Search results for: multivariate statistics.

Authors: Ephraim Gower, Thato Tsalaile, Monageng Kgwadi, Malcolm Hawksford.

Abstract:

In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.

Keywords: Circular Convolution, linear Convolution, mixture density function.

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Authors: Babu Sena Paul, Ratnajit Bhattacharjee

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Relay based communication has gained considerable importance in the recent years. In this paper we find the end-toend statistics of a two hop non-regenerative relay branch, each hop being Nakagami-m faded. Closed form expressions for the probability density functions of the signal envelope at the output of a selection combiner and a maximal ratio combiner at the destination node are also derived and analytical formulations are verified through computer simulation. These density functions are useful in evaluating the system performance in terms of bit error rate and outage probability.

Keywords: co-operative diversity, diversity combining, maximal ratio combining, selection combining.

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Authors: Zhichao Jiao, Craig Farnham, Jihui Yuan, Kazuo Emura

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It is common to use the outdoor design weather data to select the air-conditioning capacity in the building design stage. The meteorological elements of outdoor design weather data are usually selected based on their excess frequency separately while the dependency between the elements is not well considered. It means that the simultaneous occurrence probability of these elements is smaller than the original excess frequency which may cause an overestimation of selecting air-conditioning capacity. Therefore, the copula approach which can capture the dependency between multivariate data was used to model the joint distributions of the meteorological elements, like air temperature and global solar radiation. We suggest a method based on the specific simultaneous occurrence probability of these two elements of selecting more credible outdoor design conditions. The hourly weather data at 12 noon from 2001 to 2010 in Tokyo, Japan are used to analyze the dependency structure and joint distribution, the Gaussian copula represents the dependence of data best. According to calculating the air temperature and global solar radiation in specific simultaneous occurrence probability and the common exceeding, the results show that both the air temperature and global solar radiation based on simultaneous occurrence probability are lower than these based on the conventional method in the same probability.

Keywords: Copula approach, Design weather database, energy conservation, HVAC.

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Authors: Gundeep Singh Bindra

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Statistics indicate that more than 1000 phishing attacks are launched every month. With 57 million people hit by the fraud so far in America alone, how do we combat phishing?This publication aims to discuss strategies in the war against Phishing. This study is an examination of the analysis and critique found in the ways adopted at various levels to counter the crescendo of phishing attacks and new techniques being adopted for the same. An analysis of the measures taken up by the varied popular Mail servers and popular browsers is done under this study. This work intends to increase the understanding and awareness of the internet user across the globe and even discusses plausible countermeasures at the users as well as the developers end. This conceptual paper will contribute to future research on similar topics.

Keywords: Anti-phishing, countermeasures, effectiveness, fake pages, security analysis.

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Authors: Shang-En Yu

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Human society, there are many uncertainties, such as economic growth rate forecast of the financial crisis, many scholars have, since the the Song Chissom two scholars in 1993 the concept of the so-called fuzzy time series (Fuzzy Time Series)different mode to deal with these problems, a previous study, however, usually does not consider the relevant variables selected and fuzzy process based solely on subjective opinions the fuzzy semantic discrete, so can not objectively reflect the characteristics of the data set, in addition to carrying outforecasts are often fuzzy rules as equally important, failed to consider the importance of each fuzzy rule. For these reasons, the variable selection (Factor Selection) through self-organizing map (Self-Organizing Map, SOM) and proposed high-end weighted multivariate fuzzy time series model based on fuzzy neural network (Fuzzy-BPN), and using the the sequential weighted average operator (Ordered Weighted Averaging operator, OWA) weighted prediction. Therefore, in order to verify the proposed method, the Taiwan stock exchange (Taiwan Stock Exchange Corporation) Taiwan Weighted Stock Index (Taiwan Stock Exchange Capitalization Weighted Stock Index, TAIEX) as experimental forecast target, in order to filter the appropriate variables in the experiment Finally, included in other studies in recent years mode in conjunction with this study, the results showed that the predictive ability of this study further improve.

Keywords: Heterogeneity, residential mortgage loans, foreclosure.

