Search results for: Statistical

Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Petros Roussos

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The present study focused on students' statistical reasoning related to Null Hypothesis Statistical Testing and p-values. Its objective was to test the hypothesis that neither the place (classroom, at a distance, online) nor the medium that actually supports the learning (ICT, internet, books) has an effect on understanding of statistical concepts. In addition, it was expected that students' attitudes towards statistics would not predict understanding of statistical concepts. The sample consisted of 385 undergraduate and postgraduate students from six state and private universities (five in Greece and one in Cyprus). Students were administered two questionnaires: a) the Greek version of the Survey of Attitudes Toward Statistics, and b) a short instrument which measures students' understanding of statistical significance and p-values. Results suggest that attitudes towards statistics do not predict students' understanding of statistical concepts, whereas the medium did not have an effect.

Keywords: attitudes towards statistics, blended learning, e-learning, statistical reasoning

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Lukanda Kalobo

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In South Africa, the High School Mathematics Curriculum provides teachers with specific aims and skills to be developed which involves the understanding about the measures of central tendency. The exploration begins with the definitions of statistical literacy, measurement of central tendency and a discussion on why statistical literacy is essential today. It furthermore discusses the statistical literacy basics involved in understanding the concepts of measures of central tendency. The statistical literacy test on the measures of central tendency, was used to collect data which was administered to 78 first year students direct from high schools. The results indicated that students seemed to have forgotten about the statistical literacy in understanding the concepts of measure of central tendency after completing their high school study. The authors present inferences regarding the alignment between statistical literacy and the understanding of the concepts about the measures of central tendency, leading to the conclusion that there is a need to provide in-service and pre-service training.

Keywords: conceptual understanding, mean, median, mode, statistical literacy

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Petar Sarajcev, Josip Vasilj, Damir Jakus

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This paper presents a novel statistical description of the counterpoise effective length due to lightning surges, where the (impulse) effective length had been obtained by means of regressive formulas applied to the transient simulation results. The effective length is described in terms of a statistical distribution function, from which median, mean, variance, and other parameters of interest could be readily obtained. The influence of lightning current amplitude, lightning front duration, and soil resistivity on the effective length has been accounted for, assuming statistical nature of these parameters. A method for determining the optimal counterpoise length, in terms of the statistical impulse effective length, is also presented. It is based on estimating the number of dangerous events associated with lightning strikes. Proposed statistical description and the associated method provide valuable information which could aid the design engineer in optimising physical lengths of counterpoises in different grounding arrangements and soil resistivity situations.

Keywords: counterpoise, grounding conductor, effective length, lightning, Monte Carlo method, statistical distribution

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Authors: Jihye Jeon

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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: Queen Suraajini Rajendran, Sai Hung Cheung

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Statistical down scaling models are required to connect the global climate model outputs and the local weather variables for climate change impact prediction. For reliable climate change impact studies, the uncertainty associated with the model including natural variability, uncertainty in the climate model(s), down scaling model, model inadequacy and in the predicted results should be quantified appropriately. In this work, a new approach is developed by the authors for statistical classification, statistical down scaling and uncertainty assessment and is applied to Singapore rainfall. It is a robust Bayesian uncertainty analysis methodology and tools based on coupling dependent modeling error with classification and statistical down scaling models in a way that the dependency among modeling errors will impact the results of both classification and statistical down scaling model calibration and uncertainty analysis for future prediction. Singapore data are considered here and the uncertainty and prediction results are obtained. From the results obtained, directions of research for improvement are briefly presented.

Keywords: statistical downscaling, global climate model, climate change, uncertainty

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Dimitra Alexiou

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During the last 10 years, in spite of the economic crisis, the number of tourists arriving in Greece has increased, particularly during the tourist season from April to October. In this paper, the number of annual tourist arrivals is studied to explore their preferences with regard to the month of travel, the selected destinations, as well the amount of money spent. The collected data are processed with statistical methods, yielding numerical and graphical results. From the computation of statistical parameters and the forecasting with exponential smoothing, useful conclusions are arrived at that can be used by the Greek tourism authorities, as well as by tourist organizations, for planning purposes for the coming years. The results of this paper and the computed forecast can also be used for decision making by private tourist enterprises that are investing in Greece. With regard to the statistical methods, the method of Simple Exponential Smoothing of time series of data is employed. The search for a best forecast for 2017 and 2018 provides the value of the smoothing coefficient. For all statistical computations and graphics Microsoft Excel is used.

