• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.157-160
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• 1999

We show the cumulants of a minimal sufficient statistics in k parameter natural exponential family by parameter function and partial parameter function. We nd the cumulants have some merits of central moments and general cumulants both. The first three cumulants are the central moments themselves and the fourth cumulant has the form related with kurtosis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.3
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• pp.183-189
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• 2013

In this paper, uncertainties and failure criteria of structure are mathematically expressed by random variables and a limit state equation. A limit state equation is approximated by Fleishman's 3rd order polynomials and the theoretical moments of an approximated limit state equation are calculated. Fleishman introduced a 3rd order polynomial in terms of only standard normal distiribution random variables. But, in this paper, Fleishman's polynomial is extended to various random variables including beta, gamma, uniform distributions. Cumulants and a normalized limit state equation are used to calculate a theoretical moments of a limit state equation. A cumulative distribution function of a normalized limit state equation is approximated by a Pearson system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.1-7
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• 2007

Generally, an electric railroad feeding system has many problems due to the different characteristics in contrast with a load of general three-phase AC electric power system. One of them is harmonics problem caused by the switching device existing in the feeding system, and moreover, the time-varying dynamic loads of rail way is inherently another cause to increase this harmonics problem. In Korea power systems, the electric railroad feeding system is directly supplied from the substation of KEPCO. Therefore, if voltages fluctuation or unbalanced voltages are created by the voltage and current distortion or voltage drop during operation, it affects directly the source of supply. The trainloads of electric railway system have non-periodic but iterative harmonic characteristics as operating condition, because the electric characteristic of the electric railroad feeding system is changed by physical conditions of the each trainload. According to the traditional study, the estimation of harmonics has been performed by deterministic way using the steady state data at the specific time. This method is easy to analyze harmonics, but it has limits in some cases which needs an assessment of dynamic load and reliability. Therefore, this paper proposes the probabilistic estimation method, moments matching method(MW) in order to overcome the drawback of deterministic method. In this paper, distributions for each harmonics are convolved to obtain the moments and cumulants of TDD(Total Demand Distortion), and this can be generalized for any number of trains. For the case study, the electric railway system of LAT(Intra Airport Transit) in Incheon International Airport is modeled using PSCAD/EMTDC dynamic simulator. The raw data of harmonics for the moments matching method is acquired from simulation of the LAT model.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.597-609
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• 2008

In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let ${\alpha}$ : G${\rightarrow}$ AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product $\mathbb{M}=M{\times}{\alpha}$ G of M and G with respect to ${\alpha}$ is a von Neumann algebra acting on $H{\bigotimes}{\iota}^2(G)$, generated by M and $(u_g)_g{\in}G$, where $u_g$ is the unitary representation of g on ${\iota}^2(G)$. We show that $M{\times}{\alpha}(G_1\;*\;G_2)=(M\;{\times}{\alpha}\;G_1)\;*_M\;(M\;{\times}{\alpha}\;G_2)$. We compute moments and cumulants of operators in $\mathbb{M}$. By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if $F_N$ is the free group with N-generators, then the crossed product algebra $L_M(F_n){\equiv}M\;{\times}{\alpha}\;F_n$ satisfies that $$L_M(F_n)=L_M(F_{{\kappa}1})\;*_M\;L_M(F_{{\kappa}2})$$, whenerver $n={\kappa}_1+{\kappa}_2\;for\;n,\;{\kappa}_1,\;{\kappa}_2{\in}\mathbb{N}$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.10
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• pp.2409-2416
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• 2014

In this paper, an automatic recognition algorithm for linearly modulated signals like PSK, QAM under noncoherent asynchronous condition is proposed. Frequency, phase, and amplitude characteristics of digitally modulated signals are changed periodically. By using this characteristics, cyclic moments and higher order cumulants based features are utilized for the modulation recognition. Hierarchial decision tree method is used for high speed signal processing and totally 4 feature extraction parameters are used for modulation recognition. In the condition where the symbol number is 4,096, the recognition accuracy of the proposed algorithm is more than 95% at SNR 15dB. Also the proposed algorithm is effective to classify the signal which has carrier frequency and phase offset.

• Proceedings of the KIEE Conference
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• 2003.11a
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• pp.28-30
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• 2003

Probabilistic Load Flow(PLF) solution based on the method of moments is used for security assessment of bus voltages in power systems. Bus voltages, line currents, line admittances, generated real and reactive power, and bus loads are treated as complex random variables. These complex random variables are known in terms of probability density functions(PDF). Also, expressions for the convolutions of complex random variables in terms of moments and cumulants have been derived. Proposed PLF solution using the method of moments is fast, because the process of convolution of various complex random variables is performed in moment and cumulant domain. Therefore, the method is applied to security assessment of power systems in this paper. Finally, system operator also can be used information of security assessment to improve reliability of power systems.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.12
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• pp.1195-1202
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• 1991

This paper describes a newly developed method of production simulation by using the Mixture of Cumulant Approximation (MOCA). In this method, the load is modelled as random variable (r.v.) which can be interpreted in terms of partitioning the load into various categories. We can consider the load shape of multi-modal characteristics. The number of load category and demarcation points of each load category are calculated automatically by using interpolation and least square method. Each generating unit of a supply system is modelled as r.v. of unit outage capacity according to the number of unit outage subset. Since the computation burden of each subset's moments increases exponentially as units are convolved to the system, we further derive the specific recursive formulae. In simulating the energy limited units, hydro unit simulation is performed using Energy Invariance Property and the simulation of pumped storage unit is modelled as compulsory and economic operations. The proposed MOCA method is applide to the test systems and the results are compared with those of cumulant and Booth Baleriaux method. It is verified that the MOCA method is considerably reliable and stable both pathological and well behaved system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1044-1049
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• 2001

Classical deconvolution methods for source identification following linear filtering can only be used if the transfer function of the system is known. For many practical situations, however, this information is not accessible and/or is time varying. The problem addressed here is that of reconstruction of the original input from only the measured signal. This is known as 'blind deconvolution'. By using Higher Order Statistics (HOS), the restoration of the input signal is established through the maximisation of higher order moments (cumulants) with respect to the characteristics of the signals concerned. This restoration is achieved by constructing an inverse filter considering the choice of the initial inverse filter type. As a practical application, an experimental verification is carried out for the restoration of our impacting signal arising in the response of a cantilever beam with an end stop when randomly excited.

• Journal of Broadcast Engineering
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• v.19 no.2
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• pp.195-204
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• 2014

In this paper, we propose an automatic modulation classification method for ten digitally modulated baseband signals, such as 2-FSK, 4-FSK, 8-FSK, MSK, BPSK, QPSK, 8-PSK, 16-QAM, 32-QAM, and 64-QAM based on higher order statistics of cyclostationary process. The first order cyclic moments and higher order cyclic cumulants of the signal are used as features of the modulation signals. The proposed method consists of two stages. At the first stage, we classify modulation signals as M-FSK and non-FSK using peaks of the first order cyclic moment. At the next step, we apply the Gaussian mixture model-based classifier to classify non-FSK. Simulation results are demonstrated to evaluate the proposed scheme. The results show high probability of classification even in the presence of frequency and phase offsets.

• International Journal of Contents
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• v.3 no.1
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.