• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.569-580
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• 2015

두 집단의 생존분포의 비교를 위한 방법으로는 로그-순위 검정법이 널리 쓰이고 있다. 그러나 이는 두 집단의 생존분포 간에 비례위험모형 가정이 성립하는 경우에 적합한 것으로써, 두 집단의 생존분포가 교차하는 상황 하에서는 해당 검정법의 유효성을 장담할 수 없다. 그러나 두 집단의 생존분포가 교차하는 상황은 빈번히 발생하며, 이 같은 상황에서 두 생존분포의 동일성 검정을 위한 여러 연구가 진행되어왔다. 본 논문에서는 두 집단 간 생존분포가 교차하는 상황 하에서의 동일성 검정을 위한 방법들을 고려한다. 나아가 교차하는 상황을 위치에 따라 세분화하고 모의실험을 통해 각 상황에서 다양한 검정법들의 검정력을 비교하였으며, 그 결과를 토대로 주어진 상황에서 적절한 방법의 선택에 유용한 정보를 제공하고자 한다.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.223-237
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• 2021

Let n be a fixed natural number. Menger algebras of rank n can be regarded as a canonical generalization of arbitrary semigroups. This paper is concerned with studying algebraic properties of Menger algebras of rank n by first defining a special class of full n-place functions, the so-called a left translation, which possess necessary and sufficient conditions for an (n + 1)-groupoid to be a Menger algebra of rank n. The isomorphism parts begin with introducing the concept of homomorphisms, and congruences in Menger algebras of rank n. These lead us to establish a quotient structure consisting a nonempty set factored by such congruences together with an operation defined on its equivalence classes. Finally, the fundamental homomorphism theorem and isomorphism theorems for Menger algebras of rank n are given. As a consequence, our results are significant in the study of algebraic theoretical Menger algebras of rank n. Furthermore, we extend the usual notions of ordinary semigroups in a natural way.

• Journal of the Korean Data and Information Science Society
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• 제13권1호
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• pp.165-175
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• 2002

We consider the problem of estimating the change-point in mean change model with the one change-point. Lombard (1987) suggested change-point estimation based on score functions. Gombay and Huskova (1998) derived a class of change-point estimators with the score function of rank. Various change-point estimators with the log score functions of ranks are suggested and compared via simulation.

• 품질경영학회지
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• 제22권2호
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• pp.166-176
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• 1994

Some rank score tests are proposed for testing the equality of all sampling distribution functions against ordered location-scale alternatives in k-sample problem. Under the null hypothesis and a contiguous sequence of ordered location-scale alternatives, the asymptotic properties of the proposed test statistics are investigated. Also, the asymptotic local powers are compared with each others. The results show that the proposed tests based on the Hettmansperger-Norton type statistic are more powerful than others for the general ordered location-scale alternatives. However, the Shiraishi's tests based on the sum of two Bartholomew's rank analogue statistics are robust.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2006년도 가을 학술발표논문집 Vol.33 No.2 (A)
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• pp.511-515
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• 2006

집합이나 배열의 원소, 트리의 노드, 그래프의 정점과 간선 등과 같은 이산 객체는 일반적으로 주기억장치의 논리적 주소 값과 같은 정수로 표현되어 왔다. Succinct 표현은 이와 같은 n개의 이산 객체를 O(n) 비트에 표현하는 방법이다. 대부분의 succinct 표현은 rank와 select라는 함수를 기본적으로 사용하며, 다양한 연구들에 의해 현재 rank와 select 함수는 o(n)?? 비트만을 사용하여 ??O(1) 시간에 수행될 뿐만 아니라, 실제로도 실용적으로 구현되었다. 본 논문에서는 $n{\times}n$ 배열, 즉 2차원 비트 스트링에 대한 Rank 및 Select 함수를 새롭게 정의한다. 또한, $O(n^2log\;n)$ 비트를 사용하여 O(1) 시간에 Rank 질의를 수행하고 O(log n) 시간에 Select 질의를 수행하는 방법과, 보다 적은 $O(n^2)$ 비트를 사용하면서 O(log n) 시간에 Rank 질의를 수행하고 $O(log^2\;n)$ 시간에 Select 질의를 수행하는 방법을 제안한다. 본 논문에서 정의하는 2차원 배열 상의 Rank와 Select 함수는 이미 개발된 2차원 상의 써픽스 트리 등을 기반으로 향후 개발될 2차원 상의 압축된 인덱스 자료구조나 이미지 프로세싱 등에 유용하게 사용된다.

• Communications for Statistical Applications and Methods
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• 제24권2호
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• pp.115-127
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• 2017

This paper proposes a Bayesian test for the equivalence of survival functions in multiple groups. Proposed Bayesian test use the model of Cox's regression with time-varying coefficients. B-spline expansions are used for the time-varying coefficients, and the proposed test use only the partial likelihood, which provides easier computations. Various simulations of the proposed test and typical tests such as log-rank and Fleming and Harrington tests were conducted. This result shows that the proposed test is consistent as data size increase. Specifically, the power of the proposed test is high despite the existence of crossing hazards. The proposed test is based on a Bayesian approach, which is more flexible when used in multiple tests. The proposed test can therefore perform various tests simultaneously. Real data analysis of Larynx Cancer Data was conducted to assess applicability.

• Kyungpook Mathematical Journal
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• 제23권1호
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• pp.1-12
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• 1983

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2023년도 학술발표회
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• pp.160-160
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• 2023

Generally, Global Climate Models (GCM) cannot be used directly due to their inherent error arising from over or under-estimation of climate variables compared to the observed data. Several bias correction methods have been devised to solve this problem. Most of the traditional bias correction methods are one dimensional as they bias correct the climate variables separately. One such method is the Quantile Mapping method which builds a transfer function based on the statistical differences between the GCM and observed variables. Laux et al. introduced a copula-based method that bias corrects simulated climate data by employing not one but two different climate variables simultaneously and essentially extends the traditional one dimensional method into two dimensions. but it has some limitations. This study uses objective functions to address specifically, the limitations of Laux's methods on the Quantile Mapping method. The objective functions used were the observed rank correlation function, the observed moment function and the observed likelihood function. To illustrate the performance of this method, it is applied to ten GCMs for 20 stations in South Korea. The marginal distributions used were the Weibull, Gamma, Lognormal, Logistic and the Gumbel distributions. The tested copula family include most Archimedean copula families. Five performance metrics are used to evaluate the efficiency of this method, the Mean Square Error, Root Mean Square Error, Kolmogorov-Smirnov test, Percent Bias, Nash-Sutcliffe Efficiency and the Kullback Leibler Divergence. The results showed a significant improvement of Laux's method especially when maximizing the observed rank correlation function and when maximizing a combination of the observed rank correlation and observed moments functions for all GCMs in the validation period.

• 한국통신학회논문지
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• 제16권4호
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• pp.319-325
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• 1991

이 논문에서는 일반화된 관측 모델의 특수한 때에 순위 통계량을 써서 알려진 신호를 비모수 검파하는 한 가지 방법을 생각하였다. 좀더 구체적으로는 신호의존성 잡음 모델에서 알려진 신호 국소 최적 순위 검파기를 얻고 이를 순가산성 잡음 모델에서 얻은 국소 최적 순위 검파기와 견주어 보았다. 또한 국소 최적 순위 검파기의 검정 통계량을 이루는 점수 함수의 몇가지 보기를 보였다.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.