On a Class of Tests of Exponentiality

The class of statistics T, = (Σ^α _i=1, X ^α _i /n)/ ^x , where α > 0 and ≠ 1, have been considered in the literature for testing exponentiality versus omnibus alternatives. These tests have a twosided rejection region. It is shown here that tests based on these statistics are not consistent for certain alternatives. However, it is shown that one-sided tests based on these statistics are consistent for IFRA (DFRA) distributions. A Monte Carlo power study suggests that lower tail tests based on T _½ and T ₂ are very competitive for DFRA and IFRA alternatives, respectively. The null distributions of T _½ and T ₂ are approximated by members of the Johnson families of distributions.     

Nonparametric inference with generalized likelihood ratio tests

The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks’ phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section. This invited paper is discussed in the comments available at: , , , , , , , , . The work was supported by the NSF grants DMS-0354223, DMS-0532370 and DMS-0704337. The paper was initiated when Jiancheng Jiang was a research fellow at Princeton University.     

Current use of effect size or confidence interval analyses in clinical and biomedical research

The isolated use of the statistical hypothesis testing for two group comparison has limitations, and its combination with effect size or confidence interval analysis as complementary statistical tests is recommended. In the present work, we estimate the use of these complementary statistical tests (i.e. effect size or confidence interval) in recently published in research articles in clinical and biomedical areas. Methods: The ProQuest database was used to search published studies in academic journals between 2019 and 2020. The analysis was carried out using terms that represent five areas of clinical and biomedical research: “brain”, “liver”, “heart”, “dental”, and “covid-19”. A total of 119,558 published articles were retrieved. Results: The relative use of complementary statistical tests in clinical and biomedical publications was low. The highest frequency usage of complementary statistical tests was among articles that also used statistical hypothesis testing for two-sample comparison. Publications with the term “covid-19” showed the lowest usage rate of complementary statistical tests when all article were analyzed but presented the highest rate among articles that used hypothesis testing. Conclusion: The low use of effect size or confidence interval in two-sample comparison suggests that coordinate measures should be taken in order to increase the use of this analysis in clinical and biomedical research. Their use should be emphasized in statistical disciplines for college and graduate students, become a routine procedure in research laboratories, and recommended by reviewers and editors of scientific journals.

     

Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.     

Modeling and monitoring methods for spatial and image data

ABSTRACT

Intelligent sensing and computerized data analysis are inducing a paradigm shift in industrial statistics applied to discrete part manufacturing. Emerging technologies (e.g., additive manufacturing, micro-manufacturing) combined with new inspection solutions (e.g., non-contact systems, X-ray computer tomography) and fast multi-stream high-speed sensors (e.g., videos and images; acoustic, thermic, power and pressure signals) are paving the way for a new generation of industrial big-data requiring novel modeling and monitoring approaches for zero-defect manufacturing. Starting from real industrial problems, some of the main challenges to be faced in relevant industrial sectors are discussed. Viable solutions and future open issues are specifically outlined.     

Mathematical methods in psychiatric papers

A comparative study was carried out to determine the trend in the use of statistical methods in the papers published in the leading Russian, American and British psychiatric journals of the 1980–90-ies. Within 10 years the quota of papers with statistics increased considerably in the American and British journals (from 58.6% to 67.6%), especially in theArchives of General Psychiatry (88%). Qualitative changes were notable as well, tending towards the use of non-ordinary innovative methods. As regards the Russian psychiatric papers the use of statistical methods was a rare occurrence (21.8% in 1980s), that never changed within 10 years. In memory of Professor V.Nalimov, the first Russian scientometrist who initiated this investigation.     

Engineering performance prediction for ceramics

Abstract

Fracture mechanics is fundamental to the understanding of the mechanical properties of ceramics. Although the basic Griffith equation is applicable in simple cases, complications arise because the fracture surface energy or fracture toughness are not independent of crack size and vary with time, and crack interaction effects are also significant. Weibull statistics are used to discuss statistical variations in strength. Practical examples for grinding wheels and prosthetic hip joints illustrate the principles of performance prediction. Some problems associated with high-temperature deformation are introduced.

