Search results for: interval estimation.

Authors: Suparat Niwitpong

Abstract:

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

Keywords: Confidence interval, generalized confidence interval, the closed form method of variance estimation, variance.

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Authors: Kriangkrai Maneerat, Chutima Prommak

Abstract:

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.

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Authors: K. Ganesan

Abstract:

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.

Keywords: Interval arithmetic, Interval matrix, linear equations.

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Authors: Jeerapa Sappakitkamjorn, Sa-aat Niwitpong

Abstract:

In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.  

Keywords: Bounded parameters, coefficient of variation, confidence interval, Monte Carlo simulation.

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Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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Authors: Hidehiko Okada

Abstract:

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks. 

Keywords: Evolutionary algorithms, differential evolution, neural network, neuroevolution, interval arithmetic.

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Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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Authors: Tarasankar Pramanik, Sukumar Mondal, Madhumangal Pal

Abstract:

In an interval graph G = (V,E) the distance between two vertices u, v is de£ned as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V . The diameter (δ) and radius (ρ) of the graph G is respectively the maximum and minimum among all the eccentricities of G. The center of the graph G is the set C(G) of vertices with eccentricity ρ. In this context our aim is to establish the relation ρ = δ 2  for an interval graph and to determine the center of it.

Keywords: Interval graph, interval tree, radius, center.

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Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: Uniquely restricted matching, interval graph, design and analysis of algorithms, matching, induced matching, witness counting.

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Authors: Ming-Hui Lee, Tsung-Chien Chen, Tsu-Ping Yu, Horng-Yuan Jang

Abstract:

The innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux of the multilayer materials as presented in this paper. The feasibility of this method can be verified by adopting the temperature measurement experiment. The experiment modular may be designed by using the copper sample which is stacked up 4 aluminum samples with different thicknesses. Furthermore, the bottoms of copper samples are heated by applying the standard heat source, and the temperatures on the tops of aluminum are measured by using the thermocouples. The temperature measurements are then regarded as the inputs into the presented method to estimate the heat flux in the bottoms of copper samples. The influence on the estimation caused by the temperature measurement of the sample with different thickness, the processing noise covariance Q, the weighting factor γ , the sampling time interval Δt , and the space discrete interval Δx , will be investigated by utilizing the experiment verification. The results show that this method is efficient and robust to estimate the unknown time-varying heat input of the multilayer materials.

Keywords: Multilayer Materials, Input Estimation Method, IHCP, Heat Flux.

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Authors: B. S. Saini, Dilbag Singh, Moin Uddin, Vinod Kumar

Abstract:

The RR interval series is non-stationary and unevenly spaced in time. For estimating its power spectral density (PSD) using traditional techniques like FFT, require resampling at uniform intervals. The researchers have used different interpolation techniques as resampling methods. All these resampling methods introduce the low pass filtering effect in the power spectrum. The lomb transform is a means of obtaining PSD estimates directly from irregularly sampled RR interval series, thus avoiding resampling. In this work, the superiority of Lomb transform method has been established over FFT based approach, after applying linear and cubicspline interpolation as resampling methods, in terms of reproduction of exact frequency locations as well as the relative magnitudes of each spectral component.

Keywords: HRV, Lomb Transform, Resampling, RR-intervals.

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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Authors: Alessandro Barbiero

Abstract:

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

Keywords: Approximate estimators, asymptotic theory, confidence interval, Monte Carlo simulations, stress-strength, variance estimation.

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Authors: Hadeel Salim Alkutubi

Abstract:

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

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Authors: A. Falsafain, S. M. Taheri, M. Mashinchi

Abstract:

Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameters of two Normal distributions, as well as the parameters of the Exponential and Poisson distributions.

Keywords: Confidence interval. Fuzzy number. Fuzzy estimation.

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Authors: V. Churkin, M. Lopatin

Abstract:

The purpose of the paper is to estimate the US small wind turbines market potential and forecast the small wind turbines sales in the US. The forecasting method is based on the application of the Bass model and the generalized Bass model of innovations diffusion under replacement purchases. In the work an exponential distribution is used for modeling of replacement purchases. Only one parameter of such distribution is determined by average lifetime of small wind turbines. The identification of the model parameters is based on nonlinear regression analysis on the basis of the annual sales statistics which has been published by the American Wind Energy Association (AWEA) since 2001 up to 2012. The estimation of the US average market potential of small wind turbines (for adoption purchases) without account of price changes is 57080 (confidence interval from 49294 to 64866 at P = 0.95) under average lifetime of wind turbines 15 years, and 62402 (confidence interval from 54154 to 70648 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 90,7%, while in the second - 91,8%. The effect of the wind turbines price changes on their sales was estimated using generalized Bass model. This required a price forecast. To do this, the polynomial regression function, which is based on the Berkeley Lab statistics, was used. The estimation of the US average market potential of small wind turbines (for adoption purchases) in that case is 42542 (confidence interval from 32863 to 52221 at P = 0.95) under average lifetime of wind turbines 15 years, and 47426 (confidence interval from 36092 to 58760 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 95,3%, while in the second – 95,3%.

