Longitudinal data analysis based on generalized linear partially varying-coefficient models

In this article, we consider a generalized linear partially varying-coefficient model for longitudinal data analysis. A local quasi-likelihood method is proposed to estimate the constant-coefficient and varying-coefficient functions simultaneously based on the local polynomial kernel regression. The corresponding standard error estimates are derived. Large sample properties are investigated. The proposed methodologies are demonstrated by extensive simulation studies and a real example.     

Optimal bivariate step-stress accelerated life test for Type-I hybrid censored data

This paper presents a step-stress accelerated life test for two stress variables to obtain optimal hold times under a Type-I hybrid censoring scheme. An exponentially distributed life and a cumulative exposure model are assumed. The maximum-likelihood estimates are given, from which the asymptotic variance and the Fisher information matrix are obtained. The optimal test plan is determined for each combination of stress levels by minimizing the asymptotic variance of reliability estimate at a typical operating condition. Finally, simulation results are discussed to illustrate the proposed criteria. Simulation results show that the proposed optimum plan is robust, and the initial estimates have a small effect on optimal values.     

Statistical analysis of the Lomax–Logarithmic distribution

In this paper we introduce a three-parameter lifetime distribution following the Marshall and Olkin [New method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84(3):641–652] approach. The proposed distribution is a compound of the Lomax and Logarithmic distributions (LLD). We provide a comprehensive study of the mathematical properties of the LLD. In particular, the density function, the shape of the hazard rate function, a general expansion for moments, the density of the rth order statistics, and the mean and median deviations of the LLD are derived and studied in detail. The maximum likelihood estimators of the three unknown parameters of LLD are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance–covariance matrix. Finally, a real data set is analysed to show the potential of the new proposed distribution.     

基于谐波特征矩阵的负载识别

给出一种基于电流谐波特性矩阵的负载识别方法，并利用二进制数独立不重复的特性，给出了求多个数据随机组合计算值的算法。此方法首先采样计算各单一负载的谐波特性，利用随机组合计算算法得到各种负载组合后的谐波特性矩阵。之后实时地计算当前电网中的电流谐波值，并将此值与谐波特性矩阵中的数据进行比对，与吻合数据对应的负载即为当前工作在电网中的负载。此方法在试验中取得了很好的效果。     

Optimal sample size allocation for accelerated life test under progressive type-II censoring with competing risks

In this article, we study the optimization problem of sample size allocation when the competing risks data are from a progressive type-II censoring in a constant-stress accelerated life test with multiple levels. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher information matrix. We propose three optimization criteria and two search scenarios to obtain the sample size allocation at each stress level. Some numerical results are studied to illustrate the usage of the proposed methods.     

Efficiency of schemes of sampling from the inverse gaussian-weibull mixture model

The objective of this paper is to study the efficiency of sampling schemes suggested by Hosmer(1973), termed models Ml and M2, relative to the regular random sampling, termed model MO, when samples are drawn from a population having the Inverse Gaussian-Weibull (IG-W) mixture distribution.

It has been shown that whether the efficiency is based on relative variances of the maximum likelihood estimates (ML,E's) of the components of the vector of parameters or on the generalized variances of the MLE's of that vector, Hosmer's models Ml or M2 perform better than model MO.     

A note on the generalisation of cochran’s theorem

Khatri (1968) has extended Cochran’s theorem (1934) to matrices which are not necessarily symmetric. An alternative proof of the theorem is furnished here with some generalization with respect to one of Khatri’s conditions.     

浅谈图论与线性代数的联系

图论是数学的一个重要分支,它的应用也十分广泛,与此同时它与其他的数学分支也有着重要的联系,本文主要讨论图论与线性代数的联系,我们将运用线性代数中的内容解决图论中的问题。     

基于关系网络的新型学习控制

设计了一种不同于传统智能算法如自适应控制与模糊控制等的智能控制算法,该算法基于目标输入关系网络, 借鉴强化学习的思想,采用输出试探与评价进行学习,是一种模型无关的控制算法,该算法可以与随机优化算法结合,通 过实验,验证了其在控制过程中有效性,并通过与遗传算法结合,验证了与遗传算法相结合的该智能算法的控制效果。