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Authors: Dhongkyu Yoon

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Environmental statistics reveals that the pollution of acid rain in South Korea is a serious issue. Yet the awareness of people is low. Even after a gradual decrease of pollutant emission in Korea, the acidity has not been reduced. There no boundaries in the atmosphere are set and the influence of the neighboring countries such as China is apparent. Governmental efforts among China, Japan and Korea have been made on this issue. However, not much progress has been observed. Along with the governmental activities, therefore, an active monitoring of the pollution among the countries and the promotion of environmental awareness at the civil level including especially the middle and high schools are highly recommended. It will be this young generation who will face damaged country as inheritance not the current generation.

Keywords: acid rain, international collaboration, pollution, South Korea

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Authors: Theodosia Prodromou

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The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.

Keywords: Inferential reasoning, learning, modelling, statistical inference, simulation.

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Authors: Norazah Mohd Suki, Norbayah Mohd Suki

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Descriptive statistics was performed with the aim to achieve research objective of to investigate lecturers- usage of the mobile technology for teaching. A representative sample of 20 lecturers from the Faculty of Industrial Art & Design Technology of Universiti Industri Selangor (UNISEL), Malaysia was selected as the respondents. The result attested that lecturers fully accept the concept of mobility in learning and game play is appealing concept to support classroom learning. Subsequently, analogous experience on small size of keypad, screen resolution, and navigation could be the major problematic factors to students and affect their mobile learning process. Recommendation for future research is also presented.

Keywords: Academics, Mobile e-learning, Mobile technology, Readiness.

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Authors: Gulnara Moldasheva

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The research explores the relationship between management responsibility and corporate governance of listed companies in Kazakhstan. This research employs firm level data of selected listed non-financial firms and firm level data “operational” financial sector, consisted from banking sector, insurance companies and accumulated pension funds using multivariate regression analysis under fixed effect model approach. Ownership structure includes institutional ownership, managerial ownership and private investor’s ownership. Management responsibility of the firm is expressed by the decision of the firm on amount of leverage. Results of the cross sectional panel study for non-financial firms showed that only institutional shareholding is significantly negatively correlated with debt to equity ratio. Findings from “operational” financial sector show that leverage is significantly affected only by the CEO/Chair duality and the size of financial institutions, and insignificantly affected by ownership structure. Also, the findings show, that there is a significant negative relationship between profitability and the debt to equity ratio for non-financial firms, which is consistent with pecking order theory. Generally, the found results suggest that corporate governance and a management responsibility play important role in corporate performance of listed firms in Kazakhstan.

Keywords: Corporate governance, corporate performance, debt to equity ratio, ownership.

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Authors: Asaad Moosa

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In recent years with the rapid development of Internet and the Web, more and more web applications have been deployed in many fields and organizations such as finance, military, and government. Together with that, hackers have found more subtle ways to attack web applications. According to international statistics, SQL Injection is one of the most popular vulnerabilities of web applications. The consequences of this type of attacks are quite dangerous, such as sensitive information could be stolen or authentication systems might be by-passed. To mitigate the situation, several techniques have been adopted. In this research, a security solution is proposed using Artificial Neural Network to protect web applications against this type of attacks. The solution has been experimented on sample datasets and has given promising result. The solution has also been developed in a prototypic web application firewall called ANNbWAF.

Keywords: Artificial Neural Networks ANN, SQL Injection, Web Application Firewall WAF, Web Application Scanner WAS.

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Authors: Roya Maqami, Kaveh Qaderi Bagajan, Mohammad Mahdi Yousefi, Saeed Moradi

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The purpose of this study is to investigate the efficacy of solution-focused group therapy on improving the depressed mothers of child abuser families. This study was carried out in the form of a semi-pilot, pre-test and post-test on two groups (experimental and control). Subjects include all mothers and their children that are the members of Shush and Naser Khosro child home. Beck Depression Inventory and Child Trauma Questionnaire were used to collect data. First, child abuse questionnaire was completed by children, Then Beck Depression Inventory was completed by their mothers that 22 of them were recognized as depressed and randomly divided in two groups of experimental and control. After applying pre-test for both of these groups, the intervention of solution- focused group therapy was performed in five sessions on experimental group. Finally, post-test was applied on both groups and subsequently in a month, follow-up test was performed. T-test, multivariate variance, and repeated measurement analysis of variance were used to analyze the data. According to the findings, it can be concluded that this therapy leads to the improvement of depressed mother's mood. As a result, the intervention of solution-focused group therapy is useful in order to improve the depressing mood of mothers of child abuser families.