Keywords: tourism, statistical methods, exponential smoothing, land spatial planning, economy

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Authors: Encarnación Álvarez-Verdejo, Raúl Amor-Pulido, Pablo J. Moya-Fernández, Juan F. Muñoz-Rosas, Francisco J. Blanco-Encomienda

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Many companies use the statistical tool named as statistical quality control, and which can have a high cost for the companies interested on these statistical tools. The evaluation of the quality of products and services is an important topic, but the reduction of the cost of the implantation of the statistical quality control also has important benefits for the companies. For this reason, it is important to implement a economic design for the various steps included into the statistical quality control. In this paper, we describe some relevant aspects related to the economic design of a quality control chart for the proportion of defective items. They are very important because the suggested issues can reduce the cost of implementing a quality control chart for the proportion of defective items. Note that the main purpose of this chart is to evaluate and control the proportion of defective items of a production process.

Keywords: proportion, type I error, economic plan, distribution function

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Authors: Gurcharan Singh Buttar

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It has been discovered that although these two areas, statistics, and information theory, are independent in their nature, they can be combined to create applications in multidisciplinary mathematics. This is due to the fact that where in the field of statistics, statistical parameters (measures) play an essential role in reference to the population (distribution) under investigation. Information measure is crucial in the study of ambiguity, assortment, and unpredictability present in an array of phenomena. The following communication is a link between the two, and it has been demonstrated that the well-known conventional statistical measures can be used as a measure of information.

Keywords: probability distribution, entropy, concavity, symmetry, variance, central tendency

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Authors: A. Maghari, V. M. Maleki

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In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1 + (2,3)-> 1 + (2,3) as well as recombination 1 + (2,3) -> 2 + (3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the three-dimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: statistical mechanics, nonlocal separable potential, three-body interaction, faddeev equations

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Authors: Muhammet Şahal, Oğuz Köklü

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As statistical thinking and problem-solving processes have become increasingly important, teachers need to be more rigorously prepared with statistical knowledge to teach their students effectively. This study examined preservice mathematics teachers' development of statistical investigation projects using data and exploratory data analysis tools, following a design-based research perspective and statistical investigation cycle. A total of 26 pre-service senior mathematics teachers from a public university in Turkiye participated in the study. They formed groups of 3-4 members voluntarily and worked on their statistical investigation projects for six weeks. The data sources were audio recordings of pre-service teachers' group discussions while working on their projects in class, whole-class video recordings, and each group’s weekly and final reports. As part of the study, we reviewed weekly reports, provided timely feedback specific to each group, and revised the following week's class work based on the groups’ needs and development in their project. We used content analysis to analyze groups’ audio and classroom video recordings. The participants encountered several difficulties, which included formulating a meaningful statistical question in the early phase of the investigation, securing the most suitable data collection strategy, and deciding on the data analysis method appropriate for their statistical questions. The data collection and organization processes were challenging for some groups and revealed the importance of comprehensive planning. Overall, preservice senior mathematics teachers were able to work on a statistical project that contained the formulation of a statistical question, planning, data collection, analysis, and reaching a conclusion holistically, even though they faced challenges because of their lack of experience. The study suggests that preservice senior mathematics teachers have the potential to apply statistical knowledge and techniques in a real-world context, and they could proceed with the project with the support of the researchers. We provided implications for the statistical education of teachers and future research.

