Search results for: extended skew normal distribution

Authors: Hao-Hsi Tseng, Hsin-Yun Lee

Abstract:

The Most Advantageous Tender (MAT) has been criticized for its susceptibility to dictatorial situations and for its processing of same score, same rank issues. This study applies the four criteria from Arrow's Impossibility Theorem to construct a mechanism for revealing illegitimate scores in scoring methods. While commonly be used to improve on problems resulting from extreme scores, ranking methods hide significant defects, adversely affecting selection fairness. To address these shortcomings, this study relies mainly on the overall evaluated score method, using standardized scores plus normal cumulative distribution function conversion to calculate the evaluation of vender preference. This allows for free score evaluations, which reduces the influence of dictatorial behavior and avoiding same score, same rank issues. Large-scale simulations confirm that this method outperforms currently used methods using the Impossibility Theorem.

Keywords: Arrow’s impossibility theorem, cumulative normal distribution function, most advantageous tender, scoring method

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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

Procedia PDF Downloads 235

Authors: Mohadeseh Shojaei Shahrokhabadi, Ding-Geng (Din) Chen

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Positive continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical cost data. To jointly model semi-continuous longitudinal cost data and survival data and to provide marginalized covariate effect estimates, a marginalized two-part joint model (MTJM) has been developed for outcome variables with lognormal distributions. In this paper, we propose MTJM models for outcome variables from a generalized gamma (GG) family of distributions. The GG distribution constitutes a general family that includes approximately all of the most frequently used distributions like the Gamma, Exponential, Weibull, and Log Normal. In the proposed MTJM-GG model, the conditional mean from a conventional two-part model with a three-parameter GG distribution is parameterized to provide the marginal interpretation for regression coefficients. In addition, MTJM-gamma and MTJM-Weibull are developed as special cases of MTJM-GG. To illustrate the applicability of the MTJM-GG, we applied the model to a set of real electronic health record data recently collected in Iran, and we provided SAS code for application. The simulation results showed that when the outcome distribution is unknown or misspecified, which is usually the case in real data sets, the MTJM-GG consistently outperforms other models. The GG family of distribution facilitates estimating a model with improved fit over the MTJM-gamma, standard Weibull, or Log-Normal distributions.

Keywords: marginalized two-part model, zero-inflated, right-skewed, semi-continuous, generalized gamma

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Authors: Hatice Karakoyun, Mustafa Akdag

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This study has been made to examine the attitudes of pre-school teachers towards values education. The study has been made as a general scanning model. The study’s working group contains 108 pre-school teachers who worked in Diyarbakır, Turkey. In this study Values Education Attitude Scale (VEAS), which developed by Yaşaroğlu (2014), was used. In order to analyze the data for sociodemographic structure, percentage and frequency values were examined. The Kolmogorov-Smirnov method was used in determination of the normal distribution of data. During analyzing the data, KolmogorovSimirnov test and the normal curved histograms were examined to determine which statistical analyzes would be applied on the scale and it was found that the distribution was not normal. Thus, the Mann Whitney U analysis technique which is one of the nonparametric statistical analysis techniques were used to test the difference of the scores obtained from the scale in terms of independent variables. According to the analyses, it seems that pre-school teachers’ attitudes toward values education are positive. According to the scale with the highest average, it points out that pre-school teachers think that values education is very important for students’ and children’s future. The variables included in the scale (gender, seniority, age group, education, school type, school place) seem to have no effect on the pre-school teachers’ attitude grades which joined to the study.

Keywords: attitude scale, pedagogy, pre-school teacher, values education

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Authors: M. Z. Raqab, Debasis Kundu, M. A. Meraou

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In this paper, we have analyzed maximum precipitation data during a particular period of time obtained from different stations in the Global Historical Climatological Network of the USA. One important point to mention is that some stations are shut down on certain days for some reason or the other. Hence, the maximum values are recorded by excluding those readings. It is assumed that the number of stations that operate follows zero-truncated Poisson random variables, and the daily precipitation follows a lognormal random variable. We call this model a compound truncated Poisson lognormal model. The proposed model has three unknown parameters, and it can take a variety of shapes. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals also can be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model, it is observed that the proposed model provides a better fit than some of the existing models.

