Inequalities for linear combinations of gamma random variables

We study the behavior of the tail probabilities of weighted averages of certain independently and identically distributed random variables as the weights are varied. We show that the upper and lower tails are smallest when all the weights are equal. Our results apply to exponential, chi-squared, gamma, and Weibull random variables.     

Child Protection,Public Services and the Chimera of Market Force Efficiency

The different agencies and professions that contribute towards child protection services have all recently had to begin to take account of the impact of market forces on their activities, yet detailed consideration of the consequences of this are slow to emerge. This article begins to consider these changes for child protection services. Having briefly described the child protection systems in England and Wales, it looks at the theoretical underpinning to the market forces approach which has become a significant ideological position in respect of public services in the UK and increasingly throughout the world. The article then considers the impact of a market forces approach on the organization of child protection services in relation to coordination versus fragmentation, profit versus professionalism, planning versus short-termism, and cooperation versus competition. It concludes that the argument that a market forces approach to child protection will lead to greater efficiency in relation to protecting children is a chimera. The article is thus of relevance for the different professions who contribute to child protection services in all countries where a market approach to public welfare is being suggested or implemented.     

A constructivist approach to the help-seeking process of clients: A response to cultural diversity

The issue of cultural diversity presents clinicians with both delemmas and opportunities. To deal with such a challenge, I have proposed a constructivist approach to the help-seeking process of clients from diverse ethnoracial backgrounds. A model of clients' help-seeking processes provides a useful and systematic frame for clinicians to understand clients' construction of their problem situations and possible solutions. It provides a useful key for clinicians non-presumptuously to understand clients' subjective experiences, and to enhance clients' ability to resolve problems.     

Stochastic blockmodels: First steps

A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.