On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables

The distribution of the ratio of two independent normal random variables X and Y is heavy tailed and has no moments. The shape of its density can be unimodal, bimodal, symmetric, asymmetric, and/or even similar to a normal distribution close to its mode. To our knowledge, conditions for a reasonable normal approximation to the distribution of Z = X/Y have been presented in scientific literature only through simulations and empirical results. A proof of the existence of a proposed normal approximation to the distribution of Z, in an interval I centered at β = E(X) /E(Y), is given here for the case where both X and Y are independent, have positive means, and their coefficients of variation fulfill some conditions. In addition, a graphical informative way of assessing the closeness of the distribution of a particular ratio X/Y to the proposed normal approximation is suggested by means of a receiver operating characteristic (ROC) curve.     

Analysis of accelerated life tests with weibull failure distribution via generalized linear models

Efficient industrial experiments for reliability analysis of manufactured goods may consist in subjecting the units to higher stress levels than those of the usual working conditions. This results in the so called "accelerated life tests" where, for each pre-fixed stress level, the experiment ends after the failure of a certain pre-fixed proportion of units or a certain test time is reached. The aim of this paper is to determine estimates of the mean lifetime of the units under usual working conditions from censored failure data obtained under stress conditions. This problem is approached through generalized linear modelling and related inferential techniques, considering a Weibull failure distribution and a log-linear stress-response relationship. The general framework considered has as particular cases, the Inverse Power Law model, the Eyring model, the Arrhenius model and the generalized Eyring model. In order to illustrate the proposed methodology, a numerical example is provided.     

Convergence of non-linear functionals of smoothed empirical processes and kernel density estimates

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of non-linear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper [4], and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich [17] and of a modified version of the Kullback deviation.     

Parenting and children’s negative emotionality,self‐regulation,and academic skills: The moderating role of fathers’ residency

We examined whether fathers’ residency modified the associations among mothers’ supportiveness, father involvement, children’s negative emotionality during toddlerhood and children’s academic skills in pre‐kindergarten via children’s self‐regulation. Participants were 2,291 mothers (M_age = 23.24 years) and children (M_age = 14.99 months at Wave 1; 50.7% girls) in the Early Head Start Research and Evaluation Project. Results revealed distinctive associations by fathers’ residency: self‐regulation mediated the association between mothers’ supportiveness and academic skills only in resident‐father‐families. Self‐regulation mediated the association between negative emotionality and academic skills only in nonresident‐father‐families. The findings highlight the family processes of mothers, fathers, and children in low‐income family contexts that contribute to children’s academic skills, and how those family processes may vary by fathers’ residency status.     

A new value stream mapping approach for healthcare environments

Hospitals worldwide are giving a growing emphasis to the application of lean concepts in the healthcare sector, commonly known as ‘lean healthcare’. A fundamental tool that allows such implementations is the value stream mapping (VSM). The problem is that VSM models used in implementations of lean healthcare are simple adaptations of the original VSM model, which was initially directed towards manufacturing and may not always represent important support activities for the patient flow that directly impact treatment time. Within this context, this paper presents a new VSM approach for healthcare environments. This new VSM model, specifically designed for healthcare environments, contemplates all activities that directly affect the treatment time. In addition, the present paper also presents an action research in a Brazilian hospital where the proposed VSM model is compared to other VSM models found in the literature. The results shown that the proposed VSM model was able to identify some operational bottlenecks and wastes that interfere in the patient’s treatment that could not be identified by other mapping models studied.     

Cultural capital and perception of teacher-student relationships: Uncovering inequalities at schools in China

A long tradition in stratification research argues students with higher cultural capital are likely to be treated by their teachers as possessing the “right culture,” which positively affects their academic performance. Nevertheless, the literature has paid little attention to the role of students' perception in this process. Using two waves of the China Educational Panel Survey, we investigate how students' cultural capital affects their own understanding of teacher-student interactions, including its gender difference. Fixed effects regressions show a substantially positive effect of cultural capital on the perceived frequency of teachers praising and calling on students to answer questions across subjects. Nonetheless, we also find the lack of cultural capital is not punished and that the cultural capital's effect varies across its specific components and gender. These findings pave the way for elucidating the entire causal chain of intergenerational social inequality via cultural capital, teacher bias, students’ perception, and their educational outcomes.     

Incorporating preference information in interactive reference point methods for multiobjective optimization

In this paper, we introduce new ways of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of desirable values for each objective function. The idea is to take the desires of the decision maker into account more closely when projecting the reference point onto the set of nondominated solutions. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We identify different cases depending on the amount of additional information available and demonstrate the cases with examples. Finally, we summarize results of extensive computational tests that give evidence of the efficiency of the ideas proposed.