Keywords: compound Poisson lognormal distribution, EM algorithm, maximum likelihood estimation, approximate maximum likelihood estimation, Fisher information, skew distribution

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Authors: Suparman Suparman

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A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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Authors: S. Ghasemi, K. Khorasani

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In this paper, the problem of fault detection and isolation in the attitude control subsystem of spacecraft formation flying is considered. In order to design the fault detection method, an extended Kalman filter is utilized which is a nonlinear stochastic state estimation method. Three fault detection architectures, namely, centralized, decentralized, and semi-decentralized are designed based on the extended Kalman filters. Moreover, the residual generation and threshold selection techniques are proposed for these architectures.

Keywords: component, formation flight of satellites, extended Kalman filter, fault detection and isolation, actuator fault

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Authors: Abbas Hani, Maryam Jassasizadeh

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The concentrations of Cd, Pb, and Ni were determined from 40 soil samples collected in surface soils of Khark Island. Geostatistic methods and GIS were used to identify heavy metal sources and their spatial pattern. Principal component analysis coupled with correlation between heavy metals showed that level of mentioned heavy metal was lower than the standard level. Then the data obtained from the soil analyzing were studied for the purposes of normal distribution. The best way of interior finding for cadmium and nickel was ordinary kriging and the best way of interpolation of lead was inverse distance weighted. The result of this study help us to understand heavy metals distribution and make decision for remediation of soil pollution.

Keywords: geostatistics, ordinary kriging, heavy metals, GIS, Khark

Procedia PDF Downloads 137

Authors: Shumaila Ehtisham

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In Statistical Distribution Theory, considering an additional parameter to classical distributions is a usual practice. In this study, a new distribution referred to as α-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution including explicit expressions for the moment generating function, mode, quantiles, entropies and order statistics are obtained. Unknown parameters have been estimated by using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that α-Power Pareto distribution outperforms while compared to different variants of Pareto distribution on the basis of model selection criteria.

Keywords: α-power transformation, maximum likelihood estimation, moment generating function, Pareto distribution

Procedia PDF Downloads 191

Authors: Abdulnasir Hossen, Alaa Barhoum, Deepali Jaju, V. Gowri, L. Al-Kharusi, M. Hassan, K. Al-Hashmi

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Preeclampsia is a pregnancy disorder associated with increase in blood pressure and excess amount of protein in the urine. HRV analysis has been used by many researchers to identify preeclamptic pregnancy from normal pregnancy. A study in this regard to identify preeclamptic pregnancy in Oman from normal pregnant was conducted on 40 subjects (20 patients and 20 normal). The subjects were collected from two hospitals in Oman. A Fast Fourier transform (FFT) spectral analysis has shown that patients with preeclamptic pregnancy have a reduction in the power of the HF band and an increase in the power of the LF band of HRV compared with subjects with normal pregnancy. The accuracy of identification obtained was 80%.

Keywords: preelampsia, pregnancy hypertension, normal pregnant, FFT, spectral analysis, HRV

