• Journal of the Korean Data and Information Science Society
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• v.19 no.2
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• pp.635-644
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• 2008

We consider estimation of reliability P(Y

• 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 Mathematical Society
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• v.51 no.3
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• pp.527-543
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• 2014

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for Lukasiewicz's [0, 1]-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.783-792
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• 2007

We consider estimation of reliability P(Y

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.325-332
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• 2008

We consider estimation of reliability P(Y < X) and distribution of the ratio when X and Y are independent uniform random variable and power function random variable, respectively and also consider the estimation problem when X and Y are independent uniform random variable and a half-normal random variable, respectively.

• School Mathematics
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• v.16 no.1
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• pp.19-37
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• 2014

This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.967-977
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• 2008

We consider densities of quotient Y/X and ratio X/(X+Y), and estimation of reliability P(Y

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.285-299
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• 2020

In many cases, we are interested in identifying independence between variables. For continuous random variables, correlation coefficients are often used to describe the relationship between variables; however, correlation does not imply independence. For finite discrete random variables, we can use the Pearson chi-square test to find independency. For the mixed type of continuous and discrete random variables, we do not have a general type of independent test. In this study, we develop a independence test of a continuous random variable and a discrete random variable without assuming a specific distribution using kernel density estimation. We provide some statistical criteria to test independence under some special settings and apply the proposed independence test to Pima Indian diabetes data. Through simulations, we calculate false positive rates and true positive rates to compare the proposed test and Kolmogorov-Smirnov test.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.283-285
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• 2005

To account for the importance of variable in multi-sensor data fusion, random forests are applied to supervised land-cover classification. The random forests approach is a non-parametric ensemble classifier based on CART-like trees. Its distinguished feature is that the importance of variable can be estimated by randomly permuting the variable of interest in all the out-of-bag samples for each classifier. Supervised classification with a multi-sensor remote sensing data set including optical and polarimetric SAR data was carried out to illustrate the applicability of random forests. From the experimental result, the random forests approach could extract important variables or bands for land-cover discrimination and showed good performance, as compared with other non-parametric data fusion algorithms.