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.     

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%.     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

基于广义第二价格拍卖的多级带宽定价模型

在差异化服务机制的基础上，研究了互联网的多级带宽定价问题．通过导入广义第二价格拍卖，构造了基于差异化服务的互联网多级带宽定价模型．该模型能够有效地解决Internet拥塞问题，促进网络资源的合理利用．     

大中专在校学生考试分数的正态化线性转换

本文分析了考试记分方法中传统的绝对百分体制的缺陷，给出了一种正态化转换分数的算法，较适合于在校大中专学生学习水平的横向评价。     

基本剩余价值初探

剩余价值在其历史发展中相继地采取了绝对剩余价值、相对剩余价值和基本剩余价值的直接表现形式。基本剩余价值是在绝对剩余价值和相对剩余价值尚未产生或产而复失的历史场合中必须生产的 ,也是在实行绝对剩余价值生产和相对剩余价值生产的历史场合中 ,被它们凸现出来并使它们赖以产生的具有原先既定性 ,或扩张基础性和增生本体性的剩余价值形式。基本剩余价值生产与资本主义生产相始终 ,是资本主义生产目的的基本实现。它和绝对剩余价值、相对剩余价值在质和量及其历史形态上的差异 ,使剩余价值成为一个比较经济范畴