Search results for: statistical distribution functions

Authors: Masomeh Jamshid Nejad

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Nowadays, statistical literacy is no longer a necessary skill but an essential skill with broad applications across diverse fields, especially in operational decision areas such as business management, finance, and economics. As such, learning and deep understanding of statistical concepts are essential in the context of business studies. One of the crucial topics in statistical theory and its application is the normal distribution, often called a bell-shaped curve. To interpret data and conduct hypothesis tests, comprehending the properties of normal distribution (the mean and standard deviation) is essential for business students. This requires undergraduate students in the field of economics and business management to visualize and work with data following a normal distribution. Since technology is interconnected with education these days, it is important to teach statistics topics in the context of Python, R-studio, and Microsoft Excel to undergraduate students. This research endeavours to shed light on the effect of Excel-based instruction on learners’ knowledge of statistics, specifically the central concept of normal distribution. As such, two groups of undergraduate students (from the Business Management program) were compared in this research study. One group underwent Excel-based instruction and another group relied only on traditional teaching methods. We analyzed experiential data and BBA participants’ responses to statistic-related questions focusing on the normal distribution, including its key attributes, such as the mean and standard deviation. The results of our study indicate that exposing students to Excel-based learning supports learners in comprehending statistical concepts more effectively compared with the other group of learners (teaching with the traditional method). In addition, students in the context of Excel-based instruction showed ability in picturing and interpreting data concentrated on normal distribution.

Keywords: statistics, excel-based instruction, data visualization, pedagogy

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Authors: Hazem M. Al-Mofleh

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In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized Hyperbolic Secant Distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Rényi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

Keywords: bimodality, estimation, hazard function, moments, Shannon’s entropy

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Authors: Chen-Fang Tsai, Shin-Li Lu

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Distribution-free control chart is an oncoming area from the statistical process control charts in recent years. Some researchers have developed various nonparametric control charts and investigated the detection capability of these charts. The major advantage of nonparametric control charts is that the underlying process is not specifically considered the assumption of normality or any parametric distribution. In this paper, two nonparametric exponentially weighted moving average (EWMA) control charts based on nonparametric tests, namely NE-S and NE-M control charts, are proposed for monitoring process variability. Generally, weighted moving average (GWMA) control charts are extended by utilizing design and adjustment parameters for monitoring the changes in the process variability, namely NG-S and NG-M control charts. Statistical performance is also investigated on NG-S and NG-M control charts with run rules. Moreover, sensitivity analysis is performed to show the effects of design parameters under the nonparametric NG-S and NG-M control charts.

Keywords: Distribution-free control chart, EWMA control charts, GWMA control charts

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Authors: Muna Tabuni

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The paper contains an investigation of the behavior of the Zeros of Bargmann functions for one and two-mode systems. A brief introduction to Harmonic oscillator formalism for one and two-mode is given. The Bargmann analytic representation for one and two-mode has been studied. The zeros of Bargmann analytic function for one-mode are considered. The Q Husimi functions are introduced. The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros are discussed. The zeros of Bargmann analytic functions for two-mode are introduced. Various examples have been given.

Keywords: Bargmann functions, two-mode, zeros, harmonic oscillator

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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: Chaitanya Varma, Arpan Mehar

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The present study demonstrates the procedure to analyse speed data collected on various four-lane divided sections in India. Field data for the study was collected at different straight and curved sections on rural highways with the help of radar speed gun and video camera. The data collected at the sections were analysed and parameters pertain to speed distributions were estimated. The different statistical distribution was analysed on vehicle type speed data and for mixed traffic speed data. It was found that vehicle type speed data was either follows the normal distribution or Log-normal distribution, whereas the mixed traffic speed data follows more than one type of statistical distribution. The most common fit observed on mixed traffic speed data were Beta distribution and Weibull distribution. The separate operating speed model based on traffic and roadway geometric parameters were proposed in the present study. The operating speed model with traffic parameters and curve geometry parameters were established. Two different operating speed models were proposed with variables 1/R and Ln(R) and were found to be realistic with a different range of curve radius. The models developed in the present study are simple and realistic and can be used for forecasting operating speed on four-lane highways.

