• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.385-391
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• 2003

A sequence of n Bernoulli trials which violates the constant success probability assumption is termed as "Poisson trials". In this paper, the recurrence formula for the r-th central moment of number of successes with n Poisson trials is derived. Romanovsky's method, based on the differentiation of characteristic function, is used in the derivation of recurrence formula for the central moments of conventional binomial distribution. Romanovsky's method is applied to that of Poisson trials in this paper. Some central moment calculation results are given to compare the central moments of Poisson trials with those of conventional binomial distribution.

• East Asian mathematical journal
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• 제39권3호
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• pp.331-347
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• 2023

We present an identity on moments of a compound random variable by using an auxiliary counting random variable. Based on this identity, we develop a new recurrence formula for obtaining the raw and central moments of any order for a given compound random variable.

• East Asian mathematical journal
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• 제34권1호
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• pp.59-67
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• 2018

We present new recurrence formulas for the raw and central moments of a compound binomial random variable. Our approach involves relating two compound binomial random variables that have parameters with a difference of 1 for the number of trials, but which have the same parameters for the success probability for each trial. As a consequence of our recursions, the raw and central moments of a binomial random variable are obtained in a recursive manner without the use of Stirling numbers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• 한국지하수토양환경학회지:지하수토양환경
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• 제12권6호
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• pp.60-69
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• 2007

토양에서 휘발성 유기화합물(VOC, volatile organic compound)의 유동특성을 이해하는 것은 오염물질의 확산을 예측하고 오염의 정도를 평가하며 대책을 수립하는 데 있어서 매우 중요하다. 토양과 같은 다공성매질에서 유동하는 물질의 출현곡선에 대한 모멘트의 분석을 통하여 화학물질의 유동속도, 플룸의 폭 및 비대칭정도를 평가할 수 있다. 본 연구에서는 실험실 규모의 토양 컬럼실험을 사용하여 VOC의 가스상 유동실험을 실시하였으며, 모두 네 가지의 VOC에 대하여 포화도(water saturation)범위 0.04-0.46에서 출현곡선을 측정하였다. 또한 포화도 0.21에서 열한가지의 VOC에 대하여 출현곡선을 측정하였다. 측정된 출현곡선의 중심 2차(central second)및 중심 3차(central third)모멘트는 포화도와 1차 모멘트(또는 지체상수)와 비교 분석되었다. VOC 출현곡선의 모멘트분석 결과 2차 및 3차 모멘트는 1차 모멘트의 2.23제곱 및 3.16제곱 함수로서 증가하였으며, 3차 모멘트가 2차 모멘트에 대하여 보다 민감하게 반응하였다. 이는 VOC가 토양가스상에서 이동할 때, 지체상수에 비례하여 가스 플룸의 폭과 비대칭성이 증가한다는 사실을 나타낸다.

• 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.

• 한국자기학회:학술대회 개요집
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• 한국자기학회 2007년도 The 1st International Symposium on Advanced Magnetic Materials
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• pp.191.2-191.2
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• 2007

• 한국자기학회:학술대회 개요집
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• 한국자기학회 2008년도 Asian Magnetics Conference
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• pp.114.1-114.1
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• 2008

• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.393-406
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• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

• 호남수학학술지
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• 제27권3호
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• pp.505-513
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• 2005

The aim of this paper is to establish a functional central limit theorem for multivariate moving average process generated by negatively associated random vectors under the finite second moments.