D-optimal designs for logistic models with three and four parameters

Logistic functions are used in different applications, including biological growth studies and assay data analysis. Locally D-optimal designs for logistic models with three and four parameters are investigated. It is shown that these designs are minimally supported. Efficiencies are computed for equally spaced and uniform designs.     

Analysis of one-way layout of count data in the presence of over or under dispersion

This article develops test statistics for the homogeneity of the means of several treatment groups of count data in the presence of over-dispersion or under-dispersion when there is no likelihood available. The C(α)<math altimg="si64.gif" overflow="scroll">C(α)math> or score type tests based on the models that are specified by only the first two moments of the counts are obtained using quasi-likelihood, extended quasi-likelihood, and double extended quasi-likelihood. Monte Carlo simulations are then used to study the comparative behavior of these C(α)<math altimg="si65.gif" overflow="scroll">C(α)math> statistics compared to the C(α)<math altimg="si66.gif" overflow="scroll">C(α)math> statistic based on a parametric model, namely, the negative binomial model, in terms of the following: size; power; robustness for departures from the data distribution as well as dispersion homogeneity. These simulations demonstrate that the C(α)<math altimg="si67.gif" overflow="scroll">C(α)math> statistic based on the double extended quasi-likelihood holds the nominal size at the 5% level well in all data situations, and it shows some edge in power over the other statistics, and, in particular, it performs much better than the commonly used statistic based on the quasi-likelihood. This C(α)<math altimg="si68.gif" overflow="scroll">C(α)math> statistic also shows robustness for moderate heterogeneity due to dispersion. Finally, applications to ecological, toxicological and biological data are given.     

Adventures in policy modeling! Operations research in the community and beyond

The literature describing operations research in the community is somewhat of a puzzle. On the one hand, several authors have denigrated the use of traditional operations approaches in addressing community problems, yet several studies document successful applications. Arguing that the operations research mindset is itself a great strength, we will review several examples where operations research methods have been employed creatively to the benefit of the community and beyond.     

分层教学在职业学校数学教学中的应用探索

为了更好地提高职业学校数学课的教学质量,针对传统数学教学模式在目前教学中出现的诸多问题,我们在职业学校数学教学中采用＂分层次＂的教学法进行实验和研究,结果发现,＂分层次＂教学法不仅有利于提高学生学习的积极性、主动性和创造性,有利于培养学生学习兴趣和自我锻炼能力,有利于学生比较牢固地掌握知识和技能,同时,这种方法还为学生终身学习奠定了良好的基础。     

贺兰山高等真菌区系地理研究

贺兰山高等真菌区系地理成分中,世界性分布属占64.1%、种占19.5,他们多为适应性强的腐生菌类;欧亚北美分布属占35.9%、种占52.7%,未发现热带分布的属或种,充分显示出该地区真菌以北温带分布成分为主的特点;欧亚分布种占11.5%,东亚北美分布种占9.9%,表明该地区真菌区系与欧洲、北美洲的密切联系;中国&日本分布种占3.1%,可见本地区和日本在真菌区系上也有着联系;本地区特有成分较少,但从贺兰山特殊的地理位置、相对孤立的山体和复杂的地形分析,随研究工作的深入,很可能有一些山的分布的特有成分被发现.贺兰山真菌区系成分与邻近的内蒙古大青山相比较,共有种多达57种,而与地处亚热带向热带过渡的湖南莽山相比较,共有种仅有12种,更进一步说明本地区深居北温带,真菌区系以泛北极成分为主的特色.     

Selecting and checking a binomial response generalized linear model using phi-divergences

This work introduces specific tools based on phi-divergences to select and check generalized linear models with binary data. A backward selection criterion that helps to reduce the number of explanatory variables is considered. Diagnostic methods based on divergence measures such as a new measure to detect leverage points and two indicators to detect influential points are introduced. As an illustration, the diagnostics are applied to human psychology data.     

An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

An economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.