基于混合加权距离的毕达哥拉斯模糊TOPSIS多属性决策方法研究

针对决策信息为毕达哥拉斯模糊集的多属性决策问题，提出了一种基于混合加权测度的TOPSIS决策方法。在分析了现有距离测度方法不足的基础上，首先给出了一种新的毕达哥拉斯模糊距离测度——毕达哥拉斯模糊有序加权距离（PFOWD），并研究了该测度权重的确定方法；在PFOWD基础上，进一步提出了毕达哥拉斯模糊混合加权距离（PFHWD），同时探讨了其特征和与现有毕达哥拉斯模糊测度的关系；最后提出了一种基于PFHWD测度的毕达哥拉斯模糊TOPSIS多属性方法，并用实例验证了方法的有效性和可行性。     

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.     

消费者导向类型与电商全渠道决策研究

从现实出发，基于不同消费者导向类型研究了电商的全渠道决策问题。首先建立电商单渠道销售的基础模型，并得出最优产品组合、价格和交付时间。在此基础上，给出了消费者为产品导向型和渠道导向型情况下电商采取全渠道决策的条件，得出双渠道产品组合、价格及交付时间的最优决策；并进行了数值验证。研究发现，同一渠道提供的产品其最优价格相同，最优交付时间只和消费者耐心程度及交付成本函数有关。若消费者为产品导向型，仅当双渠道运营成本之差较小且消费者耐心程度较低时，电商进入线下渠道才有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供剩余产品。若消费者为渠道导向型，电商进入线下渠道必然有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供所有产品。     

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.     

Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

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%.