Procedia PDF Downloads 526

Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

Procedia PDF Downloads 314

Authors: A. J. S. P. Nileema, S. Kulatunga , S. H. Palihawadana

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Computer aided detection (CAD) system was developed for the diagnosis of pulmonary tuberculosis using digital chest X-rays with MATLAB image processing techniques using a statistical approach. The study comprised of 200 digital chest radiographs collected from the National Hospital for Respiratory Diseases - Welisara, Sri Lanka. Pre-processing was done to remove identification details. Lung fields were segmented and then divided into four quadrants; right upper quadrant, left upper quadrant, right lower quadrant, and left lower quadrant using the image processing techniques in MATLAB. Contrast, correlation, homogeneity, energy, entropy, and maximum probability texture features were extracted using the gray level co-occurrence matrix method. Descriptive statistics and normal distribution analysis were performed using SPSS. Depending on the radiologists’ interpretation, chest radiographs were classified manually into PTB - positive (PTBP) and PTB - negative (PTBN) classes. Features with standard normal distribution were analyzed using an independent sample T-test for PTBP and PTBN chest radiographs. Among the six features tested, contrast, correlation, energy, entropy, and maximum probability features showed a statistically significant difference between the two classes at 95% confidence interval; therefore, could be used in the classification of chest radiograph for PTB diagnosis. With the resulting value ranges of the five texture features with normal distribution, a classification algorithm was then defined to recognize and classify the quadrant images; if the texture feature values of the quadrant image being tested falls within the defined region, it will be identified as a PTBP – abnormal quadrant and will be labeled as ‘Abnormal’ in red color with its border being highlighted in red color whereas if the texture feature values of the quadrant image being tested falls outside of the defined value range, it will be identified as PTBN–normal and labeled as ‘Normal’ in blue color but there will be no changes to the image outline. The developed classification algorithm has shown a high sensitivity of 92% which makes it an efficient CAD system and with a modest specificity of 70%.

Keywords: chest radiographs, computer aided detection, image processing, pulmonary tuberculosis

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Authors: Mahmoudi Noureddine, Bouregba Rachid

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In this paper the stress intensity factors of a slant-cracked plate of AISI 304 stainless steel, have been calculated using extended finite element method and finite element method (FEM) in ABAQUS software, the results were compared with theoretical values.

Keywords: stress intensity factors, extended finite element method, stainless steel, abaqus

Procedia PDF Downloads 585

Authors: Fahmi Hassan, Noorizan Abdul Aziz, Yahaya Hassan, Hazlinda Abu Hassan

Abstract:

Sepsis incidence in critical care settings is a major problem in health care. Extended antibiotic infusion is thought to be superior to traditional dosing especially when treating critically ill patients with sepsis. We compared clinical outcomes of critically ill patients with sepsis receiving 30-minute meropenem infusion and three-hour meropenem infusion. A retrospective case-control study was conducted among septic patients treated with meropenem infusion in ICUs of three hospitals. Patients included in the study received either extended or standard meropenem infusion as per the practice of individual settings. Outcomes and clinical data were retrospectively collected from the electronic databases and patients’ files. A total of 108 patients received extended meropenem infusion while another 117 patients received standard meropenem infusion. Patients receiving the extended meropenem infusion were found to have a significantly lower shorter length of hospital and ICU stay. It was also found that among those receiving extended meropenem infusion, 54.7% (64/117) had a reduction of SAPS II score, while only 44% (48/108) of patients receiving standard meropenem infusion had reduced scores. This study will strengthen the evidence in using extended meropenem infusion as a standard practice in critical care settings. As this is the first study of its kind done in Malaysia, it proves that prolonged meropenem infusion may be beneficial to critically ill patients with sepsis. However, randomized clinical trials with large sample size should be carried out in local settings in order to minimize other confounders that may influence with the result of the study.

Keywords: antibiotics, beta lactams, critical care, extended infusion, meropenem

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Authors: A. Bayle, F. Plouraboué

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Water Distribution Network (WDN) still suffers from a lack of knowledge about fast pressure transient events prediction, although the latter may considerably impact their durability. Accidental or planned operating activities indeed give rise to complex pressure interactions and may drastically modified the local pressure value generating leaks and, in rare cases, pipe’s break. In this context, a numerical predictive analysis is conducted to prevent such event and optimize network management. A couple of Python/FORTRAN 90, home-made software, has been developed using Method Of Characteristic (MOC) solving for water-hammer equations. The solver is validated by direct comparison with theoretical and experimental measurement in simple configurations whilst afterward extended to network analysis. The algorithm's most costly steps are designed for parallel computation. A various set of boundary conditions and energetic losses models are considered for the network simulations. The results are analyzed in both real and frequencies domain and provide crucial information on the pressure distribution behavior within the network.