Keywords: design-based study, pre-service mathematics teachers, statistical investigation projects, statistical model

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Authors: Somruay Apichatibutarapong, Chookiat Pudprommart

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The purpose of this study was to develop of statistical analysis by using R programming via internet applied for agriculture experimental design. Data were collected from 65 items in completely randomized design, randomized block design, Latin square design, split plot design, factorial design and nested design. The quantitative approach was used to investigate the quality of learning media on statistical analysis by using R programming via Internet by six experts and the opinions of 100 students who interested in experimental design and applied statistics. It was revealed that the experts’ opinions were good in all contents except a usage of web board and the students’ opinions were good in overall and all items.

Keywords: experimental design, r programming, applied statistics, statistical analysis

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Authors: Mary Moner Botros Fanawel

Abstract:

Many companies use the statistical tool named as statistical quality control, and which can have a high cost for the companies interested on these statistical tools. The evaluation of the quality of products and services is an important topic, but the reduction of the cost of the implantation of the statistical quality control also has important benefits for the companies. For this reason, it is important to implement a economic design for the various steps included into the statistical quality control. In this paper, we describe some relevant aspects related to the economic design of a quality control chart for the proportion of defective items. They are very important because the suggested issues can reduce the cost of implementing a quality control chart for the proportion of defective items. Note that the main purpose of this chart is to evaluate and control the proportion of defective items of a production process.

Keywords: model predictive control, hierarchical control structure, genetic algorithm, water quality with DBPs objectives proportion, type I error, economic plan, distribution function bootstrap control limit, p-value method, out-of-control signals, p-value, quality characteristics

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Authors: Yunus Doğan, Ahmet Durap

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Coastal regions are the one of the most commonly used places by the natural balance and the growing population. In coastal engineering, the most valuable data is wave behaviors. The amount of this data becomes very big because of observations that take place for periods of hours, days and months. In this study, some statistical methods such as the wave spectrum analysis methods and the standard statistical methods have been used. The goal of this study is the discovery profiles of the different coast areas by using these statistical methods, and thus, obtaining an instance based data set from the big data to analysis by using data mining algorithms. In the experimental studies, the six sample data sets about the wave behaviors obtained by 20 minutes of observations from Mersin Bay in Turkey and converted to an instance based form, while different clustering techniques in data mining algorithms were used to discover similar coastal places. Moreover, this study discusses that this summarization approach can be used in other branches collecting big data such as medicine.

Keywords: clustering algorithms, coastal engineering, data mining, data summarization, statistical methods

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Authors: El Asnaoui Khalid, Aksasse Brahim, Ouanan Mohammed

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In this paper, we are interested in the problem of finding similar images in a large database. For this purpose we propose a new algorithm based on a combination of the 2-D histogram intersection in the HSV space and statistical moments. The proposed histogram is based on a 3x3 window and not only on the intensity of the pixel. This approach can overcome the drawback of the conventional 1-D histogram which is ignoring the spatial distribution of pixels in the image, while the statistical moments are used to escape the effects of the discretisation of the color space which is intrinsic to the use of histograms. We compare the performance of our new algorithm to various methods of the state of the art and we show that it has several advantages. It is fast, consumes little memory and requires no learning. To validate our results, we apply this algorithm to search for similar images in different image databases.

Keywords: 2-D histogram, statistical moments, indexing, similarity distance, histograms intersection

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Authors: Weihao Wang, Zhulin Zong

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Two-dimensional ordered statistical constant false alarm detection is a widely used method for detecting weak target signals in radar signal processing applications. The method is based on analyzing the statistical characteristics of the noise and clutter present in the radar signal and then using this information to set an appropriate detection threshold. In this approach, the reference cell of the unit to be detected is divided into several reference subunits. These subunits are used to estimate the noise level and adjust the detection threshold, with the aim of minimizing the false alarm rate. By using an ordered statistical approach, the method is able to effectively suppress the influence of clutter and noise, resulting in a low false alarm rate. The detection process involves a number of steps, including filtering the input radar signal to remove any noise or clutter, estimating the noise level based on the statistical characteristics of the reference subunits, and finally, setting the detection threshold based on the estimated noise level. One of the main advantages of two-dimensional ordered statistical constant false alarm detection is its ability to detect weak target signals in the presence of strong clutter and noise. This is achieved by carefully analyzing the statistical properties of the signal and using an ordered statistical approach to estimate the noise level and adjust the detection threshold. In conclusion, two-dimensional ordered statistical constant false alarm detection is a powerful technique for detecting weak target signals in radar signal processing applications. By dividing the reference cell into several subunits and using an ordered statistical approach to estimate the noise level and adjust the detection threshold, this method is able to effectively suppress the influence of clutter and noise and maintain a low false alarm rate.

