• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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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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• v.39 no.3
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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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• v.34 no.1
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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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• v.13 no.1
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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.

• Journal of Soil and Groundwater Environment
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• v.12 no.6
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• pp.60-69
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• 2007

Understanding the behavior of gas phase VOCs (volatile organic compounds) in unsaturated soils is of a great environmental importance for public health concerns. Moment analysis for the breakthrough curves (BTCs) during transport of chemicals in porous media was known to be a useful tool to evaluate the velocity, spreadness, and the skewness of the plume of the chemicals. In this study, the temporal moments of the BTCs of a group of VOCs were analyzed for the gaseous transport in an unsaturated soil. BTCs were measured using lab-scale column experiments for four different VOCs at the water saturation range of 0.04-0.46, and for eleven VOCs at a water saturation of 0.21. The central second and third moments of the VOCs were compared with the water saturation and the first moment. It was found that both central second and third moments increased with the first moment. The central third moment was, however, found to be more sensitive to the first moment.

• 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.

• Proceedings of the Korean Magnestics Society Conference
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• 2007.05a
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• pp.191.2-191.2
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• 2007

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.114.1-114.1
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• 2008

• Journal of the Korean Statistical Society
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• v.25 no.3
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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.

• Honam Mathematical Journal
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• v.27 no.3
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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.