Keywords: highway, mixed traffic flow, modeling, operating speed

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Authors: Rui Teixeira, Alan O’Connor, Maria Nogal

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The statistical theory of extreme events is progressively a topic of growing interest in all the fields of science and engineering. The changes currently experienced by the world, economic and environmental, emphasized the importance of dealing with extreme occurrences with improved accuracy. When it comes to the design of offshore structures, particularly offshore wind turbines, the importance of efficiently characterizing extreme events is of major relevance. Extreme events are commonly characterized by extreme values theory. As an alternative, the accurate modeling of the tails of statistical distributions and the characterization of the low occurrence events can be achieved with the application of the Peak-Over-Threshold (POT) methodology. The POT methodology allows for a more refined fit of the statistical distribution by truncating the data with a minimum value of a predefined threshold u. For mathematically approximating the tail of the empirical statistical distribution the Generalised Pareto is widely used. Although, in the case of the exceedances of significant wave data (H_s) the 2 parameters Weibull and the Exponential distribution, which is a specific case of the Generalised Pareto distribution, are frequently used as an alternative. The Generalized Pareto, despite the existence of practical cases where it is applied, is not completely recognized as the adequate solution to model exceedances over a certain threshold u. References that set the Generalised Pareto distribution as a secondary solution in the case of significant wave data can be identified in the literature. In this framework, the current study intends to tackle the discussion of the application of statistical models to characterize exceedances of wave data. Comparison of the application of the Generalised Pareto, the 2 parameters Weibull and the Exponential distribution are presented for different values of the threshold u. Real wave data obtained in four buoys along the Irish coast was used in the comparative analysis. Results show that the application of the statistical distributions to characterize significant wave data needs to be addressed carefully and in each particular case one of the statistical models mentioned fits better the data than the others. Depending on the value of the threshold u different results are obtained. Other variables of the fit, as the number of points and the estimation of the model parameters, are analyzed and the respective conclusions were drawn. Some guidelines on the application of the POT method are presented. Modeling the tail of the distributions shows to be, for the present case, a highly non-linear task and, due to its growing importance, should be addressed carefully for an efficient estimation of very low occurrence events.

Keywords: extreme events, offshore structures, peak-over-threshold, significant wave data

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Authors: Ilaria Lucrezia Amerise

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The statistical modelling of precipitation data for a given portion of territory is fundamental for the monitoring of climatic conditions and for Hydrogeological Management Plans (HMP). This modelling is rendered particularly complex by the changes taking place in the frequency and intensity of precipitation, presumably to be attributed to the global climate change. This paper applies the Wakeby distribution (with 5 parameters) as a theoretical reference model. The number and the quality of the parameters indicate that this distribution may be the appropriate choice for the interpolations of the hydrological variables and, moreover, the Wakeby is particularly suitable for describing phenomena producing heavy tails. The proposed estimation methods for determining the value of the Wakeby parameters are the same as those used for density functions with heavy tails. The commonly used procedure is the classic method of moments weighed with probabilities (probability weighted moments, PWM) although this has often shown difficulty of convergence, or rather, convergence to a configuration of inappropriate parameters. In this paper, we analyze the problem of the likelihood estimation of a random variable expressed through its quantile function. The method of maximum likelihood, in this case, is more demanding than in the situations of more usual estimation. The reasons for this lie, in the sampling and asymptotic properties of the estimators of maximum likelihood which improve the estimates obtained with indications of their variability and, therefore, their accuracy and reliability. These features are highly appreciated in contexts where poor decisions, attributable to an inefficient or incomplete information base, can cause serious damages.