Keywords: two-dimensional, ordered statistical, constant false alarm, detection, weak target signals

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Authors: Yoshio Kurosawa

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The applications of soundproof materials for reduction of high frequency automobile interior noise have been researched. This paper presents a sound pressure prediction technique including wind noise by Hybrid Statistical Energy Analysis (HSEA) in order to reduce weight of acoustic insulations. HSEA uses both analytical SEA and experimental SEA. As a result of chassis dynamo test and road test, the validity of SEA modeling was shown, and utility of the method was confirmed.

Keywords: vibration, noise, road noise, statistical energy analysis

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Authors: Mohd Zamri Osman, Mohd Aizaini Maarof, Mohd Foad Rohani

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Human skin detection recognized as the primary step in most of the applications such as face detection, illicit image filtering, hand recognition and video surveillance. The performance of any skin detection applications greatly relies on the two components: feature extraction and classification method. Skin color is the most vital information used for skin detection purpose. However, color feature alone sometimes could not handle images with having same color distribution with skin color. A color feature of pixel-based does not eliminate the skin-like color due to the intensity of skin and skin-like color fall under the same distribution. Hence, the statistical color analysis will be exploited such mean and standard deviation as an additional feature to increase the reliability of skin detector. In this paper, we studied the effectiveness of statistical color feature for human skin detection. Furthermore, the paper analyzed the integrated color and texture using eight classifiers with three color spaces of RGB, YCbCr, and HSV. The experimental results show that the integrating statistical feature using Random Forest classifier achieved a significant performance with an F1-score 0.969.

Keywords: color space, neural network, random forest, skin detection, statistical feature

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Authors: S. Zhang, L. Zhang, X. Chen

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Due to the large uncertainty on the mechanical properties of FRP (fibre reinforced plastic), the reliability evaluation of FRP structures are currently receiving much attention in industry. However, possible statistical correlation between ply mechanical properties has been so far overlooked, and they are mostly assumed to be independent random variables. In this study, the statistical correlation between ply mechanical properties of uni-directional and plain weave composite is firstly analyzed by a combination of Monte-Carlo simulation and finite element modeling of the FRP unit cell. Large linear correlation coefficients between the in-plane mechanical properties are observed, and the correlation coefficients are heavily dependent on the uncertainty of the fibre volume ratio. It is also observed that the correlation coefficients related to Poisson’s ratio are negative while others are positive. To experimentally achieve the statistical correlation coefficients between in-plane mechanical properties of FRP, all concerned in-plane mechanical properties of the same specimen needs to be known. In-plane shear modulus of FRP is experimentally derived by the approach suggested in the ASTM standard D5379M. Tensile tests are conducted using the same specimens used for the shear test, and due to non-uniform tensile deformation a modification factor is derived by a finite element modeling. Digital image correlation is adopted to characterize the specimen non-uniform deformation. The preliminary experimental results show a good agreement with the numerical analysis on the statistical correlation. Then, failure probability of laminate plates is calculated in cases considering and not considering the statistical correlation, using the Monte-Carlo and Markov Chain Monte-Carlo methods, respectively. The results highlight the importance of accounting for the statistical correlation between ply mechanical properties to achieve accurate failure probability of laminate plates. Furthermore, it is found that for the multi-layer laminate plate, the statistical correlation between the ply elastic properties significantly affects the laminate reliability while the effect of statistical correlation between the ply strength is minimal.

