• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.487-495
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• 2010

This paper develops a goodness of fit test statistic to test if the progressively Type II censored sample comes from an exponential distribution with origin known. The test is based on normalizing spacings and Stephens (1978)' modified Shapiro and Wilk (1972) test for exponentiality. The modification is for the case where the origin is known. We applied the same modification to Kim (2001a)'s statistic, which is based on the ratio of two asymptotically efficient estimates of scale. The simulation results show that Kim (2001a)'s statistic has higher power than Stephens' modified Shapiro and Wilk statistic for almost all cases.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.1065-1075
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• 2008

For the model validation of credit rating models, Kolmogorov-Smirnov(K-S) statistic has been widely used as a testing method of discriminatory power from the probabilities of default for default and non-default. For the credit rating works, K-S statistics are to test two identical distribution functions which are partitioned from a distribution. In this paper under the assumption that the distribution is known, modified K-S statistic which is formulated by using known distributions is proposed and compared K-S statistic.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.1-17
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• 2008

The ordinary least squares regression method of Haseman and Elston(1972) is most widely used in genetic linkage studies for continuous traits of sib pairs. Kruglyak and Lander(1995) suggested a statistic which appears to be a nonparametric counterpart to the Haseman and Elston(1972)'s regression method, but in fact these two methods are quite different. In this paper the relationships between these two methods are described and will be compared by simulation studies. One of the characteristics of the sib-pair linkage study is that the explanatory variable has only three different values and thus dependent variable is heavily replicated in each value of the explanatory variable. We propose a weighted least squares regression method which is more appropriate to this situation and the efficiency of the weighted regression in genetic linkage study was explored with normal and non-normal simulated continuous traits data. Simulation studies demonstrated that the weighted regression is more powerful than other tests.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.387-395
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• 1999

The goal of this paper is to study of the entropy - based on goodness-of-fit tests with several parametric models. It is also to study the relationship of the Moran's test statistic on the view of entropy.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.237-248
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• 2009

The probability of default on the credit evaluation study is represented as a linear combination of two distributions of default and non-default, and the distribution of the probability of default are generally known in most cases. Except the well-known Kolmogorov-Smirnov statistic for testing the identity of two distribution, Kuiper, Cramer-Von Mises, Anderson-Darling, and Watson test statistics are introduced in this work. Under the assumption that the population distribution is known, modified Cramer-Von Mises, Anderson-Darling, and Watson statistics are proposed. Based on score data generated from various probability density functions of the probability of default, the modified test statistics are discussed and compared.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.933-945
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• 2008

The genetic association test on age of onset trait aims to detect the putative gene by means of linear rank tests for a significant trend of onset distributions with genotypes. However, due to the selective sampling of recruiting subjects with ages less than a pre-specified limit, the genotype groups are subject to substantially different censored distributions and thus this is one reason for the low efficiencies in the linear rank tests. In testing the equality of two survival distributions, log-rank statistic is preferred to the Wilcoxon statistic, when censored observations are nonignorable. Therefore, for more then two groups, we propose a generalized log-rank test for trend as a genetic association test. Monte Carlo studies are conducted to investigate the performances of the test statistics examined in this paper.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.311-319
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• 2012

The simplest and the most important distribution in survival analysis is exponential distribution. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version based on the Kaplan-Meier product limit estimate of the distribution function; however, it could not be practical for a real data set since the statistic is for testing a simple goodness of fit hypothesis. We generalized it to the composite hypothesis for exponentiality with an unknown scale parameter. We also considered the classical Kolmogorov-Smirnov statistic and generalized it by the exact same way. The two statistics are compared through a simulation study. As a result, we can see that the generalized Koziol-Green statistic has better power in most of the alternative distributions considered.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.289-302
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• 1993

A goodness-of-fit test for the two-parameter exponential distribution, for use with the singly Type I and Type II right censored samples, is proposed. The test statistic is based on the $L_1$-norm of discrepancy between the cumulative distribution function and the empirical distribution function. To deal with the unknown parameters problem, the K- transformation is considered and modified to be applied to the censored samples. Rosenblatt's transformation is extended to the cases of Type I and Type II censored samples, in order to transform the censored samples into the complete ones. The critial values of the test statistic are obtained by Monte Carlo simulations for some finite sample sizes. The power studies are conducted to compare the proposed test with the Pettitt(1977) test for exponentiality with censored samples. It appears that the proposed test has relatively good power properties for moderate and large sample sizes.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.35-43
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• 2011

In this paper, we introduce a unit root test via discrete cosine transform in the AR(1) process. We first investigate the statistical properties of DCT coefficients under the stationary AR(1) process and the random walk process in order to verify the validity of the proposed method. A bootstrapping approach is proposed to induce the distribution of the test statistic under the unit root. We performed simulation studies for comparing the powers of the Dickey-Fuller test and the proposed test.

• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.383-391
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• 2011

This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.