To increase the calculation speed of the computational fluid dynamics (CFD) based simulation for the gas-solid flow in fluidized beds, a Markov chain model (MCM) is developed to simulate the particle movement in a two-dimensional (2D) circulating fluidized bed (CFB) riser. As a statistic model, the MCM takes the CFD-discrete element method (DEM) results as samples to calculate the transition probability matrix of particles, which can describe the macroscopic regularities of the particle movement and guide the numerical simulation of the particle motion based on the Monte Carlo method. The particle distribution snapshots, residence time distribution (RTD) and mixing obtained from both the CFD-DEM and the MCM are compared. Results show that the computational speed of the MCM is faster than that of the CFD-DEM by about 2 orders of magnitude, and the difference of the mean particle residence time calculated by the two models is less than 2%. Besides, the MCM can well describe the time-averaged particle mixing compared to the CFD-DEM.

Functional partially linear regression model, contains a functional linear part and a non-parametric part, in which testing the linear relationship between the response and the functional predictor is of fundamental importance. When functional data cannot be approximated with a few principal components, based on a pseudo estimate for the unknown non-parametric component, we develop a U-statistic of order-two in this paper. Under some regularity conditions, we use the martingale central limit theorem to prove that the proposed test statistic is asymptotically normal. The finite sample performance with simulation studies and real data application are assessed to verify the proposed test procedure.

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

GDF5 gene is involved in the development of skeletal elements, synovial joint formation, tendons, ligaments, and cartilage. Several polymorphisms are present within the gene and two of them, rs143384 and 143383, have been reported as correlated with osteoarticular disease or muscle flexibility. The aim of this research is to verify if the worldwide distribution among human populations of rs143384 polymorphism has been shaped by selective pressure, or if it’s the result of random genetic drift events. Ninety-four individuals of both sexes, 18-28 years old, from Sardinia were analyzed. We observed the following genotype frequencies: 28.72% of homozygotes AA, 13.83% of homozygotes GG, and 57.45% of heterozygotes AG. Allele frequencies were 0.574 for allele A and 0.426 for alle G. Relationships between populations were verified by Multidimensional Scaling (MDS). Our data show: i) a clear heterogeneity within the African populations; ii) a strong differentiation between Africans and the other populations: iii) the Sardinian population is placed withing the European cluster. To reveal possible traces of selective pressure, Population Branch Statistic (PBS) was calculated; both SNPs rs143384 and 143383 have low PBS values, suggesting that there are no signals of selective pressure in those areas of the gene.

This paper will discuss the application of statistic modeling to interpret a health system crisis in Sri Lanka due to COVID- 19.A strong focus on the preventive approach and the contact tracing with the utilization of available resources in a rational manner describes Sri Lanka’s response towards COVID- 19 prevention and mitigation. The early contact tracing, preemptive quarantining, isolation, and treatment were implemented as a concerted effort. This approach, proven efficient during the early phase of the pandemic, was sustainable when there was a rapid increase in the COVID- 19 patients since July 2021, exceeding the health system capacity.The country’s COVID- 19 situation during the period from 01st of August 2021 to 31st of October 2021 was taken into consideration. Variables used for analysis were; total number of cases, recovered cases, comorbid and O₂ dependent patients, ICU patients, and deaths. The regression model was applied to analyze the data by using the EViews 12 (x64) software application.The correlation coefficients of all the independent variables under consideration implies that they have a strong positive relationship with the number of deaths occurred during the said period. According to the computed multiple linear regression model, the number of positive cases and O₂ dependents have a positive relationship with the dependent variable. Further, the Durbin- Watson stat value of the model and multicollinearity test reflect that it is free from serial correlation thereby the model is fit. From the perspective of epidemiological control, these findings highlight the importance of keeping the number of cases within the limits of health system capacity.

Control charts have been widely used for monitoring process quality in manufacturing and play an important role in triggering a signal in time when detecting a change in process quality. Many control charts in literature assume that the in-control distribution of the univariate or multivariate process data is continuous and not categorical. This research develops two exponentially weighted moving average (EWMA) proportion control charts for monitoring a process with multinomial proportions when considering both large and small sample sizes. For a large sample size , the charting statistic depends on the well-known Pearson χ2 statistic, and the control limit of the EWMA proportion chart is determined by an asymptotical chi-square distribution. For a small sample size, we derive the exact mean and variance of the Pearson χ2 statistic. Hence, the exact EWMA proportion chart is determined. The proportion chart can also be applied to monitor the distribution-free continuous multivariate process as long as each categorical proportion associated with specification limits of each quality variable is known or estimated. Lastly, we investigate the detection performance of the proposed EWMA proportion chart by numerical analyses. Real data analysis demonstrates the beneficial application of the proposed EWMA proportion charts.

The testing of high-dimensional normality has been an important issue and has been intensively studied in literatures, it depends on the Variance-Covariance matrix of the sample, numerous methods have been proposed to reduce the complex of the Variance-Covariance matrix. The principle component analysis(PCA) was widely used since it can project the high-dimensional data into lower dimensional orthogonal space, and the normality of the reduced data can be evaluated by Jarque-Bera(JB) statistic on each principle direction. We propose two combined statistics, the summation and the maximum of one-way JB statistics, upon the independency of each principle direction, to test the multivariate normality of data in high dimensions. The performance of the proposed methods is illustrated by the empirical power of the simulated data of normal data and non-normal data. Two real examples show the validity of our proposed methods.

