• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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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 Korean Statistical Society
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• 제5권2호
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• pp.91-100
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• 1976

The use of the statistic $t = \sqrt{n} (x-\mu)/S$, where $\bar{X) = \sum X_i/n, \mu = E(X_i), S^2 = \sum(X_i-\bar{X})^2/(n-1)$ in statistical inference is usually done under the assumption of normality of the population. If the population is not normally distributed the tabulated values of student t are no longer valid. The moments of t are obtained as a power series in $1/\sqar{n}$ whose coefficients are functions of the cumulants of X. The cumulants are obtained from the moments in the usual manner. The first eight cumulants of t are given up to terms of order $1/n^3$. The first eight cumulants of t are given up to terms of order $1/n^3$. These results extend those of Geary who gave the first six cumulants of t to order $1/n^2$.

• Journal of the Korean Statistical Society
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• 제6권1호
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• pp.21-24
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• 1977

The cumulants of the sample variance are obtained in terms of the population cumulants using ALMAP (Algebraic Manipulation Package) and these results extend those of Fisher who gave the first six cumulants of the sample variance.

• 한국멀티미디어학회논문지
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• 제7권6호
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• pp.781-790
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• 2004

This paper presents a fourth-order cumulants based iterative algorithm for blind channel equalization. It is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum phase characteristic of the channel. In this approach, the transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel outputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple reordering and scaling. Both a closed-form and a stochastic version of the proposed algorithm are tested with three-ray multi-path channels in simulation studies, and their performances are compared with a method based on conventional second-order cumulants. Relatively good results are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권1호
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• pp.13-20
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• 2005

This paper addresses a new blind channel equalization method using fourth-order cumulants of channel inputs and a three-layer neural network equalizer. The proposed algorithm is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum-phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple recordering and scaling. By using this estimated deconvolution matrix, which is the inverse of the over-sampled unknown channel, a three-layer neural network equalizer is implemented at the receiver. In simulation studies, the stochastic version of the proposed algorithm is tested with three-ray multi-path channels for on-line operation, and its performance is compared with a method based on conventional second-order statistics. Relatively good results, withe fast convergence speed, are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

• 대한전기학회논문지
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• 제40권1호
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• pp.1-9
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• 1991

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.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-Charlier expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modeling 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 further 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 accure than any other method.

• Communications for Statistical Applications and Methods
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• 제6권1호
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• pp.305-318
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• 1999

In this paper we derive the higher order expansions of the first four cumulants of multi-dimensional Maximum Likelihood Estimator (MLE) under the general parametric model up to and including terms of order O({{{{ {n }^{-1 } }}}}) Also we obtain the explicit form of the expansion of the normalizing trans formation of multi-dimensional MLE and show that the suggested normalizing process is much better than the normal approximation based on central limit theorem through example.

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

• Journal of the Korean Statistical Society
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• 제7권1호
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• 대한전기학회:학술대회논문집
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• 대한전기학회 1990년도 하계학술대회 논문집
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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.