Search results for: Estimation of Distribution Algorithms
4155 Performance Enhancement of Motion Estimation Using SSE2 Technology
Authors: Trung Hieu Tran, Hyo-Moon Cho, Sang-Bock Cho
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Motion estimation is the most computationally intensive part in video processing. Many fast motion estimation algorithms have been proposed to decrease the computational complexity by reducing the number of candidate motion vectors. However, these studies are for fast search algorithms themselves while almost image and video compressions are operated with software based. Therefore, the timing constraints for running these motion estimation algorithms not only challenge for the video codec but also overwhelm for some of processors. In this paper, the performance of motion estimation is enhanced by using Intel's Streaming SIMD Extension 2 (SSE2) technology with Intel Pentium 4 processor.Keywords: Motion Estimation, Full Search, Three StepSearch, MMX/SSE/SSE2 Technologies, SIMD.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20994154 On Best Estimation for Parameter Weibull Distribution
Authors: Hadeel Salim Alkutubi
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The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.
Keywords: Maximum Likelihood estimation , Bayes estimation, Jeffery prior information, Simulation study
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12644153 Parameters Estimation of Multidimensional Possibility Distributions
Authors: Sergey Sorokin, Irina Sorokina, Alexander Yazenin
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We present a solution to the Maxmin u/E parameters estimation problem of possibility distributions in m-dimensional case. Our method is based on geometrical approach, where minimal area enclosing ellipsoid is constructed around the sample. Also we demonstrate that one can improve results of well-known algorithms in fuzzy model identification task using Maxmin u/E parameters estimation.
Keywords: Possibility distribution, parameters estimation, Maxmin u/E estimator, fuzzy model identification.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24264152 Electric Load Forecasting Using Genetic Based Algorithm, Optimal Filter Estimator and Least Error Squares Technique: Comparative Study
Authors: Khaled M. EL-Naggar, Khaled A. AL-Rumaih
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This paper presents performance comparison of three estimation techniques used for peak load forecasting in power systems. The three optimum estimation techniques are, genetic algorithms (GA), least error squares (LS) and, least absolute value filtering (LAVF). The problem is formulated as an estimation problem. Different forecasting models are considered. Actual recorded data is used to perform the study. The performance of the above three optimal estimation techniques is examined. Advantages of each algorithms are reported and discussed.
Keywords: Forecasting, Least error squares, Least absolute Value, Genetic algorithms
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27224151 Applying Sequential Pattern Mining to Generate Block for Scheduling Problems
Authors: Meng-Hui Chen, Chen-Yu Kao, Chia-Yu Hsu, Pei-Chann Chang
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The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems.
Keywords: Combinatorial problems, Sequential Pattern Mining, Estimation of Distribution Algorithms, Artificial Chromosomes.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17184150 Robust UKF Insensitive to Measurement Faults for Pico Satellite Attitude Estimation
Authors: Halil Ersin Soken, Chingiz Hajiyev
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In the normal operation conditions of a pico satellite, conventional Unscented Kalman Filter (UKF) gives sufficiently good estimation results. However, if the measurements are not reliable because of any kind of malfunction in the estimation system, UKF gives inaccurate results and diverges by time. This study, introduces Robust Unscented Kalman Filter (RUKF) algorithms with the filter gain correction for the case of measurement malfunctions. By the use of defined variables named as measurement noise scale factor, the faulty measurements are taken into the consideration with a small weight and the estimations are corrected without affecting the characteristic of the accurate ones. Two different RUKF algorithms, one with single scale factor and one with multiple scale factors, are proposed and applied for the attitude estimation process of a pico satellite. The results of these algorithms are compared for different types of measurement faults in different estimation scenarios and recommendations about their applications are given.Keywords: attitude algorithms, Kalman filters, robustestimation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16234149 Probability Density Estimation Using Advanced Support Vector Machines and the Expectation Maximization Algorithm
Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag
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This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.