Energy distance is used to eigenvalue distributions in this new Wishart distribution study, providing a new perspective on high-dimensional data. Multivariate statistics relies on Wishart distribution to explain covariance matrices. This analysis shows how degrees of freedom and covariance matrix configurations affect eigenvalue dispersion. We use energy distance based on eigenvalue distributions to assess Wishart distribution differences without the "curse of dimensionality" via extensive simulation simulations. This approach improves measurement accuracy and processing efficiency in distribution comparisons and enables new analytical pathways in scientific fields that need data covariance comprehension. Our results show that degrees of freedom and matrix structure considerably affect energy distances, expanding the theoretical framework and practical applications of statistical models.

Using data from the Swedish National Diabetes Register, this study examines the gender disparity among patients with type I diabetes who have experienced a specific cardiovascular complication, while exploring the association between weight variability, age group, and gender. Fourteen cardiovascular complications have been considered. This analysis is conducted by using three-way correspondence analysis (CA) which allows for the partitioning and decomposition of Pearson’s three-way chi-squared statistic. The dataset comprises of information organized in a data cube, detailing how weight variability among these patients correlates with a cardiovascular complication, age group and gender. The three-way CA method presented in this paper allows for one to assess the statistical significance of the association between these variables and to visualize this association, highlighting the gender gap among these patients. It is worth noting that the association between weight variability, age group, and gender varies among different types of cardiovascular complications.

There is high confidence that climate change has increased the probability of concurrent temperature-precipitation extremes, changed their spatial-temporal variations, and affected the relationships between drivers of such natural hazards. However, the extent of such changes has been less investigated in Australia. Daily weather data (131 years, 1889-2019) at 700 grid cells (1◦ × 1◦) across Australia was obtained to calculate annual and seasonal mean daily maximum temperature (MMT) and total precipitation (TPR). A nonparametric multivariate copula framework was adopted to estimate the return period of compound hot-dry (CHD) events based on an ‘And’ hazard scenario (hotter than a threshold ‘And’ drier than a threshold). CHD extremes were defined as years with joint return periods of larger than 25 years. Mann-Kendall nonparametric tests was used to analyse trends in MMT and TPR as well as in the frequency of univariate and CHD extremes. A general cooling-wetting trend was observed over 1889-1989. Significant increasing trends were detected over 1990-2019 in the frequency and severity of hot extremes across the country while trends in dry extremes were mostly insignificant (and decreasing). Results showed a significant increase in the association between temperature and precipitation at various temporal scales. The frequency of CHD extremes was mostly stable over 1889-1989, but significantly increased between 1990 and 2019 at 44% of studied grid cells, mostly located in the north, south-east and south-west. Spatial homogeneity (i.e. connectedness) and propagation of extreme events from one grid cell to its neighbouring cells was investigated across Australia. It can be concluded that this connectedness has not significantly changed since 1889.

Recently, there appeared in this journal (Beh and Lombardo \textbf{2022}, {\it Symmetry}, 14, 1103) a paper that showed how to perform a correspondence analysis on a two-way contingency table where Bowker's statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic can be used to visually identify departures from perfect symmetry. Interestingly, Bowker's statistic is a special case of the symmetry-version of the Cressie-Read family of divergence statistics. Therefore, this paper presents a new framework for visually assessing departures from perfect symmetry using a second-order Taylor series approximation of the Cressie-Read family of divergence statistics.

In the paper we present a new test for comparison of the means of multivariate samples with unknown distributions. The test is based on the comparison of the distributions of the distances between the samples’ elements and their means using univariate two-sample Kolmogorov-Smirnov test. The activity of the suggested method is illustrated by numerical analysis of the real-world and simulated data.

In this paper a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered and the robustness is studied on the basis of a simulation study. Previously, the composite minimum density power divergence estimator is introduced and its asymptotic properties are studied.

During the conceptual and preliminary design stage of a ship, designers need to ensure that the selected principal dimensions and parameters are good enough to deliver a stable ship (statically and dynamically) besides deadweight and speed. To support this, the initial intact stability of the proposed ship is required to be calculated, and in doing so, the lightship weight and its detailed breakdown are necessary to be known. After hull steel weight, machinery weight, mainly, marine propulsion and power generation machinery, play a vital role in the lightship weight estimate of a ship due to its robustness. The correct estimation of respective weights improves the accuracy of calculating a ship's initial stability typically to be designed and built. Hence, it would be advantageous for the designer to convince the ship owner. A total of 3006 marine propulsion (main marine diesel) engines and 348 power generation (auxiliary marine diesel) engines/generators of various power output (generators output for auxiliary engines), engine RPM and cylinder number of different engine makers are collected. These are analyzed and presented in both tabular and graphical forms to demonstrate the possible relationship between marine propulsion engine weight and power generation engine weight, and their respective power output, RPM, cylinder number, power-RPM ratio and power-RPM ratio per cylinder.In this article, the authors have attempted to investigate the behavior of marine propulsion engine weight and power generation engine/generator weight regarding engine power output, generator power output, engine RPM and cylinder number (independent variables). Further attempts have been made to identify those independent variables that influence the weight of the marine propulsion engine and power generation engine/generator (dependent variables), and their interrelationships. A mathematical model has thus been developed and proposed, as a guiding tool, for the designer to estimate the weight of main and auxiliary engines more accurately during the conceptual and preliminary design stage.