• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권2호
• /
• pp.157-160
• /
• 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.

• 한국전산구조공학회논문집
• /
• 제26권3호
• /
• pp.183-189
• /
• 2013

본 논문에서는 불확실성을 확률변수로 가정하고 구조물의 파손기준을 한계상태식(Limit State Equation)으로 정의하였다. 한계상태식을 Fleishman의 3차 다항식으로 근사하고 이론적인 확률 모멘트(Moments)를 계산하였다. Fleishman은 표준정규 분포 확률변수에 대해서만 3차 다항식을 제시하였으나, 본 논문에서는 이를 확장하여 베타, 감마, 균일 분포 등 다양한 확률 변수에 적용하였다. 확률 모멘트를 계산하기 위해서 누률(Cumulants)과 정규화된 한계상태식을 활용하였으며, 피어슨 시스템(Pearson System)을 통해 한계상태식의 확률분포를 근사하였다.

• 전기학회논문지
• /
• 제56권1호
• /
• pp.1-7
• /
• 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.

• 대한수학회지
• /
• 제45권3호
• /
• pp.597-609
• /
• 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 $n={\kappa}_1+{\kappa}_2\;for\;n,\;{\kappa}_1,\;{\kappa}_2{\in}\mathbb{N}$.

• 한국정보통신학회논문지
• /
• 제18권10호
• /
• pp.2409-2416
• /
• 2014

본 논문에서는 넌코히어런트 비동기 조건에서 PSK, QAM 등의 선형 디지털 변조 방식을 자동으로 식별하는 알고리즘을 제안한다. 디지털 변조 신호는 심볼 천이 주기간 주파수, 위상, 진폭 등의 특성이 반복적으로 변하게 된다. 이러한 특성을 이용하여 변조 방식을 식별할 수 있도록 순환 모멘트와 고차 큐뮬런트를 이용하는 방법을 제안한다. 계층적 의사 결정 트리 방식의 알고리즘 구조를 사용하여 고속으로 처리 가능하도록 구성하였으며 총 4개의 특징 추출 인자를 사용하여 식별하였다. 모의실험 결과 심볼 수 4,096개, SNR 15dB 이상에서 95% 이상의 식별 정확도를 나타내었으며, 반송 주파수와 위상 편이가 발생하더라도 신호를 분류하는데 효과적임을 확인하였다.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2003년도 추계학술대회 논문집 전력기술부문
• /
• pp.28-30
• /
• 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.

• 대한전기학회논문지
• /
• 제40권12호
• /
• pp.1195-1202
• /
• 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.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 추계학술대회논문집 II
• /
• pp.1044-1049
• /
• 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.

• 방송공학회논문지
• /
• 제19권2호
• /
• pp.195-204
• /
• 2014

이 논문에서는 순환정상 프로세스의 고차 통계 특성을 바탕으로 2-FSK, 4-FSK, 8-FSK, MSK, BPSK, QPSK, 8-PSK, 16-QAM, 32-QAM, 64-QAM 등 10개의 기저대역 디지털 변조신호를 자동으로 인식하는 방법을 제안하였다. 변조신호의 고유한 성질을 나타내는 특징변수로는 1차 순환 모멘트와 고차 순환 큐뮬런트를 이용하였다. 제안한 변조인식기는 크게 두 단계로 구성되며, 첫 번째 단계에서는 1차 순환 모멘트가 나타내는 첨두치를 이용하여 M-FSK와 비FSK로 변조신호를 분류한다. 두 번째 단계에서는 비FSK를 분류하기 위해 고차 순환 큐뮬런트 값을 이용하는 Gaussian 혼합 모델 기반의 분류기를 적용하였다. 제안한 방법의 성능을 검증하기 위해서 모의실험을 실시하였다. 모의실험 결과 제안한 분류기는 주파수와 위상 옵셋이 존재하는 환경에서도 우수한 분류확률을 나타내었다.

• International Journal of Contents
• /
• 제3권1호
• /
• pp.1-8
• /
• 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.