Keywords: generalized extreme values, likelihood estimation, precipitation data, Wakeby distribution

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Authors: Mohanad Rezeq, Tarik Aouam, Frederik Gailly

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In times of armed conflicts, various security checkpoints are placed by authorities to control the flow of merchandise into and within areas of conflict. The flow of humanitarian trucks that is added to the regular flow of commercial trucks, together with the complex security procedures, creates congestion and long waiting times at the security checkpoints. This causes distribution costs to increase and shortages of relief aid to the affected people to occur. Our research proposes a decision-support tool to assist planners and policymakers in building efficient plans for the distribution of relief aid, taking into account congestion at security checkpoints. The proposed tool is built around a multi-item humanitarian distribution planning model based on multi-phase design science methodology that has as its objective to minimize distribution and back ordering costs subject to capacity constraints that reflect congestion effects using nonlinear clearing functions. Using the 2014 Gaza War as a case study, we illustrate the application of the proposed tool, model the underlying relief-aid humanitarian supply chain, estimate clearing functions at different security checkpoints, and conduct computational experiments. The decision support tool generated a shipment plan that was compared to two benchmarks in terms of total distribution cost, average lead time and work in progress (WIP) at security checkpoints, and average inventory and backorders at distribution centers. The first benchmark is the shipment plan generated by the fixed capacity model, and the second is the actual shipment plan implemented by the planners during the armed conflict. According to our findings, modeling and optimizing supply chain flows reduce total distribution costs, average truck wait times at security checkpoints, and average backorders when compared to the executed plan and the fixed-capacity model. Finally, scenario analysis concludes that increasing capacity at security checkpoints can lower total operations costs by reducing the average lead time.

Keywords: humanitarian distribution planning, relief-aid distribution, congestion, clearing functions

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Authors: Vinicius R. Domingues, Luan C. S. M. Ozelim

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The statistical study has become indispensable for various fields of knowledge. Not any different, in Geotechnics the study of probabilistic and statistical methods has gained power considering its use in characterizing the uncertainties inherent in soil properties. One of the situations where engineers are constantly faced is the definition of a probability distribution that represents significantly the sampled data. To be able to discard bad distributions, goodness-of-fit tests are necessary. In this paper, three non-parametric goodness-of-fit tests are applied to a data set computationally generated to test the goodness-of-fit of them to a series of known distributions. It is shown that the use of normal distribution does not always provide satisfactory results regarding physical and behavioral representation of the modeled parameters.

Keywords: Kolmogorov-Smirnov test, Anderson-Darling test, Cramer-Von-Mises test, nonparametric adherence tests

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Authors: Baoshan Huang, Fanbiao Bao, Bing Li, Lianghua Zeng, Yi Zheng

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Parameter control strategy based on statistical characteristics can analyze the choice of the transmission ratio of an automobile transmission. According to the difference of the transmission gear, the number and spacing of the gear can be determined. Transmission ratio distribution of transmission needs to satisfy certain distribution law. According to the statistic characteristics of driving parameters, the shift control strategy of the vehicle is analyzed. CVT shift schedule adjustment algorithm based on statistical characteristic parameters can be seen from the above analysis, if according to the certain algorithm to adjust the size of, can adjust the target point are in the best efficiency curve and dynamic curve between the location, to alter the vehicle characteristics. Based on the dynamic characteristics and the practical application of the vehicle, this paper presents the setting scheme of the transmission ratio.

Keywords: vehicle dynamics, transmission ratio, transmission parameters, statistical characteristics

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Authors: Bashara Want

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One of the key factors limiting the performance of magnetic memory is that the coercivity has a distribution with finite width, and the reversal starts at the weakest link in the distribution. So one must first know the distribution of coercivities in order to learn how to reduce the width of distribution and increase the coercivity field to obtain a system with narrow width. First Order Reversal Curve (FORC) method characterizes a system with hysteresis via the distribution of local coercivities and, in addition, the local interaction field. The method is more versatile than usual conventional major hysteresis loops that give only the statistical behaviour of the magnetic system. The FORC method will be presented and discussed at the conference.

