Comparing the Childrearing Lifetimes of Britain's Divorce-Revolution Men and Women

British men and women who became parents in the 1960s and 1970s were about to experience a new regime of marital instability. The effect of this on the balance between men's and women's contributions to childrearing is potentially very large. This study estimates the co-residential foundations of the new gender balance, focusing on the measurement of lifetime number of years of living with dependent-aged children. A variant of the family-status life table is used to combine two data sources: census panel observations of family status across three points ten years apart, and survey data on the years between censuses. One-quarter of women who became parents in the 1960s, and one-third of women who became parents in the 1970s, have been or will be a lone mother at some point. Lone parenthood is the main way in which women's childrearing lifetimes differ from men's, with seven and eight years respectively of lone motherhood per ever-lone-mother of the 1960s and 1970s parenting cohorts. Men's lone-father years and greater numbers of years spent in second families together provide an average of two years offset against women's lone mother years.     

Testing the scale parameter of the exponential distribution with known coefficient of variation

Assuming that there is a linear relationship between the parameters of a two-parameter exponential distribution, the distribution reduces to the one with known coefficient of variation. The problem of testing the scale parameter is considered using fixed sample and sequential testing procedures. A comparison of the two procedures shows that the difference between the fixed sample sizes and the expected sample sizes in the null case is remarkable. Therefore, a truncated test is proposed and its expected sample sizes in the null case are compared with those of the sequential test.     

A side sensitive modified group runs control chart to detect shifts in the process mean

Gadre and Rattihalli [5 Gadre, M. P. and Rattihalli, R. N. 2006. Modified group runs control charts to detect increases in fraction non-conforming and shifts in the process mean. Commun. Stat. Simul. Comput., 35: 225–240. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]] have introduced the Modified Group Runs (MGR) control chart to identify the increases in fraction non-conforming and to detect shifts in the process mean. The MGR chart reduces the out-of-control average time-to-signal (ATS), as compared with most of the well-known control charts. In this article, we develop the Side Sensitive Modified Group Runs (SSMGR) chart to detect shifts in the process mean. With the help of numerical examples, it is illustrated that the SSMGR chart performs better than the Shewhart's X¯ chart, the synthetic chart [12 Wu, Z. and Spedding, T. A. 2000. A synthetic control chart for detecting small shifts in the process mean. J. Qual. Technol., 32: 32–38. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]], the Group Runs chart [4 Gadre, M. P. and Rattihalli, R. N. 2004. A group runs control chart for detecting shifts in the process mean. Econ. Qual. Control, 19: 29–43. [Crossref] [Google Scholar]], the Side Sensitive Group Runs chart [6 Gadre, M. P. and Rattihalli, R. N. 2007. A side sensitive group runs control chart for detecting shifts in the process mean. Stat. Methods Appl., 16: 27–37. [Crossref], [Web of Science ®] [Google Scholar]], as well as the MGR chart [5 Gadre, M. P. and Rattihalli, R. N. 2006. Modified group runs control charts to detect increases in fraction non-conforming and shifts in the process mean. Commun. Stat. Simul. Comput., 35: 225–240. [Taylor & Francis Online], [Web of Science ®] [Google Scholar]]. In some situations it is also superior to the Cumulative Sum chart p9 Page, E. S. 1954. Continuous inspection schemes. Biometrika, 41: 100–114. [Crossref], [Web of Science ®] [Google Scholar]] and the exponentially weighed moving average chart [10 Roberts, S. W. 1959. Control chart tests based on geometric moving averages. Technometrics, 1: 239–250. [Taylor & Francis Online] [Google Scholar]]. In the steady state also, its performance is better than the above charts.     

Alternating sums of sub-diagonal product moments of order statistics

A relation satisfied by the product moments of order statistics from an arbitrary continuous distribution symmetric about the origin has been established in this paper. We have shown that in such a situation, for samples of even size, sum of the sub-diagonal product moments of order statistics with alternating plus and minus signs assumes a compact form.     

Membranes,mitochondria and amoebae: shape models

Most real-world shapes and images are characterized by high variability- they are not rigid, like crystals, for example—but they are strongly structured. Therefore, a fundamental task in the understanding and analysis of such image ensembles is the construction of models that incorporate both variability and structure in a mathematically precise way. The global shape models introduced in Grenander's general pattern theory are intended to do this. In this paper, we describe the representation of two-dimensional mitochondria and membranes in electron microscope photographs, and three-dimensional amoebae in optical sectioning microscopy. There are three kinds of variability to all of these patterns, which these representations accommodate. The first is the variability in shape and viewing orientation. For this, the typical structure is represented via linear, circular and spherical templates, with the variability accomodated via the application of transformations applied to the templates. The transformations form groups: scale, rotation and translation. They are locally applied throughout the continuum and of high dimension. The second is the textural variability; the inside and outside of these basic shapes are subject to random variation, as well as sensor noise. For this, statistical sensor models and Markov random field texture models are used to connect the constituent structures of the shapes to the measured data. The third variability type is associated with the fact that each scene is made up of a variable number of shapes; this number is not assumed to be known a priori. Each scene has a variable number of parameters encoding the transformations of the templates appropriate for that scene. For this, a single posterior distribution is defined over the countable union of spaces representing models of varying numbers of shapes. Bayesian inference is performed via computation of the conditional expectation of the parametrically defined shapes under the posterior. These conditional mean estimates are generated using jump-diffusion processes. Results for membranes, mitochondria and amoebae are shown.     

The uses and users of population projections in Australia

It is widely recognized that population projections are increasingly used in formulating policy in many public and private sectors. However, little information exists on the nature of the projections or their users. This paper reports the results of a survey conducted to rectify this situation. The results confirm that the applications of projections are very broad and that the prime area of increase has been in small-area projections. At this level many users make their own projections rather than use official projections and the paper reviews the methodology used to make these projections. A number of suggestions are made for improving communication between national and subnational producers and local users. We would like to thank the Australian Population Association, and in particular the Secretary, Dianne Rudd, for providing us with address labels of members of the Association. We would also like to thank the Australian Bureau of Statistics, in particular Shail Jain, for advice on the development of the questionnaire. The comments of the two anonymous referees were very helpful. Finally we wish to thank our respondents for their co-operation, and especially those who wrote to encourage us in this work.