Keywords: Child Abuse, Depressed Mothers, Child Abuser Families, Solution-focused Group Therapy.

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Authors: Víctor Manuel Muñoz-Sánchez, Antonio Manuel Pérez-Flores

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This paper analyzes the institutionalization of social protest in Spain. In the current crisis Podemos party seems to represent the political positions of the most affected citizens by the economic situation. It studies using quantitative techniques (statistical bivariate analysis), focusing on the exploitation of several bases of statistics data from the Center for Sociological and Research of Spanish Government, 15M movement characterization to its institutionalization in the Podemos party. Making a comparison between the participant's profile by the 15M and the social bases of Podemos votes. Data on the transformation of the socio-demographic profile of the fans, connoisseurs and 15M participants and voters are given.

Keywords: Collective action, emerging parties, political parties, social protest.

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

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In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: Asymptotic relative efficiency, non-linear rank-based, robust, rank estimates, variogram.

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Authors: David Calderón Villegas, Thomas Kalitzky

Abstract:

Run-of-river (RoR) hydropower projects represent a viable, clean, and cost-effective alternative to dam-based plants and provide decentralized power production. However, RoR schemes’ cost-effectiveness depends on the proper selection of site and design flow, which is a challenging task because it requires multivariate analysis. In this respect, this study presents the development of an investment decision support tool for assessing the optimal size of an RoR scheme considering the technical, environmental, and cost constraints. The net present value (NPV) from a project perspective is used as an objective function for supporting the investment decision. The tool has been tested by applying it to an actual RoR project recently proposed in Colombia. The obtained results show that the optimum point in financial terms does not match the flow that maximizes energy generation from exploiting the river's available flow. For the case study, the flow that maximizes energy corresponds to a value of 5.1 m3/s. In comparison, an amount of 2.1 m3/s maximizes the investors NPV. Finally, a sensitivity analysis is performed to determine the NPV as a function of the debt rate changes and the electricity prices and the CapEx. Even for the worst-case scenario, the optimal size represents a positive business case with an NPV of 2.2 USD million and an internal rate of return (IRR) 1.5 times higher than the discount rate. 

Keywords: small hydropower, renewable energy, RoR schemes, optimal sizing, financial analysis

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Authors: N. Dahbi, M. Daoudi, A.Belghachi

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The present work deals with the calculation of transport properties of Hg0.8Cd0.2Te (MCT) semiconductor in degenerate case. Due to their energy-band structure, this material becomes degenerate at moderate doping densities, which are around 1015 cm-3, so that the usual Maxwell-Boltzmann approximation is inaccurate in the determination of transport parameters. This problem is faced by using Fermi-Dirac (F-D) statistics, and the non-parabolic behavior of the bands may be approximated by the Kane model. The Monte Carlo (MC) simulation is used here to determinate transport parameters: drift velocity, mean energy and drift mobility versus electric field and the doped densities. The obtained results are in good agreement with those extracted from literature.

Keywords: degeneracy case, Hg0.8Cd0.2Te semiconductor, Monte Carlo simulation, transport parameters.

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Authors: Mohamed Lahcen BenSaad, Sun XingMing

Abstract:

Information hiding, especially watermarking is a promising technique for the protection of intellectual property rights. This technology is mainly advanced for multimedia but the same has not been done for text. Web pages, like other documents, need a protection against piracy. In this paper, some techniques are proposed to show how to hide information in web pages using some features of the markup language used to describe these pages. Most of the techniques proposed here use the white space to hide information or some varieties of the language in representing elements. Experiments on a very small page and analysis of five thousands web pages show that these techniques have a wide bandwidth available for information hiding, and they might form a solid base to develop a robust algorithm for web page watermarking.

Keywords: Digital Watermarking, Information Hiding, Markup Language, Text watermarking, Software Watermarking.

