Estimation of monotone bivariate quantile residual life

The bivariate quantile residual life function can play an important role in statistical reliability and survival analysis. In many situations assuming a decreasing form for it is recommended. Here, we propose a new non-parametric estimator of this measure under such restriction. It has been shown that the new estimator is consistent and, with proper normalization, weakly converges to a bivariate Gaussian process. A simulation study shows that the proposed estimator is an alternative to the unrestricted estimator when the bivariate quantile residual life is decreasing. Finally, the new estimators are applied to two real data sets.     

Tobit regression for modeling mean survival time using data subject to multiple sources of censoring

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re‐weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large‐sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite‐sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait‐listed for kidney transplantation.     

Asymptotic properties of mean survival estimate based on the Kaplan-Meier curve with an extrapolated tail

Asymptotic distribution of the mean survival time based on the Kaplan-Meier curve with an extrapolated 'tail' is derived. A closed formula of the variance estimate is provided. Asymptotic properties of the estimator were studied in a simulation study, which showed that this estimator was unbiased with proper coverage probability and followed a normal distribution. An example is used to demonstrate the application of this estimator.     

基于文献萃取法的客户终生价值动态影响因素研究

客户终生价值(Customer Lifetime Value,CLV)是客户关系管理的重要内容。近年来,大量的学者结合不同的管理情境,探讨了诸多影响因素,试图推动动态CLV的建模工作。但是,这些工作均是零散、独立进行的,缺乏总结和整理,因而对动态CLV建模研究的推动比较有限。本文通过对41篇文献的精读,萃取出CLV的动态影响因素,概括为四类,即客户自身的、企业相关的、关系相关的和社会环境的四类动态影响因素。企业需要适应社会环境的影响,根据客户自身的影响因素进行合理的客户细分,从企业相关的影响因素提升着手,改善客户关系,最终获得客户的终生价值。     

The exponentiated G geometric family of distributions

We propose a new class of distributions called the exponentiated G geometric family motivated mainly by lifetime issues which can generate several lifetime models discussed in the literature. Some mathematical properties of the new family including asymptotes and shapes, moments, quantile and generating functions, extreme values and order statistics are fully investigated. We propose the log-exponentiated Weibull geometric and log-exponentiated log-logistic geometric regression models to cope with censored data. The model parameters are estimated by maximum likelihood. Three examples with real data expose quite well the new family.     

On nonparametric test for the residual probability order

Residual probability order is a partial ordering analog of the total order stochastic precedence which can be fruitfully applied in many reliability problems. We introduce a U-statistic test for the null hypothesis that two random variables are equally distributed versus the alternative that one strictly dominates the other in residual probability order. The critical value is obtained by normal approximation and bootstrap procedures. The performance of the test statistic is evaluated using a simulation study. Finally, a numerical example illustrating the theory is also given.     

Some bounds related to Harris family of distributions

As a lifetime distribution, Harris family of distributions are applied to the lifetime of a series system with random number of components. In this paper, properties of various ageing classes of mixtures of Harris family of distributions, where the tilt parameter of a Harris distribution is taken as a random variable, are studied. We obtain an upper bound for maximum error in evaluating its reliability function. Two bounds are also presented for survival function and expectation of the mixed Harris family. We also provide some interesting bounds for its residual survival function. Our results generalize several previous findings in this connection. Some illustrative examples are also provided.     

金代遗民文人李俊民生平行迹述考

李俊民当生于金世宗大定十六年（1176）六月十四日。25岁时中进士,走上仕途,先后任下邳守、沁水令、彰国军节度判官等职。一般认为其归隐是因金末时事动荡,其实主要是仕宦十余载,沉沦下僚,李氏遂厌倦而归隐。而后39至59岁,李氏在颠沛流徙申生活,先后在福昌、伊阳等地避难,甚至一度流徙到南宋之襄阳,其多首写襄阳生活和风物的诗可为明证。元太宗七年（1235）,沦为遗民的李氏应泽州守段直之邀,返乡泽州,一直到85岁辞世。晚年的李氏主要生活内容是为金源遗民,存文保道,故面对蒙元朝廷的延请,其态度是可为其筹略谋划,甚至支持重视儒家文化的忽必烈称帝,但他始终坚持隐逸之志,绝不做新朝之官。     

讲台上的朱自清

朱自清不仅是著名的作家、学者、民主战士．还是一位终身从事教育事业的教师。讲台上的朱自清是一位亲切而又严格的老师,一位能将教师职业与文学爱好融为一体的著名的作家教授,还是一位能将国学与新文学批评结合起来进行研究的批评家教授。