Rényi entropy of m-generalized order statistics

Abstract

Characterizing relations via Rényi entropy of m-generalized order statistics are considered along with examples and related stochastic orderings. Previous results for common order statistics are included.     

Social work students' conception on roles within the family in Greece

The present article is based on a small-scale research that took place with third-year students in the department of social work at Technological Educational Institute of Patras. During class the students, who undertake the laboratory course ‘Social Work with Families’, were asked to discuss family roles and depict them on drawings. Analysing their drawings in a qualitative approach the findings suggest that students adopt traditional views on family issues and the family roles. Various gender stereotypes and prejudices were reflected in students' drawings and this is alarming for both social work education and practice.     

Interval estimation for conformance proportions of multiple quality characteristics

A conformance proportion is an important and useful index to assess industrial quality improvement. Statistical confidence limits for a conformance proportion are usually required not only to perform statistical significance tests, but also to provide useful information for determining practical significance. In this article, we propose approaches for constructing statistical confidence limits for a conformance proportion of multiple quality characteristics. Under the assumption that the variables of interest are distributed with a multivariate normal distribution, we develop an approach based on the concept of a fiducial generalized pivotal quantity (FGPQ). Without any distribution assumption on the variables, we apply some confidence interval construction methods for the conformance proportion by treating it as the probability of a success in a binomial distribution. The performance of the proposed methods is evaluated through detailed simulation studies. The results reveal that the simulated coverage probability (cp) for the FGPQ-based method is generally larger than the claimed value. On the other hand, one of the binomial distribution-based methods, that is, the standard method suggested in classical textbooks, appears to have smaller simulated cps than the nominal level. Two alternatives to the standard method are found to maintain their simulated cps sufficiently close to the claimed level, and hence their performances are judged to be satisfactory. In addition, three examples are given to illustrate the application of the proposed methods.     

Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

The residual effect of a growth-decay mechanism and the distributions of covariance structures

The product of two independent or dependent scalar normal variables, sums of products, sample covariances, and general bilinear forms are considered. Their distributions are shown to belong to a class called generalized Laplacian. A growth-decay mechanism is also shown to produce such a generalized Laplacian. Sets of necessary and sufficient conditions are derived for bilinear forms to belong to this class. As a generalization, the distributions of rectangular matrices associated with multivariate normal random vectors are also discussed.     

Integrating Family Resilience and Family Stress Theory

The construct, family resilience, has been defined and applied very differently by those who are primarily clinical practitioners and those who are primarily researchers in the family field. In thisarticle, the family resilience perspective is integrated with conceptual definitions from family stress theory using the Family Adjustment and Adaptation Response (FAAR) Model in an effort to clarify distinctions between family resiliency as capacity and family resilience as a process. The family resilience process is discussed in terms of (a) the meaning of significant risk exposure (vs. the normal challenges of family life) and (b) the importance of making conceptual and operational distinctions between family system outcomes and family protective processes. Recommendations for future family resilience research are discussed.     

家族企业上市研究及其治理对策

证券发行核准制的实施为我国家族企业的进一步发展创造了难得的发展机遇 ,通过发行上市 ,家族企业在筹措到巨额发展资金的同时 ,又出现了新的“一股独大”现象 ,并由此滋生了许多亟待规范和完善的问题。