Keywords: magnetic materials, hysteresis, first-order reversal curve method, nanostructures

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Valerii Dashuk

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The usage of the confidence intervals in economics and econometrics is widespread. To be able to investigate a random variable more thoroughly, joint tests are applied. One of such examples is joint mean-variance test. A new approach for testing such hypotheses and constructing confidence sets is introduced. Exploring both the value of the random variable and its deviation with the help of this technique allows checking simultaneously the shift and the probability of that shift (i.e., portfolio risks). Another application is based on the normal distribution, which is fully defined by mean and variance, therefore could be tested using the introduced approach. This method is based on the difference of probability density functions. The starting point is two sets of normal distribution parameters that should be compared (whether they may be considered as identical with given significance level). Then the absolute difference in probabilities at each 'point' of the domain of these distributions is calculated. This measure is transformed to a function of cumulative distribution functions and compared to the critical values. Critical values table was designed from the simulations. The approach was compared with the other techniques for the univariate case. It differs qualitatively and quantitatively in easiness of implementation, computation speed, accuracy of the critical region (theoretical vs. real significance level). Stable results when working with outliers and non-normal distributions, as well as scaling possibilities, are also strong sides of the method. The main advantage of this approach is the possibility to extend it to infinite-dimension case, which was not possible in the most of the previous works. At the moment expansion to 2-dimensional state is done and it allows to test jointly up to 5 parameters. Therefore the derived technique is equivalent to classic tests in standard situations but gives more efficient alternatives in nonstandard problems and on big amounts of data.

Keywords: confidence set, cumulative distribution function, hypotheses testing, normal distribution, probability density function

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Alicia C. Sanchez

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This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.

Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation

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Authors: T. H. Young, Y. J. Tsai

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A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work.  The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.

Keywords: stress analysis, free vibration, plate buckling, nonuniform in-plane edge shear

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Rafida M. Elobaid

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Most of the literature on goodness-of-fit test try to provide a theoretical basis for studying empirical distribution functions. Such goodness-of-fit tests are Kolmogorove-Simirnov and Crumer-Von Mises Type tests. However, it is likely that most of literature has not focused in details on the relationship of the values of the test statistics and skewness or kurtosis. The aim of this study is to investigate the behavior of the values of the χ2 test statistic with the variation of the skewness of right skewed distribution. A simulation study is conducted to generate random numbers from Weibull distribution. For a fixed sample sizes, different levels of skewness are considered, and the corresponding values of the χ2 test statistic are calculated. Using different sample sizes, the results show an inverse relationship between the value of χ2 test and the level of skewness for Wiebull distribution, i.e the value of χ2 test statistic decreases as the value of skewness increases. The research results also show that with large values of skewness we are more confident that the data follows the assumed distribution. Nonparametric Kendall τ test is used to confirm these results.

Keywords: goodness-of-fit test, chi-square test, simulation, continuous right skewed distributions

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: Xinyi Huang

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As a former British colony and one of the most famous world financial centers today, Hong Kong attracts countless businessmen and tourists to visit or settle down every year. Hong Kong is a land that leads western culture to blossom in Asia, and in the meantime, it inherits the unique charm of Chinese traditional culture. The Chinese-English bilingual phenomenon can be seen everywhere in Hong Kong. The public presentation, code choice, and practical use of these two languages can also reflect the economic and social status, population distribution, and individual identity construction of a specific area. This paper mainly compares the linguistic landscape of two areas with different social functions in Hong Kong: Tsim Sha Tsui, a large commercial center in Kowloon, and Tai Wai, a residential area in New Territories. By adopting the methodology of the Walking Tour, the bilingual data of 75 photos are collected unintentionally during the field trip in the two areas. Through the methods of quantitative analysis and linguistic landscape studies, this paper deeply analyzes the similarities and differences in language distribution and the respective social functions of two languages in the two places.

Keywords: bilingualism, linguistic landscape, identity construction, commodification

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Dongxu Chen, Yipeng Li

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This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods.