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Authors: Jin-Lung Guan, Ming-Ta Yang, Jhy-Cherng Gu, Hsin-Hung Chang, Chin-Lung Huang

Abstract:

Voltage flicker problems have long existed in several of the distribution areas served by the Taiwan Power Company. In the past, those research results indicating that the estimated ΔV10 value based on the conventional method is significantly smaller than the survey value. This paper is used to study the relationship between the voltage flicker problems and harmonic power variation for the power system with electric arc furnaces. This investigation discussed thought the effect of harmonic power fluctuation with flicker estimate value. The method of field measurement, statistics and simulation is used. The survey results demonstrate that 10 ΔV estimate must account for the effect of harmonic power variation.

Keywords: Voltage Flicker, Harmonic Power, EAF.

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Authors: M. Byzedi, B. Saghafian

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Droughts are complex, natural hazards that, to a varying degree, affect some parts of the world every year. The range of drought impacts is related to drought occurring in different stages of the hydrological cycle and usually different types of droughts, such as meteorological, agricultural, hydrological, and socioeconomical are distinguished. Streamflow drought was analyzed by the method of truncation level (at 70% level) on daily discharges measured in 54 hydrometric stations in southwestern Iran. Frequency analysis was carried out for annual maximum series (AMS) of drought deficit volume and duration series. Some factors including physiographic, climatic, geologic, and vegetation cover were studied as influential factors in the regional analysis. According to the results of factor analysis, six most effective factors were identified as area, rainfall from December to February, the percent of area with Normalized Difference Vegetation Index (NDVI) <0.1, the percent of convex area, drainage density and the minimum of watershed elevation that explained 90.9% of variance. The homogenous regions were determined by cluster analysis and discriminate function analysis. Suitable multivariate regression models were evaluated for streamflow drought deficit volume with 2 years return period. The significance level of regression models was 0.01. The results showed that the watershed area is the most effective factor with high correlation with deficit volume. Also, drought duration was not a suitable drought index for regional analysis.

Keywords: Iran, Streamflow drought, truncation level method, regional analysis.

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Authors: I. Erins, J. Erina

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The aim of this article is to assess the existing business models used by the banks operating in the CEE countries in the time period from 2006 till 2011. In order to obtain research results, the authors performed qualitative analysis of the scientific literature on bank business models, which have been grouped into clusters that consist of such components as: 1) capital and reserves; 2) assets; 3) deposits, and 4) loans. In their turn, bank business models have been developed based on the types of core activities of the banks, and have been divided into four groups: Wholesale, Investment, Retail and Universal Banks. Descriptive statistics have been used to analyse the models, determining mean, minimal and maximal values of constituent cluster components, as well as standard deviation. The analysis of the data is based on such bank variable indices as Return on Assets (ROA) and Return on Equity (ROE).

Keywords: Banks, Business model, CEE, ROA, ROE.

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Authors: Valene J. Gresham, MA, Laura A. Brodie

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For the last decade, statistics show traumatic brain injury (TBI) is a growing concern in our legal system. In an effort to obtain data regarding the influence of neuropsychological expert witness testimony in a criminal case, this study tested three hypotheses. H1: The majority of jurors will vote not guilty, due to mild head injury. H2: The jurors will give more credence to the testimony of the neuropsychologist rather than the psychiatrist. H3: The jurors will be more lenient in their sentencing, given the testimony of the neuropsychologist-s testimony. The criterion for inclusion in the study as a participant is identical to those used for inclusion in the eligibility for jury duty in the United States. A chisquared test was performed to analyze the data for the three hypotheses. The results supported all of the hypotheses; however statistical significance was seen in H1 and H2 only.

Keywords: Expert witness, jury decision, neuropsychology, traumatic brain injury.

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Authors: Ondřej Nowak

Abstract:

This paper presents an exploration into the structure of the corporate governance network and interlocking directorates in the Czech Republic. First a literature overview and a basic terminology of the network theory is presented. Further in the text, statistics and other calculations relevant to corporate governance networks are presented. For this purpose an empirical data set consisting of 2 906 joint stock companies in the Czech Republic was examined. Industries with the highest average number of interlocks per company were healthcare, and energy and utilities. There is no observable link between the financial performance of the company and the number of its interlocks. Also interlocks with financial companies are very rare.