Keywords: Density Estimation, SVM, Learning Algorithms, Parameters Estimation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25054148 Exponentially Weighted Simultaneous Estimation of Several Quantiles
Authors: Valeriy Naumov, Olli Martikainen
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In this paper we propose new method for simultaneous generating multiple quantiles corresponding to given probability levels from data streams and massive data sets. This method provides a basis for development of single-pass low-storage quantile estimation algorithms, which differ in complexity, storage requirement and accuracy. We demonstrate that such algorithms may perform well even for heavy-tailed data.Keywords: Quantile estimation, data stream, heavy-taileddistribution, tail index.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15314147 Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution
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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34714146 Spread Spectrum Code Estimation by Genetic Algorithm
Authors: V. R. Asghari, M. Ardebilipour
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In the context of spectrum surveillance, a method to recover the code of spread spectrum signal is presented, whereas the receiver has no knowledge of the transmitter-s spreading sequence. The approach is based on a genetic algorithm (GA), which is forced to model the received signal. Genetic algorithms (GAs) are well known for their robustness in solving complex optimization problems. Experimental results show that the method provides a good estimation, even when the signal power is below the noise power.Keywords: Code estimation, genetic algorithms, spread spectrum.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15704145 Performance Analysis of MUSIC, Root-MUSIC and ESPRIT DOA Estimation Algorithm
Authors: N. P. Waweru, D. B. O. Konditi, P. K. Langat
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Direction of Arrival estimation refers to defining a mathematical function called a pseudospectrum that gives an indication of the angle a signal is impinging on the antenna array. This estimation is an efficient method of improving the quality of service in a communication system by focusing the reception and transmission only in the estimated direction thereby increasing fidelity with a provision to suppress interferers. This improvement is largely dependent on the performance of the algorithm employed in the estimation. Many DOA algorithms exists amongst which are MUSIC, Root-MUSIC and ESPRIT. In this paper, performance of these three algorithms is analyzed in terms of complexity, accuracy as assessed and characterized by the CRLB and memory requirements in various environments and array sizes. It is found that the three algorithms are high resolution and dependent on the operating environment and the array size.
Keywords: Direction of Arrival, Autocorrelation matrix, Eigenvalue decomposition, MUSIC, ESPRIT, CRLB.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 87564144 State Estimation of a Biotechnological Process Using Extended Kalman Filter and Particle Filter
Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte, V. Grincas
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This paper deals with advanced state estimation algorithms for estimation of biomass concentration and specific growth rate in a typical fed-batch biotechnological process. This biotechnological process was represented by a nonlinear mass-balance based process model. Extended Kalman Filter (EKF) and Particle Filter (PF) was used to estimate the unmeasured state variables from oxygen uptake rate (OUR) and base consumption (BC) measurements. To obtain more general results, a simplified process model was involved in EKF and PF estimation algorithms. This model doesn’t require any special growth kinetic equations and could be applied for state estimation in various bioprocesses. The focus of this investigation was concentrated on the comparison of the estimation quality of the EKF and PF estimators by applying different measurement noises. The simulation results show that Particle Filter algorithm requires significantly more computation time for state estimation but gives lower estimation errors both for biomass concentration and specific growth rate. Also the tuning procedure for Particle Filter is simpler than for EKF. Consequently, Particle Filter should be preferred in real applications, especially for monitoring of industrial bioprocesses where the simplified implementation procedures are always desirable.
