• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.249-259
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• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

• 응용통계연구
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• 제11권2호
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• pp.287-302
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• 1998

표본평균(sample mean)의 밀도함수(density function)와 분포함수(distribution function)에 대한 안부점 근사(saddlepoin\ulcorner approximation)는 Daniels(1954, 1987), Lugannani와 Rice(1980)등에 의하여 유도되었으며, 이 근사식들의 정확도는 대표본(large sample)의 경우는 물론 소표본(small sample)의 경우에도 매우 뛰어난 것으로 알려져 있다. 최근 Easton과 Ronchetti(1986)는 일반적 통계량(general statistics)의 밀도함수에 대한 안부점 근사법을 제안하였고, 분포함수에 대한 근사로는 밀도함수에 대한 안부점 근사식을 직접 수치적으로 적분하는 방법을 제안하였다. 본 논문에서는 일반적 통계량의 분포함수에 대한 안부점 근사법을 제안하고, 이를 표본분산(sample variance)과 스튜던트화 평균(studentizd mean)의 분포함수에 대한 근사에 적용하였다.

• 대한의생명과학회지
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• 제23권4호
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• pp.333-338
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• 2017

This study was performed to assess microbial contamination of Aronia melanocarpa, blueberry, raspberry, and cranberry sold in several markets. We investigated total aerobic bacteria and detected foodborne bacteria by multiplex PCR from Aronia melanocarpa, blueberry, raspberry, and cranberry. Total aerobic bacteria of each sample showed mean 3.54 log CFU/g for Aronia melanocarpa, mean 1.90 log CFU/g for blueberry, and mean 1.40 log CFU/g for raspberry, but not detected in cranberry. Specially, Aronia melanocarpa contained high total aerobic bacteria contamination among various berries and contamination level reached 4.17 log CFU/g in sample 5. To evaluate the effect of distribution conditions, we also investigated total aerobic bacteria of various berries. Total aerobic bacteria showed mean 2.89 log CFU/g for berries in refrigerated distribution and 1.40 log CFU/g in frozen distribution, but not in dry distribution. For assessment of foodborne bacteria contamination, we conducted PCR with multiplex primers of E. coli O157, S. aureus, B. cereus, V. parahaemolyticus, L. monocytogenes, Y. enterocolitica, Salmonella spp., Shigella spp. Among these foodborne bacteria, B. cereus was amplified in Aronia melanocarpa in sample 4 and blueberry in sample 1, 2, 3, and 5. The result of quantitative analysis of B. cereus contamination showed 4.08 log CFU/g of Aronia melanocarpa in sample 4 and higher contamination rate 4.07 log CFU/g of blueberry in sample 3. These results suggest that strict food safety control in harvest and distribution of various berries is necessary to prevent foodborne disease and improve microbiological safety.

• Journal of the Korean Data and Information Science Society
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• 제23권6호
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• pp.1271-1277
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• 2012

In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

• Fibers and Polymers
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• 제6권4호
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• pp.332-335
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• 2005

The fibrogram theory is newly derived from the superposition principle of the conventional staple diagram, in which the left-hand ends of the fibers have to share a common starting point in order for the fiber length distribution to be measured, and the right-hand ends of the fibers form points. It is shown that the fibrogram is the staple diagram of the fiber sample having different random starting points, as well as the double cumulative distribution function of the frequency length function in the length biased sample. Also, the various means, viz. the numerical mean length, numerical mean length in median, length biased mean length, and length biased mean length in median, and the various upper half means, viz. the numerical upper half mean length, numerical upper half mean length in median, length biased upper half mean length, and length biased upper half mean length in median, are discussed in relation to the cotton blending process.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.209-217
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• 2001

We obtain the approximate maximum likelihood estimators (AMLEs) for the scale and location parameters $\theta$ and $\mu$ in the three-parameter Weibull distribution based on Type-II censored samples. We also compare the AMLEs with the modified maximum likelihood estimators (MMLEs) in the sense of the mean squared error (MSE) based on complete sample.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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• pp.1211-1219
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• 2013

최근 많은 통계 이론과 응용 문제에 정규분포의 대안으로 왜정규분포에 대한 활용이 높아지고 있다. 본 논문에서는 왜정규분포에 기반한 표본평균의 분포함수에 대한 안장점근사를 다루었다. 안장점근사는 기존의 정규근사에 비해 매우 뛰어난 정확성을 보일 뿐 아니라, 소표본에서도 정확한 근사결과를 제공한다. 본 논문에서 제시한 왜정규분포에 관련된 안장점근사는 복잡한 계산이 요구되는 기존의 Gupta와 Chen (2001)과 Chen 등 (2004)에 대한 근사적 방법으로 사용될 수 있다. 모의실험을 통해 표본평균의 분포함수에 대한 제안된 안장점근사의 정확도를 확인하고, 실제 자료에 대한 응용으로 Roberts (1966)의 쌍둥이 자료의 분석에 적용하였다.

• 산업공학
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• 제17권1호
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• pp.1-12
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• 2004

In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.139-144
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• 1990

For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

• 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.