Keywords: energetic losses models, method of characteristic, numerical predictive analysis, water distribution network, water hammer

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Authors: Boudemagh Naime

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Automatic radar detection requires some methods of adapting to variations in the background clutter in order to control their false alarm rate. The problem becomes more complicated in non-Gaussian environment. In fact, the conventional approach in real time applications requires a complex statistical modeling and much computational operations. To overcome these constraints, we propose another approach based on artificial neural network (ANN-CMLD-CFAR) using a Back Propagation (BP) training algorithm. The considered environment follows a log-normal distribution in the presence of multiple Rayleigh-targets. To evaluate the performances of the considered detector, several situations, such as scale parameter and the number of interferes targets, have been investigated. The simulation results show that the ANN-CMLD-CFAR processor outperforms the conventional statistical one.

Keywords: radat detection, ANN-CMLD-CFAR, log-normal clutter, statistical modelling

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Authors: A. Bozkurt, C. Kocatepe, R. Yumurtaci, İ. C. Tastan, G. Tulun

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Efficient use of energy, with the increase in demand of energy and also with the reduction of natural energy sources, has improved its importance in recent years. Most of the losses in the system from electricity produced until the point of consumption is mostly composed by the energy distribution system. In this study, analysis of the resulting loss in power distribution transformer and distribution power cable is realized which are most of the losses in the distribution system. Transformer losses in the real distribution system were analyzed by CYME Power Engineering Software program. These losses are disclosed for different voltage levels and different loading conditions.

Keywords: distribution system, distribution transformer, power cable, technical losses

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Authors: Sharfi Dirar, Shihab Elhaj, Ahmed El Fatih

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Computational fluid dynamics were used to simulate and study the heated water boiler tube for both normal and rifled tube with a refinement of the mesh to check the convergence. The operation condition was taken from GARRI power station and used in a boundary condition accordingly. The result indicates the rifled tube has higher heat transfer efficiency than the normal tube.

Keywords: boiler tube, convergence check, normal tube, rifled tube

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Shashank Patidar, Sumit Kumar, Atul Srivastava, Suneet Singh

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Present work is concerned with the numerical investigation of thermal response of biological tissues during laser-based photo-thermal therapy for destroying cancerous/abnormal cells with minimal damage to the surrounding normal cells. Light propagation through the biological sample is mathematically modelled by transient radiative transfer equation. In the present work, application of the Lattice Boltzmann Method is extended to analyze transport of short-pulse radiation in a participating medium.In order to determine the two-dimensional temperature distribution inside the tissue medium, the RTE has been coupled with Penne’s bio-heat transfer equation based on Fourier’s law by several researchers in last few years.

Keywords: lattice Boltzmann method, transient radiation transfer equation, dual phase lag model

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Authors: Ali Moradiamani, Samaneh Sadat Sajjadi, Mahdi Jalili

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Power system analysis has been a major research topic in the generation and distribution sections, in both industry and academia, for a long time. Several load flow and fault analysis scenarios have been normally performed to study the performance of different parts of the grid in the context of, for example, voltage and frequency control. Software tools, such as PSCAD, PSSE, and PowerFactory DIgSILENT, have been developed to perform these analyses accurately. Distribution grid had been the passive part of the grid and had been known as the grid of consumers. However, a significant paradigm shift has happened with the emergence of Distributed Energy Resources (DERs) in the distribution level. It means that the concept of power system analysis needs to be extended to the distribution grid, especially considering self sufficient technologies such as microgrids. Compared to the generation and transmission levels, the distribution level includes significantly more generation/consumption nodes thanks to PV rooftop solar generation and battery energy storage systems. In addition, different consumption profile is expected from household residents resulting in a diverse set of scenarios. Emergence of electric vehicles will absolutely make the environment more complicated considering their charging (and possibly discharging) requirements. These complexities, as well as the large size of distribution grids, create challenges for the available power system analysis software. In this paper, we study the requirements of simulation tools in the distribution grid and how data-driven algorithms are required to increase the accuracy of the simulation results.

