher , had adopted the position of the natural law philosophers of the 18th century. The latter inspired the Declaration of Independence, the U.S. Constitution and its Bill of Rights, as well as the poiitical philosophy of Jeffersonian democracy , the ethos of the 18th and 19th century pioneer settlers. George rejected Social Darwinism. He saw natural law as the only true and reliable basis for a just social order. Like Karl Marx he mastered Ricardian economics ; unlike Marx, George made two factors the basis of his system, labor and land. George saw that each person had a natural right —and a natural imperative for survival —to apply his or her productive capacity to the earth –as living space and as storehouse of nutrients and raw materials. The person-land relationship , he discovered, lay at the basis of human culture. And so the land's rent , now monopolized by the few, had to be appropriated to meet the needs of society, most efficiently and justly by a land value tax.     

Moment inequalities for order statistics from ordered families of distributions

Summary In this paper some inequalities for the variance and covariance of convex monotone functions of order statistics from ordered families of distributions are presented. The considered order relations in the set of distributions are the stochastic ordering relation and the convex ordering relation. Stochastic comparisons of spacings and their sums are also given. As corollaries the results for IFR and DFR distributions are obtained.     

Unfair dismissal legislation and property rights: some reflections

Starting from the premise that workers have ‘property rights’ in their jobs, this article considers ways in which British unfair dismissal legislation might be said to uphold such rights. The evidence indicates that remedies of compensation and re-employment afford minimal property rights to unfairly dismissed workers.     

Public Schools and In-migration in North Carolina Counties, 1975–80

Abstract . The migration model presented in this paper indicates (hat the academic quality of public schools, independent of their racial composition, is an important determinant of in-migration in North Carolina counties. The failure to control for school quality is shown to lead to a significant overestimate of the negative impact of school racial mix. These results accord with the Tiebout Hypothesis and with a growing body of other research which suggests that the distributions of public services and other amenities are the principal determinants of recent migration patterns in the U.S.     

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.