• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.103-110
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• 1999

In this paper, we summarize some relative risk estimators under the two sample model with proportional hazard and examine the relative efficiencies of the nonparametric estimators relative to the maximum likelihood estimator of a parametric survival function under random censoring model by comparing their asymptotic variances.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.419-428
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• 2006

The method of Reverse Ranked Ordering-Set Sampling(RROSS) as an opposed Ranked Ordering-Set Sampling(ROSS) and Ranked-Set Sampling(RSS) is discussed. We propose the test statistic using sign test on RROSS. This method is effective when observations are expensive and measurement is perhaps destructive or invasive. This method obtains more informations than ROSS and RSS. The asymptotic relative efficiencies of RROSS with respect to ROSS and RSS are always greater than 1 for all sample sizes. We consider a simple model to describe the effect of imperfect judgment errors.

• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.625-639
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• 2020

The gamma distribution is a flexible right-skewed distribution widely used in many areas, and it is of great interest to estimate the probability of a random variable exceeding a specified value in survival and reliability analysis. Therefore, the study develops a fixed-accuracy confidence interval for P(X > c) when X follows a gamma distribution, Γ(α, β), and c is a preassigned positive constant through: 1) a purely sequential procedure with known shape parameter α and unknown rate parameter β; and 2) a nonparametric purely sequential procedure with both shape and rate parameters unknown. Both procedures enjoy appealing asymptotic first-order efficiency and asymptotic consistency properties. Extensive simulations validate the theoretical findings. Three real-life data examples from health studies and steel manufacturing study are discussed to illustrate the practical applicability of both procedures.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.27-39
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• 2007

Based on goodness of fit new testing procedures are derived for testing exponentiality against harmonic new renewal better than used in expectation (HNRBUE). For this aging properties, a nonparametric procedure (U-statistic) is proposed. The percentiles of this test statistic are tabulated for sample sizes n=5(1)30(10)50. The Pitman asymptotic efficiency (PAE) of the test is calculated and compared with, the (PAE) of the test for new renewal better than used (NRBU) class of life distribution [see Mahmoud et al (2003)]. The power of this test is also calculated for some commonly used life distributions in reliability. The right censored data case is also studied. Finally, real examples are given to elucidate the use of the proposed test statistic in the reliability analysis.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• The Korean Journal of Applied Statistics
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• v.12 no.2
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• pp.479-490
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• 1999

선형시계열모형인 AR(1)모형과 비선형시계열모형인 RCA(1), ARCH(1)모형에서 이상치(Outlier)가 존재할 경우 최소제곱추정량과 M추정량간의 점근상대효율(Asymptotic Relative Efficiency: ARE)을 구하여 두 추정량의 로버스트 성질을 비교·분석하였다. 또한 여러 유계함수(Huber, Tukey, Andrews, Hampel)들을 M추정함수에 적용하여 각각의 유계함수들을 비교·분석하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.17-28
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• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1067-1076
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• 2006

Although the proportional hazards model is the most common approach used for studying the relationship of event times and covariates, alternative models are needed for occasions when it does not fit data. In the two-sample case, proportional odds models are useful for fitting data whose hazard rates converge asymptotically. In this thesis, we propose a new estimator of the relative odds ratio of the proportional odds model when two independent random samples are observed under uncensorship. We prove the asymptotic normality and consistency of the estimator by using martingale-representation. The efficiency of the proposed is assessed through a simulation study.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.429-441
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• 2014

In this work we study two a posteriori error estimators of hierarchical type for lowest-order mixed finite element methods. One estimator is computed by solving a global defect problem based on the splitting of the lowest-order Brezzi-Douglas-Marini space, and the other estimator is locally computable by applying the standard localization to the first estimator. We establish the reliability and efficiency of both estimators by comparing them with the standard residual estimator. In addition, it is shown that the error estimator based on the global defect problem is asymptotically exact under suitable conditions.

• Journal of the Korean Statistical Society
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• v.13 no.1
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• pp.1-19
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• 1984

A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.