Keywords: smart grids, distributed energy resources, electric vehicles, battery storage systsms, simulation tools

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: R. Ahmadi, A. Khodadadi, M. Abdollahi

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The removal of copper from a dilute synthetic wastewater (10 mg/L) was studied by ion flotation at laboratory scale. Anionic sodium dodecyl sulfate (SDS) was used as a collector and ethanol as a frother. Different parameters such as pH, collector and frother concentrations, foam height and bubble size distribution (multi bubble ion flotation) were tested to determine the optimum flotation conditions in a Denver type flotation machine. To see into the effect of bubbles size distribution in this paper, a nano-micro bubble generator was designed. The nano and microbubbles that are generated in this way were combined with normal size bubbles generated mechanically. Under the optimum conditions (concentration of SDS: 192mg/l, ethanol: 0.5%v/v, pH value: 4 and froth height=12.5 cm) the best removal obtained for the system Cu/SDS with a dry foam (water recovery: 15.5%) was 85.6%. Coalescence of nano-microbubbles with bubbles of normal size belonging to mechanical flotation cell improved the removal of Cu to a maximum floatability of 92.8% and reduced the water recovery to a 13.1%.The flotation time decreased considerably at 37.5% when the multi bubble ion flotation was used.

Keywords: froth flotation, copper, water treatment, optimization, recycling

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Authors: Ali Razmi, Saeed Golian

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Climate change is known to have the potential to impact adversely hydrologic patterns for variables such as rainfall, maximum and minimum temperature and sea level rise. Long-term average of these climate variables could possibly change over time due to climate change impacts. In this study, trend analysis was performed on rainfall, maximum and minimum temperature and water level data of a coastal area in Manhattan, New York City, Central Park and Battery Park stations to investigate if there is a significant change in the data mean. Partial Man-Kendall test was used for trend analysis. Frequency analysis was then performed on data using common probability distribution functions such as Generalized Extreme Value (GEV), normal, log-normal and log-Pearson. Goodness of fit tests such as Kolmogorov-Smirnov are used to determine the most appropriate distributions. In flood frequency analysis, rainfall and water level data are often separately investigated. However, in determining flood zones, simultaneous consideration of rainfall and water level in frequency analysis could have considerable effect on floodplain delineation (flood extent and depth). The present study aims to perform flood frequency analysis considering joint probability distribution for rainfall and storm surge. First, correlation between the considered variables was investigated. Joint probability distribution of extreme water level and temperature was also investigated to examine how global warming could affect sea level flooding impacts. Copula functions were fitted to data and joint probability of water level with rainfall and temperature for different recurrence intervals of 2, 5, 25, 50, 100, 200, 500, 600 and 1000 was determined and compared with the severity of individual events. Results for trend analysis showed increase in long-term average of data that could be attributed to climate change impacts. GEV distribution was found as the most appropriate function to be fitted to the extreme climate variables. The results for joint probability distribution analysis confirmed the necessity for incorporation of both rainfall and water level data in flood frequency analysis.

Keywords: climate change, climate variables, copula, joint probability

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Authors: Juan Francisco Reinoso Gordo, Francisco Javier Ariza-López, José Rodríguez Avi, Domingo Barrera Rosillo

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The evaluation of the quality of a data product is based on the comparison of the product with a reference of greater accuracy. In the case of MDE data products, quality assessment usually focuses on positional accuracy and few studies consider other terrain characteristics, such as slope and orientation. The proposal that is made consists of evaluating the similarity of two DEMs (a product and a reference), through the joint analysis of the distribution functions of the variables of interest, for example, elevations, slopes and orientations. This is a multivariable approach that focuses on distribution functions, not on single parameters such as mean values or dispersions (e.g. root mean squared error or variance). This is considered to be a more holistic approach. The use of the Kolmogorov-Smirnov test is proposed due to its non-parametric nature, since the distributions of the variables of interest cannot always be adequately modeled by parametric models (e.g. the Normal distribution model). In addition, its application to the multivariate case is carried out jointly by means of a single test on the convolution of the distribution functions of the variables considered, which avoids the use of corrections such as Bonferroni when several statistics hypothesis tests are carried out together. In this work, two DEM products have been considered, DEM02 with a resolution of 2x2 meters and DEM05 with a resolution of 5x5 meters, both generated by the National Geographic Institute of Spain. DEM02 is considered as the reference and DEM05 as the product to be evaluated. In addition, the slope and aspect derived models have been calculated by GIS operations on the two DEM datasets. Through sample simulation processes, the adequate behavior of the Kolmogorov-Smirnov statistical test has been verified when the null hypothesis is true, which allows calibrating the value of the statistic for the desired significance value (e.g. 5%). Once the process has been calibrated, the same process can be applied to compare the similarity of different DEM data sets (e.g. the DEM05 versus the DEM02). In summary, an innovative alternative for the comparison of DEM data sets based on a multinomial non-parametric perspective has been proposed by means of a single Kolmogorov-Smirnov test. This new approach could be extended to other DEM features of interest (e.g. curvature, etc.) and to more than three variables

