• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.453-462
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• 2005

We derive the influence function on t statistic and find its feature; the influence function on t statistic has two forms depending on the value of ${\mu}_0$. Sample influence functions are used to verify the validity of the derived influence function. We use random samples from normal distribution to show the validity of the function. The simulation study proves that the obtained influence function is very accurate to in estimating changes in t statistic when an observation is added or deleted.

• Proceedings of the Korean Reliability Society Conference
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• 2000.04a
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• pp.185-191
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• 2000

A survival variable is a nonnegative random variable X with distribution function F and a survival function (equation omitted)=1－F. This variable is said to be New Better than Used of specified age $t_{0}$ if (equation omitted) for all $\chi$$\geq$0 and a fixed to. We propose the test for $H_{0}$ : (equation omitted) for all $\chi$$\geq$0 against $H_1$：(equation omitted) for all $\chi$$\geq$0 when the specified age $t_{0}$ is unknown but can be estimated from the data when $t_{0}$=${\mu}$, the mean of F, and also when $t_{0}$=$\xi_p$, the pth percentile of F. This test statistic, which is based on a linear function of the order statistics from the sample, is readily applied in the case of small sample. Also, this test statistic is more simple than the test statistic of Ahmad's test statistic (1998). Finally, the performance of this test is presented.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.811-823
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• 2018

Multivariate control chart based on Hotelling's $T^2$ statistic is a powerful tool in statistical process control for identifying an out-of-control process. It is used to monitor multiple process characteristics simultaneously. Detection of the out-of-control signal with the $T^2$ chart indicates mean vector shifts. However, these multivariate signals make it difficult to interpret the cause of the out-of-control signal. In this paper, we review methods of signal interpretation based on the Mason, Young, and Tracy (MYT) decomposition of the $T^2$ statistic. We also provide an example on how to implement it using R software and demonstrate simulation studies for comparing the performance of these methods.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.125-143
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• 1993

The primary objective of the paper is to review the development of approximations of the null distribution of a scan statistic and to show how these approximations were improved. Let $X_1, \cdots, X_N$ be a sequence of independent uniform random variables on an interval (0, t]. A can statistic is defined to be the maximum number of observations in a subinterval of length t $\leq$ T, when we continuously (or discretely) move the subinterval from 0 to T. A scan statistic is used to test whether certain events occur in a cluster aganist a null hypothesis of the uniformity. It is difficult to calculate the exact null distribution of a scan statistic. Several authors have suggested approximations of the null distribution of a scan statistic since Naus(1966). We conceive that a scan statistic can be used for detecting a "hot region" is defined to be a region at which the frequencies of mutations are relatively high. A "hot region" may be regarded as a generalized version of a hot spot. We leave it for a further study the concrete formulation of deteciton a "hot region" in a mutational spectrum.uot; in a mutational spectrum.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.133-144
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• 1998

In this paper, we propose the two-sample test statistic using Wilcoxon signed rank test on ranked-set sampling(RSS) and obtain the asymptotic relative efficiencies(ARE) of the proposed test statistic with respect to Mann-Whitney-Wilcoxon statistic on simple random sampling(SRS), the Mann-Whitney-Wilcoxon statistic on RSS, sign statistic on RSS and Wilcoxon signed rank test on SRS. From the simulation works, we compare the powers of the proposed test statistic, Mann-Whitney-Wilcoxon statistic on RSS, the usual two-sample t statistic, sign statistic on RSS, where the underlying distributions are uniform, normal, double exponential, logistic and Cauchy distributions.

• Journal of Korean Society for Quality Management
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• v.29 no.2
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• pp.37-45
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• 2001

A survival variable is a non-negative random variable X with distribution function F(t) satisfying F(0) : 0 and a survival function F(t): 1-F(t). This variable is said to be New Better than Used of specified age t$_{0}$ if F(x+ t$_{0}$)$\leq$F(x).F(t$_{0}$) for all x$\geq$0 and a fixed t$_{0}$. We propose the test for H$_{0}$ : F(x+t$_{0}$)=F(x).F(t$_{0}$) for all x$\geq$0 against H$_1$: F(x+t$_{0}$) $\leq$ F(x).F(t$_{0}$) for all x$\geq$0 when the specified age to is unknown but can be estimated from the data when t$_{0}$=ζ$_{p}$, the pth percentile of F. This test statistic, which is based on the normalized spacings between the ordered observations, is readily applied in the case of small sample. Also, our test is more simple than Ahmad's test (1998). Finally, the performance of our test is presented.our test is presented.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.659-666
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• 1999

In comparing two population means, the test statistic depends on the sample means and the variances, which are very sensitive to the extremely large or small values. This paper aims at examining the behavior of such observations using proper criterion which can measure the influence of them. We derive a computationally feasible statistic which can detect influential observations on the two-sample t-statistic.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.171-179
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• 1992

본고에서는 그래프를 이용하여 stable law분포의 index, skewness, scale, location 모수들에 대한 추정방법을 제시한다. 먼저, order statistics의 함수인 tail length statistic $K_{t}$ , skewness statistic $K_{s}$ 를 이용하여 index .alpha., scale .betha.를 추정한다. 다음에는, 추정된 .alpha., .betha.를 index로 하여 개발된 그래프들로 부터 scale .sigma., location .mu.추정에 필요한 order statistics의 함수를 결정한다. 몇가지 예를 마지막에 예시한다.

• Journal of Environmental Science International
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• v.20 no.9
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• pp.1183-1190
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• 2011

This study was aimed to establish the evaluating protocol and standard assessment for genetically modified (GM) hot pepper and to find out a proper statistic method to analyze for equality of agricultural characters between GM and non-GM pepper lines. GM and non-GM hot pepper lines were cultivated in two GMO fields in the middle region of Korea and total of 52 agricultural characters were collected during the plant growing season for 4 years, 2007 to 2010. Levene's test was conducted to confirm the homogeneity of raw data before statistic analysis. Two-way ANOVA in the multivariate tests and t-test were conducted to analyze 52 agricultural characters in order to find out the equality between H15 and P2377. From the statistical analysis through two-way ANOVA, 16 out of 16 plant growth traits, 9 out of 18 green fruit traits and 7 out of 18 red fruit traits among 4 years and 9 out of 16 plant growth traits, 4 out of 18 green fruit traits and 3 out of 18 red fruit traits between H15 and P2377 have shown the statistic differences. With the same raw data of 52 agricultural characters, t-test was also conducted. Based on the result from t-test, only 1 out of 16 plant growth traits, 2 out of 18 green fruit traits and 1 out of 18 red fruit traits have shown the differences between H15 and P2377, so that it was concluded that there is no statistic difference between H15 and P2377 in terms of agricultural characters. Also, the t-test is a proper statistic method to analyze each trait between GM and its control lines in order to evaluate agricultural characters.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.247-254
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• 2004

Tusher, Tibshirani and Chu (2001) suggested SAM (Significance Analysis of Microarrays) to compare two groups under different conditions for each gene, using microarray data. They used two sample t-statistic adding fudge factor in the denominator to prevent the value of statistic from being inflated by large sample variance, which might result in significant difference despite of a small value in the numerator. This paper aims at finding robust fudge factor and replacing it in two-sample t-statistic used in SAM, which we call Modified SAM (MSAM). Using the simulated data and data used in Dudoit et al.(2002), it is shown that MSAM find significant genes better and has less error rate than SAM.