Shortening the distance between Edgeworth and Berry–Esseen in the classical case

We obtain near optimal Berry–Esseen bounds for standardized sums of independent identically distributed random variables. This is achieved by distinguishing the lattice and the non-lattice cases, as one-term Edgeworth expansions do. The main tool is an easy inequality involving the usual second modulus of continuity, in substitution of Esseen's smoothing inequality. An illustrative example concerning the exponential distribution is also considered.     

Urban forest and environmental inequality in Campos dos Goytacazes,Rio de Janeiro,Brazil

Social and spatial inequality regarding environmental resources and services is one of most complex issues affecting contemporary urban life. The objective of this research is to study the spatial distribution of trees in public areas in Campos dos Goytacazes, Rio de Janeiro, Brazil. This research presents data gathered in ten neighborhoods in Campos. These neighborhoods were split into three distinct groups using wealth levels. Data obtained include the number of trees and private gardens and tree species diversity per neighborhood street. Our results demonstrate that the wealthier neighborhoods have both the highest tree biodiversity and number of trees. In contrast, the poorer neighborhoods present a low biodiversity level and fewer tree species. Our results also showed that age of the neighborhoods was not a factor in explaining the number of trees in public spaces. Socioeconomic and education levels of the population seem to play a more causal on tree quantity and species diversity. This inequality stresses a problem with environmental justice, a characteristic of Brazilian cities intrinsically connected to urban sustainability.     

Strategies for Developing Cross-Cultural Sensitivity

Developing cross-cultural sensitivity currently is a primary challenge for social work educators. In this article, the authors propose the use of an analogy between child abuse and cultural wounding to provide a metaphorical understanding of minority cultures. From the overtly physical wounding of castration to the more subtle forms of psychological wounding that occur through denying the importance or value of one’s culture, the range of cultural wounding that occurs as a result of oppression, devaluing or stigmatizing is presented. It will be shown that the use of the child abuse metaphor will allow the student to understand the feelings and behaviors of those oppressed and through a new level of empathy, learn to join the oppressed in a different type of problem—solving effort.     

Signed binomial approximation of binomial mixtures via differential calculus for linear operators

We obtain sharp estimates in signed binomial approximation of binomial mixtures with respect to the total variation distance. We provide closed form expressions for the leading terms, and show that the corresponding leading coefficients depend on the zeros of appropriate Krawtchouk polynomials. The special case of Pólya–Eggenberger distributions is discussed in detail. Our approach is based on a differential calculus for linear operators represented by stochastic processes, which allows us to give unified proofs.