• 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 Operations Research and Management Science Society
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• v.16 no.1
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• pp.13-34
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• 1991

A production/inventory system is considered in which a production facility produces one type of product. The demand for the product is given by a compound Poison process and is supplied directly from inventory when inventory is available and is lost when inventory is out of stock. The processing time to produce one item is assumes to follow a general distribution. An (s, S) policy is considered in which production stops at the instant the stock on hand reachs S and the setup of the production facility begins at an inspection point when the stock on hand drops to or below s for the first time. The time interval between two successive inspection points during a non-production period is a random variable which follows a general distribution.

• Journal of Korean Society of Environmental Engineers
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• v.31 no.9
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• pp.825-830
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• 2009

Pharmaceutical compounds enter the water environment through the diverse pathways. Because their concentration in the water environment was frequently detected in the level of ppt to ppb, the monitoring system should be optimized as much as possible for finding appropriate management policies and technical solutions. One Factor At a Time (OFAT) approach approximating the response with a single variable has been preferred for the optimization of LC-MS/MS operational conditions. However, it is common that variables in analytical instruments are interdependent. Therefore, the best condition could be found by using the statistical optimization method changing multiple variables at a time. In this research, response surface analysis (RSA) was applied to the LC-MS/MS analysis of emerging antibiotic compound, sulfamethoxazole, for the best sensitivity. In the screening test, fragmentation energy and collision voltage were selected as independent variables. They were changed simultaneously for the statistical optimization and a polynomial equation was fit to the data set. The correlation coefficient, $R^2$ valuerepresented 0.9947 and the error between the predicted and observed value showed only 3.41% at the random condition, fragmentation energy of 60 and collision voltage of 17 eV. Therefore, it was concluded that the model derived by RSA successfully predict the response. The optimal conditions identified by the model were fragmentation energy of 116.6 and collision voltage of 10.9 eV. This RSA can be extensively utilized for optimizing conditions of solid-phase extraction and liquid chromatography.