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.     

A generalized maximum likelihood characterization of the normal distribution

LetP be a probability measure on ℝ andI _x be the set of alln-dimensional rectangles containingx. If for allx ∈ ℝⁿ and θ ∈ ℝ the inequality holds,P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher’s (1961) maximum likelihood characterization of the normal density to a characterization ofN(0, σ²) amongall distributions (including those without density). The m.l. principle used is that of Scholz (1980).     

The excess burden of the tax and social premium system for Dutch married women

Summary The excess burden of a tax is the diminution of utility above that which would have occurred had the tax been collected as a lump sum. Computing the excess burden for the 1983 and 1985 Dutch tax and social premium system enables a partial welfare evaluation of the recent changes in the system, the so-called Tweeverdienersmaatregelen. Based on the equivalent and compensating variation, the excess burden as a percentage of the taxes and social premiums for the 1983 and 1985 system are valued at 27010 and 84010, and 37010 and 58010 respectively. This result indicates that, welfare-theoretically, the old system seems preferable to the new one.The author wishes to thank Hans Doodeman, Paul Renaud and Jacques Siegers for their critical remarks on an earlier version of this article.     

Projecting the future size and health status of the U.S. elderly population

"A projection model based on a multivariate continuous state, stochastic process is presented. The model allows multiple time-varying covariates to be used so parameters can be estimated from time series information on health changes and mortality, and their interaction. Health changes are simulated by altering parameters controlling the age trajectory and diffusion of risk factor means, variances, and covariances....By increasing the information used in projections it may be possible to better (a) anticipate the state of health at extreme ages, (b) forecast changes in health at specific ages over time, (c) stimulate the effects of specific interventions, and (d) determine the sensitivity of outcomes to a range of interventions."     

Economic humidity control: an alternative to reheat

Heat pipe technology will have a significant impact on the power consumption of many manufacturing industries, the installation costs of new or replacement air conditioning systems, and on electric utility peak demands.     

Couple's literacy level and acceptance of family planning methods: Lorenz curve analysis

The authors study the acceptance of family planning methods according to the level of couple's literacy in 14 states in India during 1986-87, using the Lorenz curve. The Gini Concentration Ratio and Index of Dissimilarity were calculated by level of couple's literacy for vasectomy, tubectomy, IUD, and all method combined. Firstly, analysis found literates to have accepted vasectomy and IUD more than tubectomy. Secondly, among the 3 methods, a high Gini Concentration Ratio was found for vasectomy when the wife was literate. Moreover, when the wife was literate, the Gini Concentration Ratio of IUD acceptance was higher than the acceptance of IUD by the wife whose husband was literate. Thirdly, the same trend was observed when the husband was illiterate. It is therefore clear that the level of a woman's literacy is a key factor in securing the acceptance of male or female methods of family planning. Planners should therefore concentrate on literacy programs for females independently of their age. Increasing the level of female literacy may ultimately help improve the understanding of family planning methods, while these women may also motivate their husbands to undergo vasectomy which will ultimately foster the success of the family planning program.     

Lifecourse migration and redistribution of the elderly across U.S. regions and metropolitan areas

This analysis investigates the assertion that the baby-boom cohorts, by virtue of their large size and new lifecourse redistribution tendencies, are likely to initiate significant shifts in the distribution of the elderly population as these cohorts enter into the 65-and-older age categories. The author contends that cohorts' pre-elderly lifecourse migration patterns should be incorporated into studies of elderly population distribution shifts. 2 questions are addressed: will the new lifecourse migration patterns provide for a more deconcentrated redistribution of the baby-boom cohorts, both prior to and after their entry into the elderly age categories, than the lifecourse migration patterns followed by earlier cohorts; and will the new lifecourse distribution pattern lead, in the long run, to a significantly more deconcentrated distribution of the elderly population. The examination of these 2 questions focuses, largely, on redistribution across 9 broad regional and metropolitan area groupings defined on the basis of 3 census regions -- the North (combining the Northeast and Midwest census regions), the South, and the West -- and 3 categories of metropolitan status -- large metropolitan areas (those with 1980 populations exceeding 1 million), other metropolitan areas, and nonmetropolitan areas. The comparison of "new" versus "old" lifecourse migration patterns contrasts the census-based age-specific migration stream rates, registered over the 1975-80 period, with those registered over the 1965-70 period. Given the sharp and broad-based shift toward deconcentrated redistribution which characterized practically all segments of the population during the 1970s, it is assumed that the age-specific migration patterns observed over the 1975-80 period approximate the more deconcentrated redistribution tendencies which will be adopted by the baby-boom cohorts (and their successors) over the remainder of their lifecourse. The 1965-70 net migration rates point up the aggregate redistribution implications associated with the "old" lifecourse migration stream patterns. Among the rates for North large metropolitan areas, the only positive net migration is observed for the 25-29 age category; the greatest net outmigration rate is shown for the 65-69 age category. The rates for South nonmetropolitan areas are negative for all age categories under age 55, and most accentuated outmigration is shown during the young-adult years. The positive net migration exhibited for the older adult and post retirement ages reflects the low outmigration rates from nonmetropolitan areas during these ages and the slight peaking of immigration for these years. The results of this analysis imply that more attention should be devoted to migration, over the entirety of the lifecourse, in future studies of population redistribution.