Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Struggles over family land? Tree crops, land and labour in Ghana's Brong-Ahafo region

Agricultural land use in much of Brong-Ahafo region, Ghana has been shifting from the production of food crops towards increased cashew nut cultivation in recent years. This article explores everyday, less visible, gendered and generational struggles over family farms in West Africa, based on qualitative, participatory research in a rural community that is becoming increasingly integrated into the global capitalist system. As a tree crop, cashew was regarded as an individual man's property to be passed on to his wife and children rather than to extended family members, which differed from the communal land tenure arrangements governing food crop cultivation. The tendency for land, cash crops and income to be controlled by men, despite women's and young people's significant labour contributions to family farms, and for women to rely on food crop production for their main source of income and for household food security, means that women and girls are more likely to lose out when cashew plantations are expanded to the detriment of land for food crops. Intergenerational tensions emerged when young people felt that their parents and elders were neglecting their views and concerns. The research provides important insights into gendered and generational power relations regarding land access, property rights and intra-household decision-making processes. Greater dialogue between genders and generations may help to tackle unequal power relations and lead to shared decision-making processes that build the resilience of rural communities.

Shared parenting, law and policy: considering power within the framework of autopoietic theory

This paper uses the last few decades’ developments in the area of shared parenting to explore power within the framework of autopoietic theory. It traces how, prompted by turbulence from the political subsystem, family law has made several unsuccessful attempts to solve the perceived problem of post-separation dual-household parenting. It agrees with Luhmann and Teubner that closed autopoietic systems’ developments are limited by their normative and cognitive frameworks, and also argues that changes, which have occurred in family law, show that closed social systems do not function in total isolation. It considers power as ego’s ability to limit alter’s choices. In our functionally differentiated society, with its recent proliferation of communication, power appears more diffuse and impossible to plot into causal one-way relationships.

Family, locality and nationality: vernacular adaptations of the Expugnatio Hibernica from late medieval Ireland

This paper examines two late medieval abridgements of Gerald of Wales’ Expugnatio Hibernica, one in Hiberno-English and one in Irish. The manuscripts in which these adaptations survive all date from the late fifteenth century and appear to bear witness to a sudden and pronounced interest in Gerald’s text. Drawing on evidence from the extant manuscripts, this paper explores the readerships of, and the nature of their interest in, these adaptations. A key conclusion is that the Expugnatio, which gives prominence to Gerald's own relatives, the Fitzgeralds, was valued as a family history by the Fitzgerald Earls of Kildare and their allies. The Earls were at the height of their power in the period in which these manuscripts were produced. Examination of this neglected evidence of the adaptation and readership of the Expugnatio in late medieval Ireland suggests that, for some medieval readers at least, the primary identities Gerald’s text expressed were familial and local rather than colonial or national.