Growth of U.S. population, 1940–1971, in the light of an interactive two-sex model

Since it is logically impossible to hold constant both male and female age-specific fertility rates, the intrinsic growth rates or the net reproduction rates for males and females, based on that assumption, are internally inconsistent. The interactive two-sex model presented in this paper holds constant a set of bivariate age-specific fertility rates by age of men and women and allows the male and female age-specific fertility rates to adjust themselves to achieve stability. The model gives the same intrinsic growth rate for both sexes and generates intrinsic age-specific fertility rates and intrinsic net reproduction rates for males and females which are consistent and can operate simultaneously on a population. The model is applied to the U.S. data for 1940–1971, and the results are compared with those obtained from the one-sex models.     

Use of n-ary block designs in diallel crosses evaluation

To fill the gap between theory and practice of modern statistical designs, this paper presents the use of n-ary block designs in the evaluation of balanced incomplete block (BIB) designs for all the four Griffing's (1956) complete dialled crosses (CDC) systems, the construction of which is proposed here by adopting a suitable BIB design and associating its treatments with the crosses under a CDC system.     

An alternative formulation of the birth function in a two-sex model

The inconsistency in Lotka's stable population model (two different intrinsic growth rates for the two sexes) arises from the fact that he considers two equations (for male and female births), and not because his equation for one sex does not involve the other. Many authors in the past have erroneously put emphasis on the latter point and modified Lotka's equations for male and female births. Since sex ratio at birth is constant, two independent equations for male and female births cannot exist. The correct approach is to attempt to form an equation for all births. The author followed this approach in his earlier works on the problem, but his birth functions were formulated from axiomatic considerations. The present paper provides a new birth function which has an intuitively appealing physical interpretation, and for which the interaction between the sexes is empirically determined from the data.     

Model-cum-design-based estimation of the prevalence rate of a disease in a locality using spatial smoothing

In this article, we study the problem of estimating the prevalence rate of a disease in a geographical area, based on data collected from a sample of locations within this area. If there are several locations with zero incidence of the disease, the usual estimators are not suitable and so we develop a new estimator, together with an unbiased estimator of its variance, which may be appropriately used in such situations. An application of this estimator is illustrated with data from a large-scale survey, which was carried out in the city of Kolkata, India, to estimate the prevalence rate of stroke. We show that spatial modelling may be used to smooth the observed data before applying our proposed estimator. Our computations show that this smoothing helps to reduce the coefficient of variation and such a model-cum-design-based procedure is useful for estimating the prevalence rate. This method may of course be used in other similar situations.     

Single replicate orthogonal block designs for circulant partial diallel crosses

Some incomplete block designs for partial diallel crosses have been given in the literature. These designs are obtained by regarding the number of crosses as treatments, and consequently require several replications of each cross. The need for resorting to a partial diallel cross itself implies that it is desired to have fewer crosses. A method for constructing single replicate incomplete block designs for circulant partial diallel crosses is provided in this paper. The designs are orthogonal, and thus they retain full efficiency for estimation of the contrasts of interest.     

Labor-use efficiency in Indian banking: A branch-level analysis

This paper uses data envelopment analysis to measure labor-use efficiency of individual branches of a large public sector bank with a sizable network of branches across India. We find considerable variation in the average levels of efficiency of bank branches across the four metropolitan regions considered in this study. In this context, we introduce the concept of area or spatial efficiency for each region relative to the nation as a whole. Our findings suggest that the policies, procedures, and incentives handed down from the corporate level cannot fully neutralize the detrimental influence of the local work culture across different regions. Most of the potential reduction in labor cost appears to be coming from possible downsizing in the clerical and subordinate staff. Our analysis identifies branches that operate at very low levels of labor-use efficiency and possible candidates for increased supervision and control.