The problem of multiple causation in population analysis, with particular reference to the poplygamy-fertility hypothesis

The hypothesis that polygyny is associated with higher fertility than monogamy was evaluated. An assessment of previous studies and of the results of a 1966-1967 study comparing the fertility levels of polygynously and monogamously married women in a rural and an urban population in Nigeria lead to the conclusion that the hypothesis was useless. The hypothesis was judged to be useless because 1) fertility rates are the product of multiple influences; 2) it is too difficult to separate out these multiple influences, given the variability involved in polygynous practices and the inadequates of the data; and 3) the influence of polygyny on fertility is too slight to take into account. In the Nigerian study, the fertility of 2742 monogamously married women was compared with the fertility of 1261 polygynously married women. Preliminary analysis revealed that the fertility rate was higher for polygynously married women; however, when marriage duration was controlled, there was no significant differences between the fertility rates observed for the polygynously and monogamously married women living in rural areas nor those living in urban area.     

The quincunx: history and mathematics

Received: December 30, 1999; revised version: July 19, 2000     

Maximum entropy sampling and optimal Bayesian experimental design

When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.     

On some probability distributions associated with random walks

The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given.     

Facilitating the Transition from Student to Social Worker: Challenges of the Younger Student

Abstract

The transition from student to social worker is a process which social work educators cannot control but can facilitate. Through classroom and field instruction faculty assumer responsibility of preparing students' professional knowledge, skills, and values; however, our responsibilities should extend beyond curriculum delivery. Drawing on Schlossberg's (1984) model of transitions, this article discusses two primary factors which affect the younger student in transition—developmental needs and the external environment—and strategies for assisting in the transition through intervention in academic advising and teaching roles.     

The behavior of estimated measures of association in small and moderate sample sizes for 2×3 tables

We consider the distributions of Goodman and Kruskal's G, Kendall's tau-b, and correlation coefficients rho and rho-s for sample sizes 10‘10’40 from 2×3 tables. The results are compared with asymptotic theory. It is found that the convergence of G to its asymptotic normal distribution is much slower than the convergence of the other measures to theirs, and that G is more likely to be significantly biased. However, the variances and biases of all four measures come close to their asymptotic values for quite moderate sample sizes.     

The pitman nearness criterion and its determination

A general method for determining Pitman Nearness is given In the case of univariate estimators. This method is then applied to some estimation problems. The concept of Pitman Nearness is also generalized to the multivariate case. The James-Stein estimators are used to illustrate the multivariate comparison.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.     

On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.