• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• KIEAE Journal
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• v.7 no.6
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• pp.23-28
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• 2007

Limited fossil fuels and unstable energy supply are considered as one of the critical problems in architecture requiring large amounts of energy. In order to this challenge, environment-friendly architecture design is required. Clear data should be prepared to apply solar energy to architecture aggressively and properly. This study used FS statistical analysis data regarding average daily solar radiation of Seoul observed over 20 years to find out standard year and standard daily solar radiation. This study also aims to compare and evaluate an appropriate method of selecting a standard year which is too close to measurement value through comparison and analysis with daily solar radiation acquired by applying overseas researchers' suggesting weight factor. As a result, the data nearest to measurement value of daily solar radiation was UK CIBSE TRY(TYPE 2) displaying 0.100in t-statistic index. For UK CIBSE TRY(TYPE 2), weight factor was applied to three climatic elements except relative humidity. TYPE 1 and TYPE 3 recorded 0.343 and 0.367, respectively, showing higher record of t-statistic than TYPE 2. TYPE 1 was calculated through FS statistical value of single data about daily solar radiation with other climatic elements excluded. For TYPE 3, relative humidity was added to TYPE 2. In particular, since TYPE 2 was closer to the measurement value compared to the others, it is necessary to consider relationship with other climate elements if other climate elements are added.

• Journal of Preventive Medicine and Public Health
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• v.39 no.5
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• pp.433-437
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• 2006

Objectives: The aim of this study is to develop a methodology for estimating a nationwide statistic for hernia operations with using the claim database of the Korea Health Insurance Cooperation (KHIC). Methods: According to the insurance claim procedures, the claim database was divided into the electronic data interchange database (EDI_DB) and the sheet database (Paper_DB). Although the EDI_DB has operation and management codes showing the facts and kinds of operations, the Paper_DB doesn't. Using the hernia matched management code in the EDI_DB, the cases of hernia surgery were extracted. For drawing the potential cases from the Paper_DB, which doesn't have the code, the predictive model was developed using the data mining technique called SEMMA. The claim sheets of the cases that showed a predictive probability of an operation over the threshold, as was decided by the ROC curve, were identified in order to get the positive predictive value as an index of usefulness for the predictive model. Results: Of the claim databases in 2004, 14,386 cases had hernia related management codes with using the EDI system. For fitting the models with applying the data mining technique, logistic regression was chosen rather than the neural network method or the decision tree method. From the Paper_DB, 1,019 cases were extracted as potential cases. Direct review of the sheets of the extracted cases showed that the positive predictive value was 95.3%. Conclusions: The results suggested that applying the data mining technique to the claim database in the KHIC for estimating the nationwide surgical statistics would be useful from the aspect of execution and cost-effectiveness.