• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2000년도 춘계학술대회
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• pp.249-263
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• 2000

This paper considers an algorithm using Johnson transformation to calculate process capability index for non-normal distribution. Johnson transformation is well known as one of methods transforming the data with non-normal distribution to normal data.

• 산업경영시스템학회지
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• 제42권2호
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• pp.18-27
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• 2019

The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2011년도 추계학술대회
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• pp.535-549
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• 2011

Control chart is most widely used in SPC(Statistical Process Control), Recently it is a critical issue that the standard control chart is not suitable to non-normal process with very small percent defective. Especially, this problem causes serious errors in the reliability procurement, such as semiconductor, high-precision machining and chemical process etc. Procuring process control technique for non-normal process with very small percent defective and perturbation is becoming urgent. Control chart technique in non-normal distribution become very important issue. In this paper, we investigate on research trend of control charts under non-normal distribution with very small percent defective and perturbation, and propose some variable-transformation methods applicable to CUSUM control charts in non-normal process.

• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.567-580
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• 2005

It is usually assumed that asset returns in the stock market are normally distributed. However, analyses of real data show that the distribution tends to be skewed and to have heavier tails than those of the normal distribution. In this paper, we investigate the method of estimating the value at risk(VaR) of stock returns. The VaR is computed by using the transformation and back-transformation method. The analysis of KOSPI and KOSDAQ data shows that the proposed estimation outperformed that under the normal assumption.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• 응용통계연구
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• 제28권3호
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• pp.511-527
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• 2015

ARMA(p, q) 모형 분석에서 분산 안정화 또는 정규화를 위해 멱변환(power transformation)이 사용된다. 변환된 자료를 이용하여 분석이 이루어지며 원 자료의 예측을 위해 재변환이 사용된다. 이때 흔히 변환된 자료 분석에서 얻어진 예측값의 역함수 값이 원자료 예측값으로 사용되지만 이는 편향이 있는 것으로 알려져 있다. 이를 해결하기 위해 로그 변환의 경우 Granger과 Newbold (1976)는 로그-정규분포의 기댓값을 이용할 것을 제안하였다. 본 연구에서는 모의실험을 통하여 제곱근 변환과 로그 변환 후 재변환을 사용할 때 예측값으로 기댓값의 역함수를 이용하는 방법과 역함수의 기댓값을 사용하였을 때의 추정의 결과를 모의실험을 통하여 비교하였다.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.595-600
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• 1999

We present a simple geometric approach which uses polar transformation and elementary trigonometry to evaluating an orthant probability in a bivariate normal distribution. Figures are provided to illustrate the situation for varying correlation coefficient. We derive the distribution of the sample correlation coefficient from a bivariate normal distribution when the sample size is 2 as an application.

• 통합자연과학논문집
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• 제13권2호
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• pp.76-82
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• 2020

If normality of an observed data is not a viable assumption, we can carry out normal-theory analyses by suitable transforming data. Power transformation by Box and Cox, one of the transformation methods, is derived the power which maximized the likelihood function. But it doesn't induces the closed form in mathematical analysis. In this paper, we compose some R the syntax of which is easier than other statistical packages for deriving the power with using numerical methods. Also, by using R, we show the transformed data approximately distributed the normal through Q-Q plot in univariate and bivariate cases with some examples. Finally, we present the value of a goodness-of-fit statistic(AD) and its p-value for normal distribution. In the similar procedure, this method can be extended to more than bivariate case.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.197-201
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• 2005

In this article, we will compare the performance of the mean control chart, the median control chart, the transformed mean control chart, the transformed median control chart, and the precedence control chart by simulation study. For control charts with transformed data, Yeo-Johnson transformation is used. Under the in-control condition, ARL's in all control charts coincide with the designed ARL in the normal distribution, but in the other distributions, only the precedence control chart provides the in-control ARL as designed. Under the out-of-control condition, the mean control chart is preferred in the normal distribution and the median control chart is preferred in the heavy-tailed distribution and the precedence control chart outperforms in the short-tailed distribution.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.289-300
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• 2007

The stock return is changed by factors of inside and outside or is changed by factor of market system. But most studies have not considered the changes of stock return distribution when estimate the VaR. Such study may lead us to wrong conclusion. In this paper we calculate the VaR of price-to-earnings ratios by the distribution that have considered the change point and used transformation to satisfy normal distribution.