MST/394     

A decade of database research publications: a look inside

The database management technology has played a vital role in the advancements of the information technology field. Database researchers are one of the key players and main sources to the growth of the database systems. They are playing a foundational role in creating the technological infrastructure from which database advancements evolve. We analyze the database research publications of nine top-tier and prestigious database research venues. In particular, we study the publications of four major core database technology conferences (SIGMOD, VLDB, ICDE, EDBT), two main theoretical database conferences (PODS, ICDT) and three database journals (TODS, VLDB Journal, TKDE) over a period of 10 years (2001–2010). Our analysis considers only regular papers as we do not include short papers, demo papers, posters, tutorials or panels into our statistics. In this study, we report the list of the authors with the highest number of publications for each conference/journal separately and in combined. We analyze the preference of the database research community towards publishing their work in prestigious conferences or major database journals. We report about the most successful co-authorship relationships in the database research community in the last decade. Finally, we analyze the growth in the number of research publications and the size of the research community in the last decade.     

Random Balance Experimentation

Random balance experimental design has been used in industrial applications of statistical methods since 1956. The purpose of this report is to record and discuss in specific form key points regarding this technique. This report will be divided into several parts that are essentially separate.

The topics to be covered include the following: 1. Random design and the motivations for use of random designs in industrial, engineering and research activities.

2. Techniques for analysis of random data and the apparent application domains for which each technique is appropriate.

3. Fundamental problems of statistical analysis that are of critical importance in some random balance applications.

     

Process monitoring research with various estimator-based MEWMA control charts

Multivariate exponentially weighted moving average (MEWMA) control chart with five different estimators as population covariance matrix is rarely applied to monitor small fluctuations in the statistical process control. In this article, mathematical models of the five estimators (S₁, S₂, S₃, S₄, S₅) are established, with which the relevant MEWMA control charts are obtained, respectively. Thereafter, the process monitoring performance of the five control charts is simulated. And the simulation results show that the S₄ estimator-based MEWMA control chart is of the best performance both in step offset failure mode and ramp offset failure mode. Since the inline process monitoring of photovoltaic manufacturing is intended to be a problem of multivariate statistics process analysis, the feasibility and effectiveness of the proposed model are elaborated in the case study during the cell testing and sorting process control for the fabrication of multicrystalline silicon solar cells.     

Atomic interference in the micromaser and statistical properties of the micromaser field

Abstract

In this paper we report on atomic interferometry in the micromaser. The atomic inversion is recorded while scanning the cavity frequency across the atomic resonance. For high pump rates, interference patterns are observed on the low-frequency wing of the maser line. The interferences are due to the non-adiabatic mixing of dressed states of the atoms at the entrance and exit holes of the maser cavity, leading to a Ramsey-type two-field interaction. Furthermore, statistical properties of the maser field are investigated via a measurement of the statistics of the pump atoms that leave the maser cavity. Theoretical expressions for the time dependence of the Fano–Mandel parameter Q _A(t) are compared with the experimental data. We demonstrate, that metastability of the maser field and atomic interference strongly influence the approach to a steady-state value of Q _A(t).     

The role of Ch3 and ch2 reactions in the kinetic modeling of methane / air flames

ABSTRACT

The use of second-order statistics in identification or deconvolution incurs error due to additive Gaussian noise. In contrast, higher-order statistics (HOS) are insensitive to Gaussian perturbation and can be used to characterize nonminimum phase (NMP) systems. In this paper we propose batch, recursive and adaptive form algorithms based on third- and fourth-order cumulants to solve the identification and deconvolution problems. A new order determination procedure is also presented. Simulation results demonstrate that our algorithms do have superior performance when compared with existing algorithms.     

Difficulties and challenges of Chinese scientific journals: Statistical analysis of Chinese literatures using Chinese Science Bulletin as example

Using statistical method, the author analyzed the citation rate of articles published in Chinese Science Bulletin (CSB) between 1995 and 1999 in Science Citation Index Expanded (SCIE) databases. Results indicated that: 1. Majority of authors who published in CSB were Chinese; 2. The articles were basically cited by the authors themselves in the first year after publication; 3. The peak of total citation rate appeared in the third year after publication and the peak of non-self-citation rate was further delayed. There are relatively high self-citation rates of articles from CSB and most of these citations are from Chinese scientific journals. This indicates that our citation environment is limited to a closed circle. The author, therefore, proposed a strategy for changing the current conditions of Chinese scientific journals to raise their influence. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quantum Statistical Properties of Coupled Nonlinear Oscillators with Losses

Abstract

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.     

