A LIMIT THEOREM FOR THE GALTON-WATSON PROCESS WITH IMMIGRATION

It is difficult, in general, to optain an explicit expression for the limiting-stationary distribution, when such a distribution exists, of the process in which teh individuals reproduce as in a Galton-Wastson process, but are also subject to an independent immigration component at each generation. The main result of this paper is a limit theorem which suggests a means of approximating this distribution by a gamma density, when the mean of the offspring distribution is less than, but close to, unity. Following along the same lines, it is easy to show that a similar limit theorem holds for the asymptotic conditional limit distribution of an ordinary subcritical Galton-Watson process, whereby this distribution approaches the exponential as the offspring mean approaches unity.     

Estimation of infant mortality rates categorized by social class for an Australian population

"This paper reports a method of deriving simultaneous confidence intervals for [Australian] infant mortality rates based on a birth sample rather than the birth population. The large sample size employed enables the use of asymptotic multivariate techniques....[The authors find that] where the population distribution of a characteristic such as social class is not known, confidence intervals can be estimated for rates based on the distribution of this characteristic in a sample of that population."     

Common Factors That Enhance the Quality of Life for Women Living in Their Own Homes or in Aged Care Facilities

A qualitative study of older women living in their own homes and older women living in aged care facilities found that the concerns of the women living in their own homes were the realities of life for the residents in the aged care facilities. Twenty-five female residents across two facilities and 11 older women living in their own homes were interviewed. The positive outcomes of aging at home are relevant and desirable for residents of aged care facilities. A smooth transition from community living to residential aged care involves retaining some of these positive aspects of their lives.     

The Hopes and Fears of Older Australians: for Self,Family, and Society

This study refutes negative ageist stereotypes of how older people view themselves and society by reporting on their freely expressed main hope and main fear for the future. Data were collected through a population based cross‐sectional telephone interview survey conducted in NSW in 1999/2000. Participants (n=8,881) were randomly selected community dwelling older Australians (65+). Analyses revealed that participants were more likely to express a hope than a fear, and that a sizeable proportion of their hopes and fears were focused outwardly to family, or more broadly to social and environmental issues both locally and globally. These latter hopes and fears indicate awareness, interest and concern on a wide range of issues outside self and family. Some differences by gender and age were identified but views varied considerably among individuals. These findings provide evidence to dispel the negative image of older people as a self interested undifferentiated group whose members become progressively fearful as they age, by revealing an altruistic and outwardly focused dimension.     

Professional collaboration in services for mentally handicapped people

There has been growing academic and practitioner interest in the problems of and opportunities for joint working in the care of mentally handicapped people. The paper outlines alternative methods of such joint working and tests these against survey and case study evidence. Attention is drawn to the danger that joint working may have little impact at patient level and the paper recommends an emphasis on the appointment of frontline key workers.     

PROBABILITY APPROXIMATIONS FOR DIVISIBLE DISCRETE DISTRIBUTIONS

If an integer-valued random variable can be represented as a sum of independent random variables, then powerful tools exist to derive approximations to its distribution. We apply this idea to examples in some of which it is not clear how to give a physical interpretation to the independent sum-mands. We consider bounds on the accuracy of single term approximations, Edgeworth expansions and saddlepoint approximations for both individual probabilities and cumulative probabilities.