Keywords: Biomass concentration, Extended Kalman Filter, Particle Filter, State estimation, Specific growth rate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29534143 Spread Spectrum Code Estimationby Particle Swarm Algorithm
Authors: Vahid R. Asghari, Mehrdad Ardebilipour
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In the context of spectrum surveillance, a new method to recover the code of spread spectrum signal is presented, while the receiver has no knowledge of the transmitter-s spreading sequence. In our previous paper, we used Genetic algorithm (GA), to recover spreading code. Although genetic algorithms (GAs) are well known for their robustness in solving complex optimization problems, but nonetheless, by increasing the length of the code, we will often lead to an unacceptable slow convergence speed. To solve this problem we introduce Particle Swarm Optimization (PSO) into code estimation in spread spectrum communication system. In searching process for code estimation, the PSO algorithm has the merits of rapid convergence to the global optimum, without being trapped in local suboptimum, and good robustness to noise. In this paper we describe how to implement PSO as a component of a searching algorithm in code estimation. Swarm intelligence boasts a number of advantages due to the use of mobile agents. Some of them are: Scalability, Fault tolerance, Adaptation, Speed, Modularity, Autonomy, and Parallelism. These properties make swarm intelligence very attractive for spread spectrum code estimation. They also make swarm intelligence suitable for a variety of other kinds of channels. Our results compare between swarm-based algorithms and Genetic algorithms, and also show PSO algorithm performance in code estimation process.Keywords: Code estimation, Particle Swarm Optimization(PSO), Spread spectrum.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21354142 An Enhanced Floor Estimation Algorithm for Indoor Wireless Localization Systems Using Confidence Interval Approach
Authors: Kriangkrai Maneerat, Chutima Prommak
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Indoor wireless localization systems have played an important role to enhance context-aware services. Determining the position of mobile objects in complex indoor environments, such as those in multi-floor buildings, is very challenging problems. This paper presents an effective floor estimation algorithm, which can accurately determine the floor where mobile objects located. The proposed algorithm is based on the confidence interval of the summation of online Received Signal Strength (RSS) obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSN).We compare the performance of the proposed algorithm with those of other floor estimation algorithms in literature by conducting a real implementation of WSN in our facility. The experimental results and analysis showed that the proposed floor estimation algorithm outperformed the other algorithms and provided highest percentage of floor accuracy up to 100% with 95-percent confidence interval.
Keywords: Floor estimation algorithm, floor determination, multi-floor building, indoor wireless systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 32044141 On Maneuvering Target Tracking with Online Observed Colored Glint Noise Parameter Estimation
Authors: M. A. Masnadi-Shirazi, S. A. Banani
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In this paper a comprehensive algorithm is presented to alleviate the undesired simultaneous effects of target maneuvering, observed glint noise distribution, and colored noise spectrum using online colored glint noise parameter estimation. The simulation results illustrate a significant reduction in the root mean square error (RMSE) produced by the proposed algorithm compared to the algorithms that do not compensate all the above effects simultaneously.
Keywords: Glint noise, IMM, Kalman Filter, Kinematics, Target Tracking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16414140 Parameter Estimation for Viewing Rank Distribution of Video-on-Demand
Authors: Hyoup-Sang Yoon
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Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.
Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17904139 Estimation of R= P [Y < X] for Two-parameter Burr Type XII Distribution
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In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.
Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22954138 Choosing Search Algorithms in Bayesian Optimization Algorithm
Authors: Hao Wu, Jonathan L. Shapiro
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The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.
Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16974137 Fast Depth Estimation with Filters
Authors: Yiming Nie, Tao Wu, Xiangjing An, Hangen He
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Fast depth estimation from binocular vision is often desired for autonomous vehicles, but, most algorithms could not easily be put into practice because of the much time cost. We present an image-processing technique that can fast estimate depth image from binocular vision images. By finding out the lines which present the best matched area in the disparity space image, the depth can be estimated. When detecting these lines, an edge-emphasizing filter is used. The final depth estimation will be presented after the smooth filter. Our method is a compromise between local methods and global optimization.Keywords: Depth estimation, image filters, stereo match.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12494136 Implementation of Channel Estimation and Timing Synchronization Algorithms for MIMO-OFDM System Using NI USRP 2920
Authors: Ali Beydoun, Hamzé H. Alaeddine
