• Journal of Korean Society for Quality Management
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• v.43 no.2
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• pp.169-184
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• 2015

Purpose: This paper is concerned with optimally designing accelerated degradation test (ADT) plans based on a gamma process for the degradation model. Methods: By minimizing the asymptotic variance of the MLE of the q-th quantile of the lifetime distribution at the use condition, the test stress levels and the proportion of test units allocated to each stress level are optimally determined. Results: The optimal plans of ADT are developed for various combination of parameters. In addition, a method for determining the sample size is developed, and sensitivity analysis procedures are illustrated with an example. Conclusion: It is important to optimally design ADT based on a gamma process under the condition that a degradation process should be always nonnegative and strictly increasing over time.

• Wind and Structures
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• v.6 no.5
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• pp.357-386
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• 2003

A number of methods based on various ideas have been proposed for simulating the non-Gaussian stationary process. However, these methods have some limitations. This paper reviewed several simulation methods based on the translation method using logarithmic and polynomial functions, which have emerged in the history of statistics and in the field of civil engineering. The applicability of each method is discussed from the viewpoint of the reproducibility of higher order statistics of the object function in the simulated sample functions, and examined using pressure signals measured from wind tunnel experiments for various shapes of buildings. The parameter estimation methods, i.e. the method of moments and quantile plot, are also reviewed, and the useful aspects of each method are discussed. Additionally, a simple worksheet for parameter estimation is derived based on the method of moment for practical application, and the accuracy is discussed comparing with a set of previously proposed formulae.

• Journal of Korean Society for Quality Management
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• v.24 no.3
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• pp.37-49
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• 1996

For highly reliable devices it is often defined to "fail" when its performance degrades below a specified value. In this paper we consider a method for optimally designing accelerated degradation tests(ADTs) in which the performance over exposure time and stress has Weibull distribution. For the product whose performance has Weibull distribution, the optimum plan - low stress level and sample proportions allocated to each test condition - is obtained, which minimize the asymptotic variance of maximum likelihood estimator of a stated quantile at design stress. We also present compromise ADTs plan that can be used for the practical purpose.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.397-419
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• 2017

A four-parameter extended fatigue lifetime model called the odd Birnbaum-Saunders geometric distribution is proposed. This model extends the odd Birnbaum-Saunders and Birnbaum-Saunders distributions. We derive some properties of the new distribution that include expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood and a Bayesian approach are adopted to estimate the model parameters; in addition, various simulations are performed for different parameter settings and sample sizes. We propose two new models with a cure rate called the odd Birnbaum-Saunders mixture and odd Birnbaum-Saunders geometric models by assuming that the number of competing causes for the event of interest has a geometric distribution. The applicability of the new models are illustrated by means of ethylene data and melanoma data with cure fraction.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.359-368
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• 1998

Let ξ$_{p}$(z$_{0}$) be the pth quantile of the distribution of the survival time of an individual with time-invariant covariate vector z$_{0}$ in the additive risk model. We propose an estimator of (ξ$_{p}$(z$_{0}$) and derive its asymptotic distribution, and then construct an approximate confidence interval of ξ$_{p}$(z$_{0}$) . Simulation studies are carried out to investigate performance of the proposed estimator far practical sample sizes in terms of empirical coverage probabilities. Also, the estimator is illustrated on small cell lung cancer data taken from Ying, Jung, and Wei (1995) .d Wei (1995) .

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1433-1441
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• 2016

Small area model provides reliable and accurate estimations when the sample size is not sufficient. Our dataset has an inherent nonlinear pattern which signicantly affects our inference. In this case, we could consider semiparametric models such as truncated polynomial basis function and radial basis function. In this paper, we study four Bayesian semiparametric models for small areas to handle this point. Four small area models are based on two kinds of basis function and different knots positions. To evaluate the different estimates, four comparison measurements have been employed as criteria. In these comparison measurements, the truncated polynomial basis function with equal quantile knots has shown the best result. In Bayesian calculation, we use Gibbs sampler to solve the numerical problems.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.627-641
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• 2021

An asymmetric least squares estimation method has been employed to estimate linear models for percentile regression. An asymmetric maximum likelihood estimation (AMLE) has been developed for the estimation of Poisson percentile linear models. In this study, we propose generalized nonlinear percentile regression using the AMLE, and the use of the parametric bootstrap method to obtain confidence intervals for the estimates of parameters of interest and smoothing functions of estimates. We consider three conditional distributions of response variables given covariates such as normal, exponential, and Poisson for three mean functions with one linear and two nonlinear models in the simulation studies. The proposed method provides reasonable estimates and confidence interval estimates of parameters, and comparable Monte Carlo asymptotic performance along with the sample size and quantiles. We illustrate applications of the proposed method using real-life data from chemical and radiation epidemiological studies.

• Journal of Korea Water Resources Association
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• v.43 no.9
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• pp.813-822
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• 2010

An important problem in frequency analysis is the estimation of the quantile for a certain return period. In frequency analysis an assumed probability distribution is fitted to the observed sample data to estimate the quantile at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness of fit tests. The goodness of fit test method can be described as a method for examining how well sample data agrees with an assumed probability distribution as its population. However it gives generally equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling (AD) test statistics are provided using simulation and the power study are performed to compare the efficiency of other goodness of fit tests. The power test results indicate that the modified AD test has better rejection performances than the traditional tests. In addition, the applications to real world data are discussed and shows that the modified AD test may be a powerful test for selecting an appropriate distribution for frequency analysis when extreme cases are considered.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.621-636
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• 2018

Research on the application of informative sampling technique has been conducted in order to reduce the influence of non-response. Chung and Shin (Korean Journal of Applied Statistics, 30, 993-1004, 2017) showed that the estimation accuracy improved when using exponential response rate information for the parameter estimation if the distribution of errors included in the super population model follows normal distribution. However this method divides the stratum into equally spaced substrata to obtain the sample weight of the informative sampling technique and shows that the accuracy of the estimation improves as the number of substrata increases. In this study, with the given number of total sample size, the optimal substratum boundary points are calculated using equal space, quantile, and LH algorithm; consequently, the results using those methods are compared through simulation. We also studied the criteria to determine the number of substrata and substratum boundaries that can be used in practice with various types of auxiliary variable distributions.