Keywords: Corporate Governance, Interlocking Directorates, Network Theory, Czech Republic.

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Authors: F. F. Howard, I. Yakubu, C. B. Boye, J. S. Y. Kuma

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Natural and human activities, such as mining operations, expose the natural soil to adverse environmental conditions, leading to contamination of soil, groundwater, and surface water, which has negative effects on humans, flora, and fauna. Bare or partly exposed soil is most liable to fluvial erosion. This paper enumerates various methods used to identify, map, and model fluvial erosion in a mining environment. Classical, Artificial Intelligence (AI), and GIS methods have been reviewed. One of the many classical methods used to estimate river erosion is the Revised Universal Soil Loss Equation (RUSLE) model. The RUSLE model is easy to use. Its reliance on empirical relationships that may not always be applicable to specific circumstances or locations is a flaw. Other classical models for estimating fluvial erosion are the Soil and Water Assessment Tool (SWAT) and the Universal Soil Loss Equation (USLE). These models offer a more complete understanding of the underlying physical processes and encompass a wider range of situations. Although more difficult to utilise, they depend on the availability and dependability of input data for correctness. AI can help deal with multivariate and complex difficulties and predict soil loss with higher accuracy than traditional methods, and also be used to build unique models for identifying degraded areas. AI techniques have become popular as an alternative predictor for degraded environments. However, this research proposed a hybrid of classical, AI, and GIS methods for efficient and effective modelling of fluvial erosion.

Keywords: Fluvial erosion, classical methods, Artificial Intelligence, Geographic Information System.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

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In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Ritu Shitak

Abstract:

Humans are social mammals, of the primate order. Our biology, our behaviour and our pathologies are unique to us. In our desire to understand, reduce solitary confinement one source of information is the many reports of social isolation of other social mammals, especially primates. A behavioural study was conducted in the department of pharmacology at Indira Gandhi Medical College, Shimla in Himachalpradesh province in India using white albino mice. Different behavioural parameters were observed by using open field, tail suspension, tests for aggressive behaviour and social interactions and the effect of isolation was studied. The results were evaluated and the standard statistics were applied. The said study was done to establish facts that isolation itself impairs social behaviour and can lead to alcohol dependence as well as related drug dependence.

Keywords: Albino Mice, Drug Dependence, Social isolation.

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Authors: Norwati Mustapha, Manijeh Jalali, Abolghasem Bozorgniya, Mehrdad Jalali

Abstract:

Web usage mining algorithms have been widely utilized for modeling user web navigation behavior. In this study we advance a model for mining of user-s navigation pattern. The model makes user model based on expectation-maximization (EM) algorithm.An EM algorithm is used in statistics for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. The experimental results represent that by decreasing the number of clusters, the log likelihood converges toward lower values and probability of the largest cluster will be decreased while the number of the clusters increases in each treatment.

Keywords: Web Usage Mining, Expectation maximization, navigation pattern mining.

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Authors: U. Datta

Abstract:

The main objective of this study is to find a suitable approach to monitor the land infrastructure growth over a period of time using multispectral satellite images. Bi-temporal change detection method is unable to indicate the continuous change occurring over a long period of time. To achieve this objective, the approach used here estimates a statistical model from series of multispectral image data over a long period of time, assuming there is no considerable change during that time period and then compare it with the multispectral image data obtained at a later time. The change is estimated pixel-wise. Statistical composite hypothesis technique is used for estimating pixel based change detection in a defined region. The generalized likelihood ratio test (GLRT) is used to detect the changed pixel from probabilistic estimated model of the corresponding pixel. The changed pixel is detected assuming that the images have been co-registered prior to estimation. To minimize error due to co-registration, 8-neighborhood pixels around the pixel under test are also considered. The multispectral images from Sentinel-2 and Landsat-8 from 2015 to 2018 are used for this purpose. There are different challenges in this method. First and foremost challenge is to get quite a large number of datasets for multivariate distribution modelling. A large number of images are always discarded due to cloud coverage. Due to imperfect modelling there will be high probability of false alarm. Overall conclusion that can be drawn from this work is that the probabilistic method described in this paper has given some promising results, which need to be pursued further.

