• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• International Journal of Reliability and Applications
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• v.15 no.2
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• pp.85-98
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• 2014

Accelerated life testing (ALT) is a well famous technique in life testing and reliability studies, this is particularly used to induce so high stress leading to failure of the highly reliable units quickly under stipulated duration of time. The step-stress ALT is one of the systematic experimental strategy of ALT applied to fail the units in steps. In this article we focus on two important issues (i) necessity of life tests at higher steps with relevant causes (ii) to develop a new optimum test plan for 3-step SSALT under the modified cumulative exposure model proposed by Khamis and Higgins (1998). It is assumed that the lifetime of test units follows Rayleigh distribution and its scale parameter at constant stress level is assumed to be a log-linear function of the stress. The maximum likelihood estimates of the parameters involved in the step-stress ALT model are obtained. A simulation study is performed for numerical investigation of the proposed new optimum plan 3-step, step-stress ALT. The necessity of the life test units at 3-step step-stress is also numerically examined in comparison to simple step-stress setup.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.1
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• pp.139-146
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• 1986

This study is concerned with the development of statistical life test plans for the mean lifetime of an item whose underlying lifetime distribution is a two parameter Weibull, which is perhaps the most widely used lifetime model. For this purpose, I used the likelihood ratio test method, and I verified the developed test plans and determined the sampling size and censoring number by computer similation.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.103-111
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• 1996

This paper provides a test of the composite hypothesis that a random sample is (two parameter) gamma distributed when both the scale and shape parameters are estimated from the data. The test statistic is a variant of the usual Anderson-Darling statistic, the primary difference being that the statistic is based on the maximum likelihood estimator of the shape parameter of the assumed gamma distribution. The percentage points are developed via simulation and are presented graphically. Examples are provided.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.49-58
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• 2004

In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.

• 한국데이터정보과학회:학술대회논문집
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• 2004.10a
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• pp.25-32
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• 2004

In this study, we use various change-point detection methods to detects Korea economic crisis of 1997, and then compares their performance. In change-point detection method, there are three major categories: (1) the parametric approach, (2) the nonparametric approach, and (3) the model-based approach. Through the application to Korea foreign exchange rate during her economic crisis, we compare the employed change-point detection methods and, furthermore, determine which of them performs better.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.459-468
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• 2002

A class of asymmetric beta-ARCH processes is proposed and connections to traditional ARCH models are explained. Geometric ergodicity of the model is discussed. Conditional least squares as well as maximum likelihood estimators of parameters and their limit results are also presented. A test for symmetry of the model is studied with limiting power of test statistic given.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.585-592
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• 2004

This study detects Korea economic crisis of 1997 using various change-point detection methods and then compares their performance. In change-point detection method, there are three major categories: (1) the parametric approach, (2) the nonparametric approach, and (3) the model-based approach. Through the application to Korea foreign exchange rate during her economic crisis, we compare the employed change-point detection methods and, furthermore, determine which of them performs better.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.689-694
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• 2004

We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.67-77
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• 1999

For a orientation-shift model supported on the unit sphere, Euler angles are the conventional measure to parametrize orientation-shifts. The essential role which is played by rotationally symmetry of an underlying distribution is reviewed. In this paper we propose the inference procedure based on Euler angles for the rotationally symmetric spherical distribution. The likelihood ratio test(LRT) based on the Euler angles is worked out. The asymptotic distribution of the test under the null hypotheses and certain contiguous alternatives is obtained.