On the Exact and Near-Exact Distributions of the Product of Generalized Gamma Random Variables and the Generalized Variance

In this article, the authors first obtain the exact distribution of the logarithm of the product of independent generalized Gamma r.v.’s (random variables) in the form of a Generalized Integer Gamma distribution of infinite depth, where all the rate and shape parameters are well identified. Then, by a routine transformation, simple and manageable expressions for the exact distribution of the product of independent generalized Gamma r.v.’s are derived. The method used also enables us to obtain quite easily very accurate, manageable and simple near-exact distributions in the form of Generalized Near-Integer Gamma distributions. Numerical studies are carried out to assess the precision of different approximations to the exact distribution and they show the high accuracy of the approximations provided by the near-exact distributions. As particular cases of the exact distributions obtained we have the distribution of the product of independent Gamma, Weibull, Frechet, Maxwell-Boltzman, Half-Normal, Rayleigh, and Exponential distributions, as well as the exact distribution of the generalized variance, the exact distribution of discriminants or Vandermonde determinants and the exact distribution of any linear combination of generalized Gumbel distributions, as well as yet the distribution of the product of any power of the absolute value of independent Normal r.v.’s.     

Computationally simple estimation and improved efficiency for special cases of double truncation

Doubly truncated survival data arise when event times are observed only if they occur within subject specific intervals of times. Existing iterative estimation procedures for doubly truncated data are computationally intensive (Turnbull 38:290–295, 1976; Efron and Petrosian 94:824–825, 1999; Shen 62:835–853, 2010a). These procedures assume that the event time is independent of the truncation times, in the sample space that conforms to their requisite ordering. This type of independence is referred to as quasi-independence. In this paper we identify and consider two special cases of quasi-independence: complete quasi-independence and complete truncation dependence. For the case of complete quasi-independence, we derive the nonparametric maximum likelihood estimator in closed-form. For the case of complete truncation dependence, we derive a closed-form nonparametric estimator that requires some external information, and a semi-parametric maximum likelihood estimator that achieves improved efficiency relative to the standard nonparametric maximum likelihood estimator, in the absence of external information. We demonstrate the consistency and potentially improved efficiency of the estimators in simulation studies, and illustrate their use in application to studies of AIDS incubation and Parkinson’s disease age of onset.     

Estimation of scale functions to model heteroscedasticity by regularised kernel-based quantile methods

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Regularised kernel methods (RKMs) – also called support vector machines in a wide sense – are well established to estimate location functions like the conditional median or the conditional mean. We investigate the estimation of scale functions by RKMs when the conditional median is unknown, too. Estimation of scale functions is important, e.g. to estimate the volatility in finance. We consider the median absolute deviation (MAD) and the interquantile range as measures of scale. Our main result shows the consistency of MAD-type RKMs.     

On two-dimensional optimal controlled nearest proportional to size sampling designs

Using quadratic programming and utilizing the concept of ‘nearest proportional to size sampling design’, we propose a method for two-dimensional optimal controlled selection, which ensures zero probability to non-preferred samples. An alternative strategy for estimation of population total and variance is also suggested. The utility of the proposed procedure is demonstrated with the help of examples.     

Social work as art revisited

In this article we revisit 'social work as art', noting that it is just over 20 years since England's book on the subject provided a direction for the profession's early defence against empiricism. Those who picked up the ball handed to them by England tended to focus discussions of social work's 'art' on its soft side, embedding it in notions of 'creativity', 'meaning', 'self-expression', 'intuition' and 'quality', all of which were said to characterise the 'aesthetic dimensions' of social work practice as a counterpoint to the rising tide of hard empiricism, proceduralism and managerialism. Within these 'aesthetic dimensions', proponents of social work as art sought to resolve tensions through advocating a value-based 'artistic' approach to care. Against this we argue that art is struggle and resolution, soft and hard, joy and grief. Further, we posit that social work's art lies not in the social worker as artist but rather in social work as the 'work' of art, which is implicitly a 'non-productivist' endeavour. In a fundamental sense we argue that it is the art of social work and not the social worker that assembles what is practice, that provides bounds and lets everything stand in relation to everything else. This enables us to construct a speculative 'radical agonistics' for social work that draws attention to the relation between art, truth and event. In so doing, we substitute a subjectivist reading of social work as art with an ontological analysis drawing on Heidegger's phenomenology, supplemented by the work of Alain Badiou, to cast social work as art first, as artistic attunement, and second, as an art in the service of a politics of liberation.     

Continuous Utility Functions Through Scales

We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.      

How We Can Promote Behavior That Serves All of Us in the Future

The health and vitality of relationships, groups, and society at large is strongly challenged by social dilemmas or conflicts between short-term self-interest and long-term collective interest. Pollution, depletion of natural resources, and intergroup conflict can be characterized as examples of urgent social dilemmas. This article advances a conceptual framework in which we analyze social dilemmas in terms of social and temporal concerns relevant to the social (individual vs. collective) and temporal (short-term vs. long-term) conflicts underlying social dilemmas. We discuss the plasticity of social orientations (altruism, cooperation, egalitarianism, individualism, competition, aggression) and temporal orientations (short-term orientation, future orientation), and illustrate their "logical effects" and "paradoxical effects" on behavior that supports collectively desired outcomes. This analysis enables us to suggest a set of novel recommendations for policy and intervention to help solve various social dilemmas in contemporary society.     

The Role of Maternal Behavior in the Relation between Shyness and Social Reticence in Early Childhood and Social Withdrawal in Middle Childhood

The moderating effect of maternal behavior in the relations between social reticence and shyness in preschool and subsequent social withdrawal was investigated. Eighty children (47 females) were judged for degree of social reticence during play with unfamiliar peers at the age of four and mothers completed the Colorado child temperament inventory (CCTI). At the age of seven, the children were coded for degree of social withdrawal during peer play and mothers and children were observed during structured and unstructured activities. Two significant interaction effects indicated that maternal report of shyness was a positive predictor of age‐seven social withdrawal when mothers lacked positivity; whereas observed social reticence was associated with higher degrees of social withdrawal when mothers were highly negative. Maternal positivity and negativity differentially influenced the development of social withdrawal in childhood, such that maternal negativity is associated with poor social functioning in children who have an established history of social withdrawal; whereas maternal positivity is associated with better social outcome for preschoolers who are viewed as temperamentally shy.     

Ethnic Differences in the Effects of Parental Depression on Preschool Children's Socioemotional Functioning

The present study describes the depressive symptomatology of 393 parents of prekindergarten children and assesses ethnic differences in the depression scores of these parents and their differential consequences for children's social competence. Data are drawn from the National Center for Early Development and Learning (NCEDL) classroom study, a national, longitudinal study examining the quality and outcomes of prekindergarten programs operated in schools or under the direction of state and local educational agencies, and the supplemental NCEDL familial and social environments study. Analyses indicated that Latino parents were more likely than African‐American and White parents to be depressed. However, as reported by both parents and teachers, behavioral outcomes for African‐American children of parents with elevated depressive symptomatology were worse than children of their Latino and White counterparts. Interactions between ethnicity and depressive symptomatology emerged in the parent‐child relationship, with African‐American parents with elevated depressive symptoms reporting significantly greater levels of conflict in the parent–child relationship than their non‐depressed counterparts. African‐American parents with elevated depression scores were also less likely to be in marital relationships than their non‐depressed counterparts. Among African‐American families, parent–child conflict served as a mediator of the effects of parental depression on child outcomes. Implications for intervention are discussed.