Keywords: image denoising, Poisson noise, information geometry, nonlocal-means

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Authors: Seon Soon Choi

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Magnesium alloy has been widely used in structure such as an automobile. It is necessary to consider probabilistic characteristics of a structural material because a fatigue behavior of a structure has a randomness and uncertainty. The purpose of this study is to find the characteristics of the cumulative distribution function (CDF) of the grown crack size at a specified fatigue crack propagation life and to investigate a statistical crack propagation in magnesium alloys. The statistical fatigue data of the grown crack size are obtained through the fatigue crack propagation (FCP) tests under different maximum fatigue load conditions conducted on the replicated specimens of magnesium alloys. The 3-parameter Weibull distribution is used to find the CDF of grown crack size. The CDF of grown crack size in case of larger maximum fatigue load has longer tail in below 10 percent and above 90 percent. The fatigue failure occurs easily as the tail of CDF of grown crack size becomes long. The fatigue behavior under the larger maximum fatigue load condition shows more rapid propagation and failure mode.

Keywords: cumulative distribution function, fatigue crack propagation, grown crack size, magnesium alloys, maximum fatigue load

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Authors: Hamdi Amroun, Yacine Benziani, Mehdi Ammi

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In this paper, we propose an approach of detecting the behavior of the viewers of a TV program in a non-controlled environment. The experiment we propose is based on the use of three types of connected objects (smartphone, smart watch, and a connected remote control). 23 participants were observed while watching their TV programs during three phases: before, during and after watching a TV program. Their behaviors were detected using an approach based on The Dempster Shafer Theory (DST) in two phases. The first phase is to approximate dynamically the mass functions using an approach based on the correlation coefficient. The second phase is to calculate the approximate mass functions. To approximate the mass functions, two approaches have been tested: the first approach was to divide each features data space into cells; each one has a specific probability distribution over the behaviors. The probability distributions were computed statistically (estimated by empirical distribution). The second approach was to predict the TV-viewing behaviors through the use of classifiers algorithms and add uncertainty to the prediction based on the uncertainty of the model. Results showed that mixing the fusion rule with the computation of the initial approximate mass functions using a classifier led to an overall of 96%, 95% and 96% success rate for the first, second and third TV-viewing phase respectively. The results were also compared to those found in the literature. This study aims to anticipate certain actions in order to maintain the attention of TV viewers towards the proposed TV programs with usual connected objects, taking into account the various uncertainties that can be generated.

Keywords: Iot, TV-viewing behaviors identification, automatic classification, unconstrained environment

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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: 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: 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: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: Lu Ren, You-Liang Fang, Yan-Gang Zhao

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In recent years, the application of BIM (Building Information Modelling) to construction schedule plan has been the focus of more and more researchers. In order to assess the reasonable level of the BIM-based construction schedule plan, that is whether the schedule can be completed on time, some researchers have introduced reliability theory to evaluate. In the process of evaluation, the uncertain factors affecting the construction schedule plan are regarded as random variables, and probability distributions of the random variables are assumed to be normal distribution, which is determined using two parameters evaluated from the mean and standard deviation of statistical data. However, in practical engineering, most of the uncertain influence factors are not normal random variables. So the evaluation results of the construction schedule plan will be unreasonable under the assumption that probability distributions of random variables submitted to the normal distribution. Therefore, in order to get a more reasonable evaluation result, it is necessary to describe the distribution of random variables more comprehensively. For this purpose, cubic normal distribution is introduced in this paper to describe the distribution of arbitrary random variables, which is determined by the first four moments (mean, standard deviation, skewness and kurtosis). In this paper, building the BIM model firstly according to the design messages of the structure and making the construction schedule plan based on BIM, then the cubic normal distribution is used to describe the distribution of the random variables due to the collecting statistical data of the random factors influencing construction schedule plan. Next the reliability analysis of the construction schedule plan based on BIM can be carried out more reasonably. Finally, the more accurate evaluation results can be given providing reference for the implementation of the actual construction schedule plan. In the last part of this paper, the more efficiency and accuracy of the proposed methodology for the reliability analysis of the construction schedule plan based on BIM are conducted through practical engineering case.

Keywords: BIM, construction schedule plan, cubic normal distribution, reliability analysis

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