Keywords: Co-registration, GLRT, infrastructure growth, multispectral, multitemporal, pixel-based change detection.

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Authors: F. Azna A. Shahabuddin, Kamarulzaman Ibrahim, Abdul Aziz Jemain

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Many works have been carried out to compare the efficiency of several goodness of fit procedures for identifying whether or not a particular distribution could adequately explain a data set. In this paper a study is conducted to investigate the power of several goodness of fit tests such as Kolmogorov Smirnov (KS), Anderson-Darling(AD), Cramer- von- Mises (CV) and a proposed modification of Kolmogorov-Smirnov goodness of fit test which incorporates a variance stabilizing transformation (FKS). The performances of these selected tests are studied under simple random sampling (SRS) and Ranked Set Sampling (RSS). This study shows that, in general, the Anderson-Darling (AD) test performs better than other GOF tests. However, there are some cases where the proposed test can perform as equally good as the AD test.

Keywords: Empirical distribution function, goodness-of-fit, order statistics, ranked set sampling

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Authors: Rami H. Fouad

Abstract:

The purpose of this study is to identify and evaluate the scale of implementation of Just-In-Time (JIT) in the different industrial sectors in the Middle East. This study analyzes the empirical data collected by a questionnaire survey distributed to companies in three main industrial sectors in the Middle East, which are: food, chemicals and fabrics. The following main hypotheses is formulated and tested: (The requirements of JIT application differ according to the type of industrial sector).Descriptive statistics and Box plot analysis were used to examine the hypotheses. This study indicates a reasonable evidence for accepting the main hypotheses. It reveals that there is no standard way to adopt JIT as a production system. But each industrial sector should concentrate in the investment on critical requirements that differ according to the nature and strategy of production followed in that sector.

Keywords: Just-In-Time, JIT, Questionnaire, Types of Industrial Sectors.

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Authors: J. Ruso, M. Krsmanovic, A. Trajkovic, Z. Rakicevic

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Since the late 1970s, quality management has become an important tool for achieving a high quality of public e-administration services in many countries. Very important part of quality management in e-administration is measurement of quality indicators related to this sector. Therefore, this paper gives a description of e-administration, including statistics about it and other examples from many countries worldwide, as well as the explanation of quality management in public e-administration. The paper also gives a list and description of quality indicators relevant to e-administration, as part of quality management within the e-administration. Through a literature review and best practices, the paper aims to analyze quality indicators measurement and other parts of good quality management when it comes to the public e-administration and consequently to show the usefulness of quality management in public e-administration in order to provide services of high quality.

Keywords: e-Administration, quality indicators, quality management.

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Authors: Jimeng Shi, Mahek Jain, Giri Narasimhan

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Time Series Forecasting (TSF) is used to predict the target variables at a future time point based on the learning from previous time points. To keep the problem tractable, learning methods use data from a fixed length window in the past as an explicit input. In this paper, we study how the performance of predictive models change as a function of different look-back window sizes and different amounts of time to predict into the future. We also consider the performance of the recent attention-based transformer models, which had good success in the image processing and natural language processing domains. In all, we compare four different deep learning methods (Recurrent Neural Network (RNN), Long Short-term Memory (LSTM), Gated Recurrent Units (GRU), and Transformer) along with a baseline method. The dataset (hourly) we used is the Beijing Air Quality Dataset from the website of University of California, Irvine (UCI), which includes a multivariate time series of many factors measured on an hourly basis for a period of 5 years (2010-14). For each model, we also report on the relationship between the performance and the look-back window sizes and the number of predicted time points into the future. Our experiments suggest that Transformer models have the best performance with the lowest Mean   Absolute Errors (MAE = 14.599, 23.273) and Root Mean Square Errors (RSME = 23.573, 38.131) for most of our single-step and multi-steps predictions. The best size for the look-back window to predict 1 hour into the future appears to be one day, while 2 or 4 days perform the best to predict 3 hours into the future.

Keywords: Air quality prediction, deep learning algorithms, time series forecasting, look-back window.

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