Statistics of stained glass images

Abstract

The notion of applying statistical techniques to stained glass images is an intriguing one. This paper introduces systematic procedures to calculate statistics on digital images, gives a review of first-order statistics, second-order statistics, higher-order statistics and run-length statistics, and applies the measures to a collection of digital images of stained glass windows. Values of the statistics are reported. The scale invariance property of images is examined carefully, and characteristic scaling behaviours of stained glass images are found.     

A new parameter for (normalized) evaluation of H-index: countries as a case study

It is known that the H-indexes of individuals, research groups, institutions, scientific journals, and countries strongly depend on the field of study, slowly increase with the number of publications, N, and can be described by empirical power-law functions of the type H?=?C?×?N^a (C and a are constants and depend on the specific field being analyzed). In this paper, we use this function and propose a new index [Montazerian–Zanotto–Eckert (MZE)], which is normalized by the number of publications and typically varies from ??1 to +?1, to characterize the relative standing of a research group, institution, or author to those of his/her peer groups. Due to the rich statistics available, as an example, here we analyzed and tested the new parameter against the citation-related performance (H-index) of countries. We found that the MZE index readily distinguishes between countries that stand above or below the average (for any given number of publications). Generally, publications of countries with a positive MZE index are more interesting or visible than the average. Analyzing publication output in this manner instead of the H-index allows for a less biased comparison between researchers, journals, universities, or countries for any particular combination of H-index and publication output.

     

Comparison of pure and “Latinized” centroidal Voronoi tessellation against various other statistical sampling methods

A recently developed centroidal Voronoi tessellation (CVT) sampling method is investigated here to assess its suitability for use in statistical sampling applications. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-dimensional parameter spaces. On several 2-D test problems CVT has recently been found to provide exceedingly effective and efficient point distributions for response surface generation. Additionally, for statistical function integration and estimation of response statistics associated with uniformly distributed random-variable inputs (uncorrelated), CVT has been found in initial investigations to provide superior points sets when compared against latin-hypercube and simple-random Monte Carlo methods and Halton and Hammersley quasi-random sequence methods. In this paper, the performance of all these sampling methods and a new variant (“Latinized” CVT) are further compared for non-uniform input distributions. Specifically, given uncorrelated normal inputs in a 2-D test problem, statistical sampling efficiencies are compared for resolving various statistics of response: mean, variance, and exceedence probabilities.     

Organizing distributed data bases for parallel searching

Abstract

This paper is mainly concerned with the problem of distributing a data base (i.e., a set of segments) in a computer network system so as to facilitate parallel searching. In our distributed data base model, we assume that all segments are stored in nodes. Each time a query occurs, all nodes are searched concurrently. For convenience, we define the time required to access a segment from any node as a time unit. For a network with d nodes, the response time of a query is then identical to the maximum (n ₁ , n ₂, …, n_d ), where n_i , is the number of segments that satisfies the query and is stored in node i. Unfortunately, the solution for finding an optimal way to organize a distributed data base for parallel searching is still at large. In other words, given a data base, there is no efficient polynomial time algorithm for finding an optimal arrangement of segments onto nodes. In this article, we shall present a “heuristic algorithm” based upon a multivariant analysis method in statistics to distribute a data base in a network system. Some experimental results will show that our method is indeed feasible and effective.     

Making an Impact in Materials Science

Published scientific information comes in all shapes and sizes. This variety allows for freedom of expression and for the creative presentation of scientific developments, but unfortunately not all scientific information is of the same quality. Scientific journals provide one of the most important routes for the dissemination of this information, and therefore, those responsible for the journals are duty bound to adhere to the ethics of good science and to apply the most rigorous quality control and selection procedures possible. While all top journals are dedicated to these aims, it is difficult to quantify the effectiveness of the procedures applied, and questions of whether a particular type of presentation of scientific research is more attractive than another type is really a question of taste. However, there are some indicators, such as Impact Factors and journal‐usage statistics, which provide some clues. In the following, I would like to present some information on the latest indicators as they relate to Advanced Materials, and provide some news of upcoming developments.