When is n large enough? Looking for the right sample size to estimate proportions

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions.     

Estimation of discrete survival function for error‐prone diagnostic tests

The product limit or Kaplan‐Meier (KM) estimator is commonly used to estimate the survival function in the presence of incomplete time to event. Application of this method assumes inherently that the occurrence of an event is known with certainty. However, the clinical diagnosis of an event is often subject to misclassification due to assay error or adjudication error, by which the event is assessed with some uncertainty. In the presence of such errors, the true distribution of the time to first event would not be estimated accurately using the KM method. We develop a method to estimate the true survival distribution by incorporating negative predictive values and positive predictive values, into a KM‐like method of estimation. This allows us to quantify the bias in the KM survival estimates due to the presence of misclassified events in the observed data. We present an unbiased estimator of the true survival function and its variance. Asymptotic properties of the proposed estimators are provided, and these properties are examined through simulations. We demonstrate our methods using data from the Viral Resistance to Antiviral Therapy of Hepatitis C study.     

基于DYNAFORM的轿车后背门冲压成形的仿真模拟

文章根据该外覆盖件特点运用CAE软件DYNAFORM进行精模拟,制定关键技术设计的方案,在此基础上,通过拉延筋的综合优化（拉延筋圆角半径和拉延筋筋高等）,达到制件无拉裂、少起皱、小回弹,保证冲压件质量,对实际生产起指导作用.较采用传统的“试错法”设计模具可以降低研发成本,从而增强企业在市场中的竞争力.     

气体钻井井下燃爆分析

与常规钻井相比,气体钻井在提高机械钻速、发现和保护油气藏等方面优势明显,由于负压钻进时,地层流体极易进入井筒,地层产出的可燃气体和氧气混合后具有燃烧、爆炸的潜在危险,容易发生严重的灾害性事故,在气体钻井应用中往往需要充分预测和评估钻遇气层的危险程度并提前采取应对措施。结合气体钻井实际施工情况,简要介绍了气体钻井过程中井下燃爆方面的研究进展,分析了气体钻井过程中可燃气体发生燃爆的条件。并从混合可燃气体组成、温度、压力,以及惰性气体含量等几个方面,展开论述了爆炸极限的主要影响因素。依据经验公式计算了某井气体钻井过程中可燃气体爆炸极限的变化情况,得出可燃气体下限值随井深增加略有减小,可燃气体上限值随井深增加明显增大的结论。结合该井实际施工情况,验证了计算的可靠性,可以看出氮气钻井过程中的氧含量安全范围很窄（2.43%4.20%）。     

涠西南凹陷流沙港组成岩相与有效储层研究

在岩石薄片、粘土X 衍射、镜质体反射率研究基础上,划分流沙港组砂岩于早成岩B 至中成岩B 阶段,通过成岩参数定量分析,区分8 种成岩相,厘定了压实是主要成岩作用。研究区中深层存在差异孔隙演化,岩石类型与成岩差异对孔隙演化起控制作用。根据地层测试、岩类孔渗关系综合确定常规有效储层渗透率下限为5 mD。采用经验公式法作为基本孔隙演化模型,孔隙预测误差为0.2%2.8%。建立以孔隙度、渗透率、岩石类型、压力、产能多因素约束的精细度储层分类。中等—好储层类型与三角洲水下分流河道和中等压实成岩相有关。同深度背景条件下,湖底扇浊流储层性质比三角洲滩坝差。     

A Bitcoin-inspired infinite-server model with a random fluid limit

The synchronization process inherent to the Bitcoin network gives rise to an infinite-server model with the unusual feature that customers interact. Among the closed-form characteristics that we derive for this model is the busy period distribution which, counterintuitively, does not depend on the arrival rate. We explain this by exploiting the equivalence between two specific service disciplines, which is also used to derive the model’s stationary distribution. Next to these closed-form results, the second major contribution concerns an asymptotic result: a fluid limit in the presence of service delays. Since fluid limits arise under scalings of the law-of-large-numbers type, they are usually deterministic, but in the setting of the model discussed in this paper the fluid limit is random (more specifically, of growth-collapse type).     

Assessing Risk‐Based Upper Limits of Melamine Migration from Food Containers

Melamine contamination of food has become a major food safety issue because of incidents of infant disease caused by exposure to this chemical. This study was aimed at establishing a safety limit in Taiwan for the degree of melamine migration from food containers. Health risk assessment was performed for three exposure groups (preschool children, individuals who dine out, and elderly residents of nursing homes). Selected values of tolerable daily intake (TDI) for melamine were used to calculate the reference migration concentration limit (RMCL) or reference specific migration limit (RSML) for melamine food containers. The only existing values of these limits for international standards today are 1.2 mg/L (0.2 mg/dm²) in China and 30 mg/L (5 mg/dm²) in the European Union. The factors used in the calculations included the specific surface area of food containers, daily food consumption rate, body weight, TDI, and the percentile of the population protected at a given migration concentration limit (MCL). The results indicate that children are indeed at higher risk of melamine exposure at toxic levels than are other groups and that the 95th percentile of MCL (specific surface area = 5) for children aged 1–6 years should be the RMCL (0.07 mg/dm²) for protecting the sensitive and general population.     

A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

We establish a central limit theorem for multivariate summary statistics of nonstationary α‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.     

Model Checks in Inverse Regression Models with Convolution‐Type Operators

Abstract. We consider the problem of testing parametric assumptions in an inverse regression model with a convolution‐type operator. An L ₂ ‐type goodness‐of‐fit test is proposed which compares the distance between a parametric and a non‐parametric estimate of the regression function. Asymptotic normality of the corresponding test statistic is shown under the null hypothesis and under a general non‐parametric alternative with different rates of convergence in both cases. The feasibility of the proposed test is demonstrated by means of a small simulation study. In particular, the power of the test against certain types of alternative is investigated. Finally, an empirical example is provided, in which the proposed methods are applied to the determination of the shape of the luminosity profile of the elliptical galaxy NGC 5017.