• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.1
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• pp.201-216
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• 2013

Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.685-696
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• 2012

These days the interest of quality leads to the necessity of control charts for monitoring the process in various fields of practical applications. The $\overline{X}$ chart is one of the most widely used tools for quality control that also performs well under the normality of quality characteristics. However, quality characteristics tend to have nonnormal properties in real applications. Numerous recent studies have tried to find and explore the performance of $\overline{X}$ chart due to non-normality; however previous studies numerically examined the effects of non-normality and did not provide any theoretical justification. Moreover, numerical studies are restricted to specific type of distributions such as Burr or gamma distribution that are known to be flexible but can hardly replace other general distributions. In this paper, we approximate the false alarm rate(FAR) of the $\overline{X}$ chart using the Edgeworth expansion up to 1/n-order with the fourth cumulant. This allows us to examine the theoretical effects of nonnormality, as measured by the skewness and kurtosis, on $\overline{X}$ chart. In addition, we investigate the effect of skewness and kurtosis on $\overline{X}$ chart in numerical studies. We use a skewed-normal distribution with a skew parameter to comprehensively investigate the effect of skewness.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.154-157
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• 1990

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.C.A), which is the general case of mixture of normals approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charller expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modelling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we futher developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A and Booth-Baleriaux method. It is verified that the M.O.C.A method is faster and more accurate than any other methods.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.7
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• pp.72-85
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• 1998

In this paper, we propose a new method that sequentially estimates TDOA(Time Delay Of Arrival) and FDOA(Frequency Delay Of Arrival) for extracting the information about the bearing and relative velocity of a target in passive radar or sonar arrays. The objective is to efficiently estimate the TDOA and FDOA between two sensor signal measurements, corrupted by correlated Gaussian noise sources in an unknown way. The proposed method utilizes the one dimensional slice function of the third order cumulants between the two sensor measurements, by which the effect of correlated Gaussian measurement noises can be significantly suppressed for the estimation of TDOA. Because the proposed sequential algoritjhm uses the one dimensional complex ambiguity function based on the TDOA estimate from the first step, the amount of computations needed for accurate estimationof FDOA can be dramatically reduced, especially for the cases where high frequency resolution is required. It is demonstrated that the proposed algorithm outperforms existing TDOA/FDOA estimation algorithms based on the ML(maximum likelihood) criterionandthe complex ambiguity function of the third order cumulant as well, in the MSE(mean squared error) sense and computational burden. Various numerical resutls on the detection probability, MSE and the floatingpoint computational burden are presented via Monte-Carlo simulations for different types of noises, different lengths of data, and different signal-to-noise ratios.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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• pp.2356-2376
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• 2021

In this paper, we proposed a novel modulation recognition method based on quantum elephant herding algorithm (QEHA) evolving neural network under impulse noise environment. We use the adaptive weight myriad filter to preprocess the received digital modulation signals which passing through the impulsive noise channel, and then the instantaneous characteristics and high order cumulant features of digital modulation signals are extracted as classification feature set, finally, the BP neural network (BPNN) model as a classifier for automatic digital modulation recognition. Besides, based on the elephant herding optimization (EHO) algorithm and quantum computing mechanism, we design a quantum elephant herding algorithm (QEHA) to optimize the initial thresholds and weights of the BPNN, which solves the problem that traditional BPNN is easy into local minimum values and poor robustness. The experimental results prove that the adaptive weight myriad filter we used can remove the impulsive noise effectively, and the proposed QEHA-BPNN classifier has better recognition performance than other conventional pattern recognition classifiers. Compared with other global optimization algorithms, the QEHA designed in this paper has a faster convergence speed and higher convergence accuracy. Furthermore, the effect of symbol shape has been considered, which can satisfy the need for engineering.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1211-1219
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• 2013

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.

• Journal of the Korean Chemical Society
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• v.52 no.1
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• pp.7-15
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• 2008

Molecular motion influencing the absorption spectrum of a chromophore in liquid is theoretically described by a quantum mechanical time correlation function. In the present paper, we developed a theoretical method to calculate such a quantum mechanical time-correlation function from a classical time-correlation function using semi-classical approximations. The calculated time-correlation function was combined with the second order cumulant expansion method to calculate the absorption spectrum of nile blue in acetonitrile. Reasonably good agreement with experimental spectrum was obtained. From the comparison with experimental spectrum, we concluded that the time scale of solvation dynamics of the system should be longer then 1ps and the first shell of solvent is the major contribution to the solvation dynamics.

• ETRI Journal
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• v.43 no.5
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• pp.869-880
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• 2021

Herein, we estimate the direction of arrival (DOA) of non-Gaussian signals for nested arrays (NAs) by implementing the fourth-order difference co-array (FODC) and successive methods. In particular, considering the property of the fourth-order cumulant (FOC), we first construct the FODC of the NA, which can obtain O(N⁴) virtual elements using N physical sensors, whereas conventional FOC methods can only obtain O(N²) virtual elements. In addition, the closed-form expression of FODC is presented to verify the enhanced degrees of freedom (DOFs). Subsequently, we exploit the vectorized FOC (VFOC) matrix to match the FODC of the NA. Notably, the VFOC matrix is a single snapshot vector, and the initial DOA estimates can be obtained via the discrete Fourier transform method under the underdetermined correlation matrix condition, which utilizes the complete DOFs of the FODC. Finally, fine estimates are obtained through the spatial smoothing-Capon method with partial spectrum searching. Numerical simulation verifies the effectiveness and superiority of the proposed method.