• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.653-660
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• 2003

In this paper, we prove that the transformed sample Lorenz curve, normalized sample Lorenz curve, and the test statistics for testing of normality based on the normalized sample Lorenz curve and the modified Lorenz curve which were introduced by Kang and Cho (2001a, 2002) are location and scale invariant statistics.

• 응용통계연구
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• 제18권1호
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• pp.197-210
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• 2005

본 연구에서는 중등학교 통계교육을 위하여, 제7차 수학과 교육과정 중 고등학교에서 사용하는 검정교과서 수학 1과 국정교과서 확률과 통계의 확률통계 영역을 중심으로 용어와 개념 및 표현을 비교, 연구하였다. 검정과 국정교과서의 표본표준편차의 정의가 일치되지 않았으며, 표분평균의 분산과 중심극한정리에 대한 개념설명이 교과서마다 상이하였다. 또한, 확률변수 개념 설명이 불분명 한 교과서도 발견되었다. 본 연구에서는 오류의 수정과 더불어 표본분산으로 불편추정량을 사용할 것을 제안하였다.

• 대한수학회보
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• 제51권5호
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• pp.1399-1409
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• 2014

In this article, we establish the $\mathfrak{F}_p$-uniform moderate deviation principles of the sample quantiles and order statistics for a sequence of independent and identically distributed samples.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.523-529
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• 2004

In Korea, mathematics education has been changed according to the 7th national mathematics curriculum renovated by the Ministry of Education and Human Resources Development announcement in 1997. The education of probability and Statistics has been carried out as a part of this curriculum. We analyze and compare 3 kinds of mathematics textbooks for 10-12 grade students. Descriptions of random variable, sample variance and sample standard deviation, distribution of sample mean, and etc. which are on some textbooks, are misleaded in school education. We suggest the unbiased estimator of sample variance in textbooks and distributions of sample means with normal population assumption.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.403-420
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• 1994

An economic design of the $\bar{X}-R$ chart using variable sample size (VSS) scheme is proposed in this paper. In this design the sample size at each sampling time changes according to the values of the previous two sample statistics, sample mean and range. The VSS scheme uses large sample if the sample statistics appear near inside the control limits and smaller sample otherwise. The set of process parameters, such as the sampling interval, control limits and the sample sizes, are chosen to minimize the expected cost per hour. The efficiency of the VSS scheme is compared to the fixed sample size one for cases where there is multiple of assignable causes. Percent reductions of the expected cost in the VSS design are calculated for some given sets of cost parameters. It is shown that the VSS scheme improves the confidence of the procedure and performs statistically better in terms of the number of false alarms and the average time to signal, respectively.

• Communications for Statistical Applications and Methods
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• 제18권4호
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• pp.457-465
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• 2011

Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

• Communications for Statistical Applications and Methods
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• 제3권1호
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• pp.207-217
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• 1996

The problem of detecting change with independent data is considered. The asymptotic distribution of the sample change process with the sample Fourier coefficients is shown as a Brownian Bridge process. We suggest to use dynamic statistics such as a sample Brownian Bridge and graphs as statistical animation. Graphs including change PP plots are given by way of illustration with the simulated data.

• Communications for Statistical Applications and Methods
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• 제22권4호
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• pp.389-399
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• 2015

It is important not to overcalculate sample sizes for clinical trials due to economic, ethical, and scientific reasons. Kang and Kim (2014) investigated the accuracy of a well-known sample size calculation formula based on the approximate power for continuous endpoints in equivalence trials, which has been widely used for Development of Biosimilar Products. They concluded that this formula is overly conservative and that sample size should be calculated based on an exact power. This paper extends these results to binary endpoints for three popular metrics: the risk difference, the log of the relative risk, and the log of the odds ratio. We conclude that the sample size formulae based on the approximate power for binary endpoints in equivalence trials are overly conservative. In many cases, sample sizes to achieve 80% power based on approximate powers have 90% exact power. We propose that sample size should be computed numerically based on the exact power.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.13-19
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• 2002

In nonparametric entropy estimation, both mass and mean-preserving maximum entropy distribution (Theil, 1980) and the underlying distribution of the sample entropy (Vasicek, 1976), the most widely used entropy estimator, consist of nb mass-preserving densities based on disjoint Intervals of the simple averages of two adjacent order statistics. In this paper, we notice that those nonparametric density functions do not actually keep the mass-preserving constraint, and propose a modified sample entropy by considering the generalized 0-statistics (Kaigh and Driscoll, 1987) in averaging two adjacent order statistics. We consider the proposed estimator in a goodness of fit test for normality and compare its performance with that of the sample entropy.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.859-871
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• 2003

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the slope of regression model under the symmetric and continuous underlying error distributions. This selector statistics is based on the residuals after the preliminary fit L$_1$ (least absolute estimator) and the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying symmetric distributions in the location model. If we use L$_1$ as a preliminary fit to get residuals, we find the asymptotic distribution of sample quantiles of residual are slightly different from that of sample quantiles in the location model. If we use the functions of sample quantiles of residuals as selector statistics, we find the suitable quantile points of residual based on maximizing the asymptotic distance index to discriminate distributions under consideration. In Monte Carlo study, this adaptive M-estimation method using selector statistics works pretty good in wide range of underlying error distributions.