Keywords: failure probability, FRP, reliability, statistical correlation

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Authors: Mohammad A. Alolayan, John S. Evans, James K. Hammitt

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The value of statistical life has been estimated for a middle eastern country with high economical subsidization system. In this study, in-person interviews were conducted on a stratified random sample to estimate the value of mortality risk. Double-bounded dichotomous choice questions followed by open-ended question were used in the interview to investigate the willingness to pay of the respondent for mortality risk reduction. High willingness to pay was found to be associated with high income and education. Also, females were found to have lower willingness to pay than males. The estimated value of statistical life is larger than the ones estimated for western countries where taxation system exists. This estimate provides a baseline for monetizing the health benefits for proposed policy or program to the decision makers in an eastern country. Also, the value of statistical life for a country in the region can be extrapolated from this this estimate by using the benefit transfer method.

Keywords: mortality, risk, VSL, willingness-to-pay

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Authors: B. H. Aitchanov, Sh. K. Aitchanova, O. A. Baimuratov

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This paper is focused on dynamic pulse-frequency modulation (DPFM) control systems. Currently, the control law based on DPFM control signals is widely used in direct digital control subsystems introduced in the automated control systems of technological processes. Statistical analysis of automatic control systems is reduced to its construction of functional relationships between the statistical characteristics of the errors processes and input processes. Structural and dynamic Volterra models of digital pulse-frequency control systems can be used to develop methods for generating the dependencies, differing accuracy, requiring the amount of information about the statistical characteristics of input processes and computing labor intensity of their use.

Keywords: digital dynamic pulse-frequency control systems, dynamic pulse-frequency modulation, control object, discrete filter, impulse device, microcontroller

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Authors: Maxim A. Kadatskiy, Konstantin V. Khishchenko

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Iron alloys are widespread components in various types of structural materials which are exposed to intensive thermal and mechanical loads. Various quantum-statistical cell models with the approximation of self-consistent field can be used for the prediction of the behavior of these materials under extreme conditions. The application of these models is even more valid, the higher the temperature and the density of matter. Results of Hugoniot calculation for iron alloys in the framework of three quantum-statistical (the Thomas–Fermi, the Thomas–Fermi with quantum and exchange corrections and the Hartree–Fock–Slater) models are presented. Results of quantum-statistical calculations are compared with results from other reliable models and available experimental data. It is revealed a good agreement between results of calculation and experimental data for terra pascal pressures. Advantages and disadvantages of this approach are shown.

Keywords: alloy, Hugoniot, iron, terapascal pressure

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Authors: Ibtihaj Al-Siyabi

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The crisis of COVID-19 posed enormous challenges to the statistical providers. While official statistics were disrupted by the pandemic and related containment measures, there was a growing and pressing need for real-time data and statistics to inform decisions. This paper gives an account of the way the pandemic impacted the operations of the National Statistical Offices (NSOs) in general in terms of data collection and methods used and the main challenges encountered by them based on international surveys. It highlights the performance of the Statistical Centre for the Cooperation Council for the Arab Countries of the Gulf, GCC-STAT, and its responsiveness to the pandemic placing special emphasis on environmental statistics. The paper concludes by confirming the GCC-STAT’s resilience and success in facing the challenges.

Keywords: NSO, COVID-19, statistics, crisis, pandemic

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Authors: Daniel S. Brox

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Starting from earthquake fault dynamic equations, a correspondence between earthquake occurrence statistics in a seismic region before a major earthquake and eigenvalue statistics of a differential operator whose bound state eigenfunctions characterize the distribution of stress in the seismic region is derived. Modeling these eigenvalue statistics with a 2D Coulomb gas statistical physics model, previously reported deviation of seismic activation earthquake occurrence statistics from Gutenberg-Richter statistics in time intervals preceding the major earthquake is derived. It also explains how statistical physics modeling predicts a finite-dimensional nonlinear dynamic system that describes real-time velocity model evolution in the region undergoing seismic activation and how this prediction can be tested experimentally.

