• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.395-401
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• 1997

We show that if I is an ideal of a $C^*$-algebra A such that the unitary group of I is connected then cer(A) $\leq$ cer(I) + cer(A/I), where cer(A) denotes the $C^*$-exponential rank of A.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1195-1205
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• 2014

Compared with single design, powers of rank transformed statistic for testing main and interaction effects for $2{\times}2$ factorial in $4{\times}4$ latin square design are rapidly increased as effect size and replication size are increased. In general powers of rank transformed statistic are superior without regard to the diversified effect composition and the type of error distributions as nontesting factors are few and effect size are small. Powers of rank transformed statistic show much higher level than those of parametric statistic in exponential and double exponential distributions. Further powers of rank transformed statistic are very similar with those of parametric statistic in normal and uniform distributions.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.467-478
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• 1999

This paper deals with the problem of change-point estimation where there is one level change in location with iid errors. A change-point estimator using rank average is proposed with the proof of its consistency. A comparison study of various change-point estimators is done by simulation on the mean the proportion and the variance when the errors are from the normal and the double exponential distributions.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.111-120
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• 2006

In a two-stage two-level balanced nested design, type I error rates for the parametric tests and the rank transformed tests for the main effects and the nested effects are in overall similar to each other. Furthermore, powers for the rank transformed statistic for the main effects and the nested effects in a two-stage two-level balanced nested design are generally superior to powers for the parametric statistic When the effect size and the sample size are increased, we can find that powers increase for the parametric statistic and the rank transformed statistic are dramatically improved. Especially for the case of the fixed effects in the asymmetric distributions such as an exponential distribution, powers for the rank transformed tests are quite high rather than powers for the parametric tests.

• Journal of the Korean Data and Information Science Society
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• v.22 no.2
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• pp.245-253
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• 2011

Powers of rank transformed statistic for testing main effects and interaction effects for $2{\times}2$ factorial design in randomized complete block design are very superior to powers of parametric statistic without regard to the block size, composition method of effects and the type of population distributions such as exponential, double exponential, normal and uniform. $2{\times}2$ factorial design in RCBD increases error effects and decreases powers of parametric statistic which results in conservativeness. However powers of rank transformed statistic maintain relative preference. In general powers of rank transformed statistic show relative preference over those of parametric statistic with small block size and big effect size.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.683-691
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• 2012

In $4{\times}4$ graeco-latin square design, powers of rank transformed statistic for testing the main effect are superior to powers of parametric statistic without regard to the effect structure with equally or unequally spaced effect levels as well as the type of population distributions such as exponential, double exponential, normal and uniform distribution. As numbers of block effect or effect sizes are decreased, powers of rank transformed statistic are much higher than powers of parametric statistic. In case that block effects are smaller than a main effect or one block effect is higher than other block effects, powers of rank transformed statistic are much higher than powers of parametric statistic in $4{\times}4$ graeco-latin square design with three block effects and one main effect.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.143-152
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• 2017

Restriction of completely randomization within a block can be handled by a split plot factorial design splitted by several plots. $3{\times}3$ split plot factorial design with two fixed main factors and one fixed block shows that powers of the rank transformed statistic for testing whole plot factorial effect and split plot factorial effect are superior to those of the parametric statistic when existing effect size is small or the remaining effect size is relatively smaller than the testing factorial effect size. Powers of the rank transformed statistic show relatively high level for exponential and double exponential distributions, whereas powers of the parametric and rank transformed statistic maintain similar level for normal and uniform distributions. Powers of the parametric and rank transformed statistic with two fixed main factors and one random block are respectively lower than those with all fixed factors. Powers of the parametric andrank transformed statistic for testing split plot factorial effect with two fixed main factors and one random block are slightly lower than those for testing whole plot factorial effect, but powers of the rank transformed statistic show comparative advantage over those of the parametric statistic.

• Journal of the Korean School Mathematics Society
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• v.19 no.2
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• pp.177-196
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• 2016

In this paper, we analyze the influence of mathematics teaching-learning for high level math problems of A-type of mathematics section on the College Scholastic Ability Test(CSAT). To analyze the influence, we compare and analyze units and field of questions set at examinations based on the rate of wrong answers in A-type mathematics test of the CSAT from 2012 to 2016. Also, we study the recognition of academic high school students and teachers about units and fields on math which need to allow more time to improve grade for A-type of mathematics section on the CSAT. We found following facts. First, high level math problems determining rank of high rank students on the CSAT was taken mostly from the unit related a exponential function and a logarithmic function. Second, these problems need more time for a calculation rather than an ability for students to deepen their understanding of the concept and quality of education. Third, high rank students spend a lot of time to study more important units and fields of mathematics on the CSAT such as a exponential function and a logarithmic function, and teachers spend a lot of time to teach them.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.07a
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• pp.148-149
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• 2010

최근 널리 보급되고 있는 IPTV의 주요 서비스인 주문형 비디오 서비스의 시청 순위는 Zipf의 법칙을 따른다고 알려져 있으며 이를 기반으로 계층형 네트워크 스토리지 구조로 서비스를 제공하여 네트워크 비용과 스토리지 비용을 절감하고 있다. 그러나, 최근 연구에 의하면 미디어 시청 순위는 stretched exponential 함수에 더 근사함이 알려졌다. 본 연구에서는 국내에서 현재 상용 서비스 중인 대규모 주문형 비디오 서비스의 시청 순위-회수 데이터를 분석하여, 시청 순위로부터 stretched exponential 함수의 모수를 추정하여 시청 순위의 분포함수를 파악하고자 한다. 특히, 콘텐츠 파일 크기, 콘텐츠 파일 전달방식, 콘텐츠 장르 등의 요인과 시청 순위 분포함수의 모수 사이에 상관관계가 있는지 분석하고자 한다.