Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data

In this paper, a competing risks model is considered under adaptive type-I progressive hybrid censoring scheme (AT-I PHCS). The lifetimes of the latent failure times have Weibull distributions with the same shape parameter. We investigate the maximum likelihood estimation of the parameters. Bayes estimates of the parameters are obtained based on squared error and LINEX loss functions under the assumption of independent gamma priors. We propose to apply Markov Chain Monte Carlo (MCMC) techniques to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. To evaluate the performance of the estimators, a simulation study is carried out.     

On the Nearness of Records to Population Quantiles with Respect to Order Statistics in the Sense of Pitman Closeness

In this paper, Pitman closeness criterion is used to compare the nearness of record values and order statistics from two independent samples to a specific population quantile of the parent distribution while the underlying distributions are the same. General expressions for the associated Pitman closeness probability are obtained when the support of the parent distribution is bounded and also unbounded. Some distribution-free results are achieved for symmetric distributions. The exponential and uniform distributions are considered for illustrative proposes and exact expressions are obtained in each case.     

Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the log GED are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and log-normal distributions, and to derive the asymptotic distribution of the partial maximum of an independent and identically distributed sequence obeying the log GED.     

The competing risks analysis for parallel and series systems using Type-II progressive censoring

Abstract

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach.     

工程质量政府监督多层次利益分配与激励协同机制探究

The implementation of the government supervision of the quality of the project is an international practice. The basic form of government supervision of engineering quality is government supervision on the quality behavior of the engineering main bodies and its results by the competent government department entrusted. Its essence is a dual principal-agent process. The frequent accidents of the engineering quality reflect the loss and failure of the government law enforcement supervision of the engineering quality to some extent. Its root lies in the lack of endogenous power in the law enforcement supervision of the project quality government supervisors in the law enforcement supervision. Therefore, the incentive coordination mechanism of the government supervision based on the multi-level interest distribution is worth explored. In views of the multi-level management system which is formed by the government departments, government quality supervision organizations, quality supervision team (or group) for the government supervision of engineering quality. The benefit distribution function between every party is constructed, and the game model of the multi-level incentive and coordination for the government supervision in engineering quality is built. To solve and deduce from the first stage of the cooperative game and the second stage of the non-cooperative game, the cooperative game can obtain the reward coefficient: . The coordination degree of the best effort can be obtained by the non cooperative game. The result shows that:the coordination degree of government engineering quality supervisor is related to the coordination costs, and had nothing to do with fixed costs. The benefit distribution coefficient not only depends on the efforts of the quality government monitors, but also on the efficiency of other parties' efforts. The quality supervisors of the project will also focus on the coordination with other parties when enhancing their management capabilities to improve the overall performance of project quality government supervision. The strategy of the incentive coordination mechanism for the supervision and cooperation of the project quality government is:the government quality supervision team should set up the supervisory team properly, improve the coordination efficiency and reduce the cost of supervision-coordination to maximize the value of self-motivation. Quality supervision team (or group) should establish the partnership to improve the coordination efficiency for achieving the maximization of their own incentive value.The model and conclusion of incentive synergy mechanism based on multi-level benefit allocation mechanism are researched. It can provide theoretical support and practice reference for the market governance and supervision of general public goods.     

The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

Multivariate normal mean–variance mixture distribution based on Birnbaum–Saunders distribution

A multivariate normal mean–variance mixture based on a Birnbaum–Saunders (NMVMBS) distribution is introduced and several properties of this new distribution are discussed. A new robust non-Gaussian ARCH-type model is proposed in which there exists a relation between the variance of the observations, and the marginal distributions are NMVMBS. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of this normal mean–variance mixture distribution is given. A simulation study and some real data are used to demonstrate the modelling strength of this new model.     

黄国雄教授商品流通理论研究回顾

黄国雄教授是中国现代商品流通理论的奠基人.文章通过文献梳理和实际观察,对黄国雄教授的商品流通理论研究进行了回顾.黄国雄教授的商品流通理论主要包括三个方面:在内容方面,聚焦于商品流通理论的研究;在方法方面,多使用经验主义范式;在主要贡献方面,奠定了现代商学理论的根基,具体包括提出了“商业创造价值论”“流通产业基础论”和“商道即人道论”等三大理论,以及建立了现代商学的学科体系.     

On An Intriguing Distributional Identity

For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω₁ → Ω₂ a continuous, strictly increasing function, such that Ω₁∩Ω₂?(a, b), but otherwise arbitrary, we establish that the random variables F(X) ? F(g(X)) and F(g^{? 1}(X)) ? F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U ? ψ(U) = ^dψ^{? 1}(U) ? U for U ～ U(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.