Keywords: seismic activation, statistical physics, geodynamics, signal processing

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Authors: Okolie Chukwulozie Paul, Iwenofu Chinwe Onyedika, Sinebe Jude Ebieladoh, M. C. Nwosu

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The research work is based on the statistical analysis of the processing data. The essence is to analyze the data statistically and to generate a design model for the production mix of soap manufacturing products in Bejoy manufacturing company Nkpologwu, Aguata Local Government Area, Anambra state, Nigeria. The statistical analysis shows the statistical analysis and the correlation of the data. T test, Partial correlation and bi-variate correlation were used to understand what the data portrays. The design model developed was used to model the data production yield and the correlation of the variables show that the R2 is 98.7%. However, the results confirm that the data is fit for further analysis and modeling. This was proved by the correlation and the R-squared.

Keywords: General Linear Model, correlation, variables, pearson, significance, T-test, soap, production mix and statistic

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Authors: Da-Ming Huang, Ya-Ting Tsai, Shyh-Hau Wang

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Ultrasound signals backscattered from the soft tissues are mainly depending on the size, density, distribution, and other elastic properties of scatterers in the interrogated sample volume. The quantitative analysis of ultrasonic backscattering is frequently implemented using the statistical approach due to that of backscattering signals tends to be with the nature of the random variable. Thus, the statistical analysis, such as Nakagami statistics, has been applied to characterize the density and distribution of scatterers of a sample. Yet, the accuracy of statistical analysis could be readily affected by the receiving signals associated with the nature of incident ultrasound wave and acoustical properties of samples. Thus, in the present study, efforts were made to explore such effects as the ultrasound operational modes and attenuation of biological tissue on the estimation of corresponding Nakagami statistical parameter (m parameter). In vitro measurements were performed from healthy and pathological fibrosis porcine livers using different single-element ultrasound transducers and duty cycles of incident tone burst ranging respectively from 3.5 to 7.5 MHz and 10 to 50%. Results demonstrated that the estimated m parameter tends to be sensitively affected by the use of ultrasound operational modes as well as the tissue attenuation. The healthy and pathological tissues may be characterized quantitatively by m parameter under fixed measurement conditions and proper calibration.

Keywords: ultrasound backscattering, statistical analysis, operational mode, attenuation

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Authors: Zahid Ullah, Atlas Khan

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The rapid growth of data in diverse domains has created an urgent need for effective utilization of mathematical and statistical sciences in data analytics. This abstract explores the journey from theory to practice, emphasizing the importance of harnessing mathematical and statistical innovations to unlock the full potential of data analytics. Drawing on a comprehensive review of existing literature and research, this study investigates the fundamental theories and principles underpinning mathematical and statistical sciences in the context of data analytics. It delves into key mathematical concepts such as optimization, probability theory, statistical modeling, and machine learning algorithms, highlighting their significance in analyzing and extracting insights from complex datasets. Moreover, this abstract sheds light on the practical applications of mathematical and statistical sciences in real-world data analytics scenarios. Through case studies and examples, it showcases how mathematical and statistical innovations are being applied to tackle challenges in various fields such as finance, healthcare, marketing, and social sciences. These applications demonstrate the transformative power of mathematical and statistical sciences in data-driven decision-making. The abstract also emphasizes the importance of interdisciplinary collaboration, as it recognizes the synergy between mathematical and statistical sciences and other domains such as computer science, information technology, and domain-specific knowledge. Collaborative efforts enable the development of innovative methodologies and tools that bridge the gap between theory and practice, ultimately enhancing the effectiveness of data analytics. Furthermore, ethical considerations surrounding data analytics, including privacy, bias, and fairness, are addressed within the abstract. It underscores the need for responsible and transparent practices in data analytics, and highlights the role of mathematical and statistical sciences in ensuring ethical data handling and analysis. In conclusion, this abstract highlights the journey from theory to practice in harnessing mathematical and statistical sciences in data analytics. It showcases the practical applications of these sciences, the importance of interdisciplinary collaboration, and the need for ethical considerations. By bridging the gap between theory and practice, mathematical and statistical sciences contribute to unlocking the full potential of data analytics, empowering organizations and decision-makers with valuable insights for informed decision-making.

Keywords: data analytics, mathematical sciences, optimization, machine learning, interdisciplinary collaboration, practical applications

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