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MIMO-OFDM communication system presents a key solution for the next generation of mobile communication due to its high spectral efficiency, high data rate and robustness against multi-path fading channels. However, MIMO-OFDM system requires a perfect knowledge of the channel state information and a good synchronization between the transmitter and the receiver to achieve the expected performances. Recently, we have proposed two algorithms for channel estimation and timing synchronization with good performances and very low implementation complexity compared to those proposed in the literature. In order to validate and evaluate the efficiency of these algorithms in real environments, this paper presents in detail the implementation of 2 × 2 MIMO-OFDM system based on LabVIEW and USRP 2920. Implementation results show a good agreement with the simulation results under different configuration parameters.Keywords: MIMO-OFDM system, timing synchronization, channel estimation, STBC, USRP 2920.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8434135 Estimation of Skew Angle in Binary Document Images Using Hough Transform
Authors: Nandini N., Srikanta Murthy K., G. Hemantha Kumar
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This paper includes two novel techniques for skew estimation of binary document images. These algorithms are based on connected component analysis and Hough transform. Both these methods focus on reducing the amount of input data provided to Hough transform. In the first method, referred as word centroid approach, the centroids of selected words are used for skew detection. In the second method, referred as dilate & thin approach, the selected characters are blocked and dilated to get word blocks and later thinning is applied. The final image fed to Hough transform has the thinned coordinates of word blocks in the image. The methods have been successful in reducing the computational complexity of Hough transform based skew estimation algorithms. Promising experimental results are also provided to prove the effectiveness of the proposed methods.Keywords: Dilation, Document processing, Hough transform, Optical Character Recognition, Skew estimation, and Thinning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 32654134 Genetic Algorithms with Oracle for the Traveling Salesman Problem
Authors: Robin Gremlich, Andreas Hamfelt, Héctor de Pereda, Vladislav Valkovsky
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By introducing the concept of Oracle we propose an approach for improving the performance of genetic algorithms for large-scale asymmetric Traveling Salesman Problems. The results have shown that the proposed approach allows overcoming some traditional problems for creating efficient genetic algorithms.
Keywords: Genetic algorithms, Traveling Salesman Problem, optimal decision distribution, oracle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17214133 Characteristic Function in Estimation of Probability Distribution Moments
Authors: Vladimir S. Timofeev
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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.
Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22544132 Color Constancy using Superpixel
Authors: Xingsheng Yuan, Zhengzhi Wang
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Color constancy algorithms are generally based on the simplified assumption about the spectral distribution or the reflection attributes of the scene surface. However, in reality, these assumptions are too restrictive. The methodology is proposed to extend existing algorithm to applying color constancy locally to image patches rather than globally to the entire images. In this paper, a method based on low-level image features using superpixels is proposed. Superpixel segmentation partition an image into regions that are approximately uniform in size and shape. Instead of using entire pixel set for estimating the illuminant, only superpixels with the most valuable information are used. Based on large scale experiments on real-world scenes, it can be derived that the estimation is more accurate using superpixels than when using the entire image.Keywords: color constancy, illuminant estimation, superpixel
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14604131 Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution
Authors: F. Z. Doğru, O. Arslan
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In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. The simulation results show that the proposed robust estimators generally outperform the classical estimators in terms of bias and root mean square errors when there are outliers in data.
Keywords: Burr XII distribution, robust estimator, M-estimator, maximum likelihood, least squares.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26584130 A New Distribution and Application on the Lifetime Data
Authors: Gamze Ozel, Selen Cakmakyapan
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We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.
Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13874129 Networks with Unreliable Nodes and Edges: Monte Carlo Lifetime Estimation
Authors: Y. Shpungin
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Estimating the lifetime distribution of computer networks in which nodes and links exist in time and are bound for failure is very useful in various applications. This problem is known to be NP-hard. In this paper we present efficient combinatorial approaches to Monte Carlo estimation of network lifetime distribution. We also present some simulation results.Keywords: Combinatorial spectrum, Monte Carlo, Networklifetime, Unreliable nodes and edges.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18394128 Maximum Likelihood Estimation of Burr Type V Distribution under Left Censored Samples
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The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.
Keywords: Fisher information matrix, confidence intervals, censoring.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17094127 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods
Authors: Autcha Araveeporn
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This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.
Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14344126 Classification of Extreme Ground-Level Ozone Based on Generalized Extreme Value Model for Air Monitoring Station
Authors: Siti Aisyah Zakaria, Nor Azrita Mohd Amin, Noor Fadhilah Ahmad Radi, Nasrul Hamidin
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Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.
Keywords: Extreme value theory, generalized extreme value distribution, ground-level ozone, return level.
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