Boundedly complete families which are not complete

Summary Completeness of a family of probability distributions implies its bounded completeness but not conversely. An example of a family which is boundedly complete but not complete was presented by Lehmann and Scheffe [5]. This appears to be the only such example quoted in the statistical literature. The purpose of this note is to provide further examples of this type. It is shown that any given family of power series distributions can be used to construct a class containing infinitely many boundedly complete, but not complete, families. Furthermore, it is shown that the family of continuous distributions , is boundedly complete, but not complete, whereU denotes the uniform distribution on [a, b] and {P _ϑ,ϑ ∈ IR}, is a translation family generated by a distributionP ₀ with mean value zero, which is continuous with respect to the Lebesgue measure.     

Educational attainment and cohort size

"We argue that the postwar baby boom [in the United States] caused substantial fluctuations in both the economic rewards to education and educational attainment over the last 3 decades. If substitutability between young and old workers diminishes with education, the present value of lifetime earnings for a boom cohort is depressed more for highly educated workers, reducing incentives for educational attainment. The opposite is true for pre- and postboom cohorts. The diminishing substitutability hypothesis explains the declines in both the returns to college and college completion rates in the 1970s and predicts a substantial increase in educational attainment for postboomers."     

Agricultural practices in Eastern Maputaland

The various agricultural practices employed in eastern Maputaland are described.

Agricultural strategies utilized in Maputaland are low in productivity but aim to minimize risk. The area is marginal for agriculture as soils are sandy and rainfall unreliable. Insects and plant diseases accentuate the problem. Infrastructure is lacking in the area. Traditional agricultural systems predominate.

Farming in the area is generally of a subsistence nature and can be divided into gardening, swamp farming and field cropping. Steps towards modernization of agriculture must take into account all existing constraints.     

Maximizing purchase decision factors other than price

Assessing and acquiring technology does not have to be chaotic, driven solely by price, clinical preference, and emotion. With the tools available, it can be distilled to a process of organized common sense, which results in maximum flexibility for the user and allows materiel managers to procure the best, most cost-effective equipment for the hospital.     

The case of the unpopular pay plan

Three years after launching the team-based Quality For All program, Top Chemical Company CEO Sam Verde was searching for a team-based compensation system that would reflect his company's new philosophy. With a committee gathered to discuss the issue, Verde confronts the fact that changing pay plans is an issue few people can agree on. "Very simply," explains vice president for compensation Gilbert Porterfield, "the plan is designed to give employees working on teams real incentives for constant improvement and overall excellence. The variable aspect of the system pays employees for the performance of their group." This doesn't sit well with the others. "It's going to punish teams like mine for the failings of others instead of rewarding us for the work we do and have already done," says packaging team representative Ruth Gibson. Another committee member feels that team-based anything is a "motivational happy land that doesn't square with how people really work." While Verde likes the proposed pay plan, he has doubts over whether his employees will accept the risk. Upper management has no problem basing 60% of its pay on TopChem's performance. But getting line employees to risk part of their salaries--even as little as 4%--on the ups and downs of the chemical industry may be more trouble than it's worth. Four experts on compensation reveal where Top Chemical went wrong in its plan and how Sam Verde might bring about change successfully.     

On modeling incentive systems which utilize pollution charges for pollution abatement

This paper examines a scheme of economic incentives for environmental protection, in which spatially differentiated pollution taxes are in use in compensating the pollution abatement costs. A simple mathematical model is described which determines an incentive system that encourages polluters to reduce the discharges to an acceptable level of ambient quality standards in a cost-effective manner. It is shown that the vector of pollution charges has to be proportional to the marginal abatement cost vector, but is smaller than the latter in magnitude. It is demonstrated that a necessary incentive effect may be achieved even if the total pollution charge is much lower (about three times) than the total abatement costs. It is also estimated how this charge incentive system reconciles conflicting criteria of cost-effectiveness and of equity. These conclusions are verified by numerical experiments with real data.