Keywords: Bass model, generalized Bass model, replacement purchases, sales forecasting of innovations, statistics of sales of small wind turbines in the United States.

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Authors: Sudipta Majumdar, Akansha Singh

Abstract:

Frequency estimation of a sinusoid in white noise using maximum entropy power spectral estimation has been shown to be very sensitive to initial sinusoidal phase. This paper presents use of wavelet transform to find an analytic signal for frequency estimation using maximum entropy method (MEM) and compared the results with frequency estimation using analytic signal by Hilbert transform method and frequency estimation using real data together with MEM. The presented method shows the improved estimation precision and antinoise performance.

Keywords: Frequency estimation, analytic signal, maximum entropy method, wavelet transform.

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Authors: Susovan Chakrabortty, Madhumangal Pal, Prasun Kumar Nayak

Abstract:

A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed which works well on interval number optimization under consideration. Finally, the designed algorithm is illustrated with numerical example.

Keywords: EOQ, Inventory, Interval Number, Demand, Production, Simulation

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Authors: H.Panahi, S.Asadi

Abstract:

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.

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Authors: Arsham Borumand Saeid

Abstract:

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

Keywords: BG-algebra, fuzzy BG-subalgebra, interval-valued fuzzy set, interval-valued fuzzy BG-subalgebra.

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Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: V.Rezaie, M.Khanmohammady

Abstract:

An original DEA model is to evaluate each DMU optimistically, but the interval DEA Model proposed in this paper has been formulated to obtain an efficiency interval consisting of Evaluations from both the optimistic and the pessimistic view points. DMUs are improved so that their lower bounds become so large as to attain the maximum Value one. The points obtained by this method are called ideal points. Ideal PPS is calculated by ideal of efficiency DMUs. The purpose of this paper is to rank DMUs by this ideal PPS. Finally we extend the efficiency interval of a DMU under variable RTS technology.

Keywords: Data envelopment analysis (DEA), Decision makingunit (DMU), Interval DEA, Ideal points, Ideal PPS, Return to scale(RTS).

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Authors: Yiannis G. Smirlis

Abstract:

The classification and the prediction of efficiencies in Data Envelopment Analysis (DEA) is an important issue, especially in large scale problems or when new units frequently enter the under-assessment set. In this paper, we contribute to the subject by proposing a grid structure based on interval segmentations of the range of values for the inputs and outputs. Such intervals combined, define hyper-rectangles that partition the space of the problem. This structure, exploited by Interval DEA models and a dominance relation, acts as a DEA pre-processor, enabling the classification and prediction of efficiency scores, without applying any DEA models.

Keywords: Data envelopment analysis, interval DEA, efficiency classification, efficiency prediction.

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Authors: Youngpo Lee, Seokho Yoon

Abstract:

In this paper, we propose a distance estimation scheme for radar systems using direct sequence ultra wideband (DS-UWB) signals. The proposed distance estimation scheme averages out the noise by accumulating the correlator outputs of the radar, and thus, helps the radar to employ a short-length DS-UWB signal reducing the correlation processing time. Numerical results confirm that the proposed distance estimation scheme provides a better estimation performance and a reduced correlation processing time compared with those of the conventional DS-UWB radars.

Keywords: Radar, DS-UWB, distance estimation, correlation accumulation.

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Authors: Youngpo Lee, Seokho Yoon

Abstract:

In this paper, we propose a novel frequency offset estimation scheme for orthogonal frequency division multiplexing (OFDM) systems. By correlating the OFDM signals within the coherence phase bandwidth and employing a threshold in the frequency offset estimation process, the proposed scheme is not only robust to the timing offset but also has a reduced complexity compared with that of the conventional scheme. Moreover, a timing offset estimation scheme is also proposed as the next stage of the proposed frequency offset estimation. Numerical results show that the proposed scheme can estimate frequency offset with lower computational complexity and does not require additional memory while maintaining the same level of estimation performance.

Keywords: OFDM, frequency offset estimation, threshold.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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Authors: Chen-Chien Hsu, Chun-Hui Gao

Abstract:

In this paper, a PSO-based approach is proposed to derive a digital controller for redesigned digital systems having an interval plant based on resemblance of the extremal gain/phase margins. By combining the interval plant and a controller as an interval system, extremal GM/PM associated with the loop transfer function can be obtained. The design problem is then formulated as an optimization problem of an aggregated error function revealing the deviation on the extremal GM/PM between the redesigned digital system and its continuous counterpart, and subsequently optimized by a proposed PSO to obtain an optimal set of parameters for the digital controller. Computer simulations have shown that frequency responses of the redesigned digital system having an interval plant bare a better resemblance to its continuous-time counter part by the incorporation of a PSO-derived digital controller in comparison to those obtained using existing open-loop discretization methods.

Keywords: Digital redesign, Extremal systems, Particle swarm optimization, Uncertain interval systems

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Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.

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Authors: N. Feroze, M. Aslam

Abstract:

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.

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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