Keywords: data quality, DEM, kolmogorov-smirnov test, multivariate DEM comparison

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Authors: Abd El Hady N. Ebraheim

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This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: exponentiated, inversion method, maximum likelihood estimation, transmutation map

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Authors: K. A. Adepoju, O. I. Shittu, A. U. Chukwu

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In this paper, a new four-parameter generalized version of the Fisher Snedecor distribution called Beta- F distribution is introduced. The comprehensive account of the statistical properties of the new distributions was considered. Formal expressions for the cumulative density function, moments, moment generating function and maximum likelihood estimation, as well as its Fisher information, were obtained. The flexibility of this distribution as well as its robustness using cancer remission time data was demonstrated. The new distribution can be used in most applications where the assumption underlying the use of other lifetime distributions is violated.

Keywords: fisher-snedecor distribution, beta-f distribution, outlier, maximum likelihood method

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Authors: Hongyu Chen, Li Jiang

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Ubiquitous anomalies endanger the security of our system con- stantly. They may bring irreversible damages to the system and cause leakage of privacy. Thus, it is of vital importance to promptly detect these anomalies. Traditional supervised methods such as Decision Trees and Support Vector Machine (SVM) are used to classify normality and abnormality. However, in some case, the abnormal status are largely rarer than normal status, which leads to decision bias of these methods. Generative adversarial network (GAN) has been proposed to handle the case. With its strong generative ability, it only needs to learn the distribution of normal status, and identify the abnormal status through the gap between it and the learned distribution. Nevertheless, existing GAN-based models are not suitable to process data with discrete values, leading to immense degradation of detection performance. To cope with the discrete features, in this paper, we propose an efficient GAN-based model with specifically-designed loss function. Experiment results show that our model outperforms state-of-the-art models on discrete dataset and remarkably reduce the overhead.

Keywords: GAN, discrete feature, Wasserstein distance, multiple intermediate layers

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Authors: Soniya Takshak, R. K. Sharma

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Let q and n be positive integers, then Fᵩ denotes the finite field of q elements, and Fqn denotes the extension of Fᵩ of degree n. Also, Fᵩ* represents the multiplicative group of non-zero elements of Fᵩ, and the generators of Fᵩ* are called primitive elements. A normal element α of a finite field Fᵩⁿ is such that {α, αᵠ, . . . , αᵠⁿ⁻¹} forms a basis for Fᵩⁿ over Fᵩ. Primitive normal elements have several applications in coding theory and cryptography. So, establishing the existence of primitive normal elements under certain conditions is both theoretically important and a natural issue. In this article, we provide a sufficient condition for the existence of a primitive normal element α in Fᵩⁿ of a prescribed primitive norm and non-zero trace over Fᵩ such that f(α) is also primitive, where f(x) ∈ Fᵩⁿ(x) is a rational function of degree sum m. Particularly, we investigated the rational functions of degree sum 4 over Fᵩⁿ, where q = 11ᵏ and demonstrated that there are only 3 exceptional pairs (q, n), n ≥ 7 for which such kind of primitive normal elements may not exist. In general, we show that such elements always exist except for finitely many choices of (q, n). To arrive to our conclusion, we used additive and multiplicative character sums.

Keywords: finite field, primitive element, normal element, norm, trace, character

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: dynamic system modeling, neural network, normal equation, second order gradient descent

Procedia PDF Downloads 100