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.     

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.     

区块链技术在版权登记中的创新应用

随着数字版权时代的发展，作品的传播方式变得更加灵活，传播速度也更加迅捷。传统版权登记制度因存在登记成本较高、标准不一、泄露隐私等弊端，在实际应用中面临困境，区块链技术的出现为推动版权登记的适时发展提供了一种新思路。区块链技术应用于版权登记，其去中心化特质可以降低登记成本；分布式共享机制能够统一登记标准；难以篡改的性质能够提高登记的证明效力；弥补了既有版权登记制度的缺陷。同时，区块链技术利用自身特性建立新的版权信任机制，既能清晰地分配版权利益，又能创新传统的版权商业模式，推动版权市场的发展，最大化地利用版权的固有价值。区块链技术在与版权登记相结合的过程中，会出现一些技术上难以解决的问题，既无法对作品的独创性进行准确的判断，也无法发挥版权制度原有的公示力作用。因此，必须创新版权登记规则，加快制定区块链版权平台市场准入机制，并设置统一的监管机构，将区块链锁在版权制度的笼子里，防止出现滥用区块链技术的情形，以最终实现技术和法律的融合发展。     

试论投资基金的治理结构

投资基金的治理结构包含三个层次,即基金的各方当事人权利义务的制度安排、基金内部约束机制、外部市场压力及监管制度。针对我国基金治理结构目前存在的问题,可通过引入独立董事制度、将基金经理的报酬机制与公司的经营业绩挂钩、增强外部市场的竞争压力等途径,使之逐步完善。     

Parental Divorce and Interpersonal Trust in Adult Offspring

It has been proposed that recent increases in parental divorce have inhibited the development of trust among offspring. This proposition is tested by examining whether parental divorce is associated with offspring trust in parents, intimate partners, and others. Data come from the Marital Instability Over the Life Course Study. Results reveal that although parental divorce is negatively associated with trust, these effects largely disappear once the quality of the past parent‐teen relationship is taken into account. The one exception is trust in fathers where children of divorce remain at higher risk of mistrust. Trust in parents, intimates, and others is strongly linked to positive parent‐teen relationships regardless of parental divorce. Contemporary relationship experiences also influence trusting intimates and others.     

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.     

Robustness of a Class of Partial Diallel Cross Designs to the Unavailability of a Complete Block of Observations

Complete and partial diallel cross designs are examined as to their construction and robustness against the loss of a block of observations. A simple generalized inverse is found for the information matrix of the line effects, which allows evaluation of expressions for the variances of the line-effect differences with and without the missing block. A-efficiencies, based on average variances of the elementary contrasts of the line-effects, suggest that these designs are fairly robust. The loss of efficiency is generally less than 10%, but it is shown that specific comparisons might suffer a loss of efficiency of as much as 40%.     

信任关系的不完全信息动态博弈模型

以往理论研究与经验研究均指出"信任"关系具有外部效应,但对这种效应是怎样取得的并无共识.我们尝试建立一个不完全信息动态博弈模型,说明"信任"关系如何产生正的外部性,亦即产生超出个体理性计算之外的利益.我们的分析得出这样的结论,在一个多人互动的环境中,能否达到彼此信任,虽然会受到欺骗者所遭到的惩罚与欺骗利益多少的影响,但主要受到所处环境中具有信任者人数比例的影响.因此,可以说"信任"关系具有正的外部性,信任者人数越多,信任者所享受到的利益越大.