• 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.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.135-144
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• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.403-414
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• 2000

A diagnostic tool for testing homogeneity for random effects is proposed in unbalanced linear mixed model based on score statistic. The finite sample behavior of the test statistic is examined using Monte Carlo experiments examine the chi-square approximation of the test statistic under the null hypothesis.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.155-166
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• 2018

Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA(0, d, 0) by using modified R/S statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac{1}{2}$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.

• 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.

• Journal of the Korean Statistical Society
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• v.13 no.2
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• pp.73-80
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• 1984

In this paper, likelihood-ratio test has been derived for testing multisample sphericity in complex multivariate Gaussian populations. The $h^{th}$ moment of the test statistic is given and its exact distribution has been derived using inverse Mellin transform. Asymptotic distribution of the statistic is also given.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.603-613
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• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.112-121
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• 1995

Let $p_1$ and $p_2$ be the proportions of two populations. To test the hypothesis $H_0 : p_1 = p_2$, we usually use the $x^2$ statistic, the large sample binomial statistic Z, and the Generalized Likelihood Ratio statistic-2log $\lambda$developed based on different mathematical rationale, respectively. Since testing the above hypothesis is equivalent to testing whether two populations follow the common Bernoulli distribution, one may also test the hypothesis by comparing 1 with the ratio of each density estimate and the hypothesized common density estimate, called comparison density, which was devised by Parzen(1988). We show that the above traditional test statistics ate actually estimating the measure of distance between the true densities and the common density under $H_0$ by representing them with the comparison density.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.709-717
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• 2008

The difference of two one-sided kernel estimators is usually used to detect the location of the discontinuity points of regression function. The large absolute value of the statistic imply discontinuity of regression function, so we may use the difference of two one-sided kernel estimators as the test statistic for testing null hypothesis of a smooth regression function. The problem is, however, we only know the asymptotic distribution of the test statistic under $H_0$ and we hardly expect the good performance of test if we rely solely on the asymptotic distribution for determining the critical points. In this paper, we show that if we adjust the bias of test statistic properly, the asymptotic rules hold for even small sample size situation.

• Journal of Korean Society for Quality Management
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• v.16 no.2
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• pp.18-33
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• 1988

A new diagnostic statistic for detecting outliers and influential observations in linear models is suggested and studied in this paper. The proposed statistic is a weighted sum of two measures ; one is for detecting outliers and the other is for detecting influential ovservations. The merit of this statistic is that it is possible to distinguish outliers from influential observations. This statistic can be used for not only regression models but also factorial design models. A Monte Carlo simulation study is reported to suggest critical values for detecting outliers and influential observations for simple regression models when the number of observations is 11. 21, 31, 41 or 51.