Monte Carlo exact goodness‐of‐fit tests for nonhomogeneous Poisson processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model failure data from repairable systems, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness‐of‐fit tests for parametric NHPPs. The idea is to use conditional tests given a sufficient statistic under the null hypothesis model. The tests are performed by simulating conditional samples given the sufficient statistic. Algorithms are presented for testing goodness‐of‐fit for the power law and the log‐linear law NHPP models. It is noted that while exact algorithms for the power law case are well known in the literature, the availability of such algorithms for the log‐linear case seems to be less known. A data example, as well as simulations, are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

由一个生成元张成的平移不变空间的注记

In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2（0, 1） and L^2（R）. In this paper, in terms of bases for L^2（0, α）, two sampling theorems for αZ-shift invariant spaces with a single generator are obtained.     

An efficient surrogate-based method for computing rare failure probability

In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966–8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation—it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10⁻¹² ∼ 10⁻⁶ with only several hundreds samples.     

Highly luminescent silica-coated ZnO nanoparticles dispersed in an aqueous medium

Highly luminescent silica-coated ZnO nanoparticles dispersed in an aqueous medium were synthesized using the sol-gel process. The samples prepared at various temperatures exhibited an emission peak at around 480 nm (blue color) and a quantum efficiency of 60% at maximum by the quantum confinement effect of ZnO nanoparticles, with diameters ranging from 3.1 to 3.5 nm, under ultraviolet excitation. No degradation of the quantum efficiencies and no peak shifting in the emission spectra were observed for 7 days following the preparation, which indicated no growth of ZnO nanoparticles in the aqueous medium.     

Breath Analysis: Comparison among Methodological Approaches for Breath Sampling

Despite promising results obtained in the early diagnosis of several pathologies, breath analysis still remains an unused technique in clinical practice due to the lack of breath sampling standardized procedures able to guarantee a good repeatability and comparability of results. The most diffuse on an international scale breath sampling method uses polymeric bags, but, recently, devices named Mistral and ReCIVA, able to directly concentrate volatile organic compounds (VOCs) onto sorbent tubes, have been developed and launched on the market. In order to explore performances of these new automatic devices with respect to sampling in the polymeric bag and to study the differences in VOCs profile when whole or alveolar breath is collected and when pulmonary wash out with clean air is done, a tailored experimental design was developed. Three different breath sampling approaches were compared: (a) whole breath sampling by means of Tedlar bags, (b) the end-tidal breath collection using the Mistral sampler, and (c) the simultaneous collection of the whole and alveolar breath by using the ReCIVA. The obtained results showed that alveolar fraction of breath was relatively less affected by ambient air (AA) contaminants (p-values equal to 0.04 for Mistral and 0.002 for ReCIVA Low) with respect to whole breath (p-values equal to 0.97 for ReCIVA Whole). Compared to Tedlar bags, coherent results were obtained by using Mistral while lower VOCs levels were detected for samples (both breath and AA) collected by ReCIVA, likely due to uncorrected and fluctuating flow rates applied by this device. Finally, the analysis of all data also including data obtained by explorative analysis of the unique lung cancer (LC) breath sample showed that a clean air supply might determine a further confounding factor in breath analysis considering that lung wash-out is species-dependent.     

王水溶样-电感耦合等离子体质谱（ICP-MS）法测定地质样品中的金

称取10.00 g样品放于马弗炉中700℃条件下焙烧后,加入约60 mL王水,盖上表面皿于低温电热板(1000 W)溶解40 min,加入5 mL动物胶(20 g/L),搅拌均匀后加入等体积的水,抽滤,滤液定溶至500 mL,分液后以10 ng/mL的Rh为内标建立了王水溶样-电感耦合等离子体质谱(ICP-MS)法快速测定地质样品中金的分析方法。方法适用于检测0.1~10μg/g品位的矿石样品,对国家一级标准物质GBW07209、GBW07808、GBW07809、GBW07300进行12次测定,其相对标准偏差RSD均小于5%,相对误差RE均小于2%。方法具有简单快速等优势,在实际应用中得到满意的结果。     

Development of a stability-indicating high performance liquid chromatography method for assay of erythromycin ethylsuccinate in powder for oral suspension dosage form

In this study an effective method was developed to assay erythromycin ethylsuccinate for an oral suspension dosage form. The chromatographic separation was achieved on an X-Terra™ C₁₈ analytical column. A mixture of acetonitrile–ammonium dihydrogen phosphate buffer (0.025 mol L^-1) (60:40, V/V) (pH 7.0) was used as the mobile phase, effluent flow rate monitored at 1.0 mL min⁻¹, and UV detection at 205 nm. In forced degradation studies, the effects of acid, base, oxidation, UV light and temperature were investigated showing no interference in the peak of drug. The proposed method was validated in terms of specificity, linearity, robustness, precision and accuracy. The method was linear at concentrations ranging from 400 to 600 μg mL⁻¹, precise (intra- and inter-day relative standard deviations <0.65), accurate (mean recovery; 99.5%). The impurities and degradation products of erythromycin ethylsuccinate were selectively determined with good resolution in both the raw material and the final suspension forms. The method could be useful for both routine analytical and quality control assays of erythromycin ethylsuccinate in commercial powder for an oral suspension dosage form and it could be a very powerful tool to investigate the chemical stability of erythromycin ethylsuccinate.     

Evaluating students’ conceptual and procedural understanding of sampling distributions

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their understanding of sampling distributions, students should have a strong conceptual foundation that is balanced with procedural knowledge. To address this issue, this study was designed to examine the relationship between college students’ procedural and conceptual knowledge of sampling distributions. With this aim in mind, an achievement test consisting of two sections – procedural and conceptual knowledge – was prepared. In answering the questions related to procedural knowledge, the participants were more successful in identifying the relationship between standard deviation of a population and sample means. However, they lacked theoretical knowledge about statements that they had heard or knew intuitively. Simulation activities provided in statistics courses may support students in developing their conceptual understanding in this regard.     

Estimating functions for jump–diffusions

Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.     

Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models

We consider the estimation problem of misspecified ergodic Lévy driven stochastic differential equation models based on high-frequency samples. We utilize a widely applicable and tractable Gaussian quasi-likelihood approach which focuses on mean and variance structure. It is shown that the Gaussian quasi-likelihood estimators of the drift and scale parameters still satisfy polynomial type probability estimates and asymptotic normality at the same rate as the correctly specified case. In their derivation process, the theory of extended Poisson equation for time-homogeneous Feller Markov processes plays an important role. Our result confirms the reliability of the Gaussian quasi-likelihood approach for SDE models.