• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.611-622
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• 2013

Mudholkar and Tian (2002) proposed an entropy-based test of fit for the inverse Gaussian distribution; however, the test can be applied to only the composite hypothesis of the inverse Gaussian distribution with an unknown location parameter. In this paper, we propose an entropy-based goodness-of-fit test for an inverse Gaussian distribution that can be applied to the composite hypothesis of the inverse Gaussian distribution as well as the simple hypothesis of the inverse Gaussian distribution with a specified location parameter. The proposed test is based on the probability integration transformation. The critical values of the test statistic estimated by simulations are presented in a tabular form. A simulation study is performed to compare the proposed test under some selected alternatives with Mudholkar and Tian (2002)'s test in terms of power. The results show that the proposed test has better power than the previous entropy-based test.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.713-723
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• 2013

An objective Bayesian estimation procedure of the two-parameter Pareto distribution is presented under the reference prior and the noninformative prior. Bayesian estimators are obtained by Gibbs sampling. The steps to generate parameters in the Gibbs sampler are from the shape parameter of the gamma distribution and then the scale parameter by the adaptive rejection sampling algorism. A numerical study shows that the proposed objective Bayesian estimation outperforms other estimations in simulated bias and mean squared error.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.12
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• pp.1305-1311
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• 2015

A butterfly valve is a type of flow-control device typically used to regulate a fluid flow. This paper presents an estimation of the shape parameter of the Weibull distribution, characteristic life, and $B_{10}$ life for a concentric butterfly valve based on a statistical analysis of the reliability test data taken before and after the valve improvement. The difference in the shape and scale parameters between the existing and improved valves is reviewed using a statistical hypothesis test. The test results indicate that the shape parameter of the improved valve is similar to that of the existing valve, and that the scale parameter of the improved valve is found to have increased. These analysis results are particularly useful for a reliability qualification test and the determination of the service life cycles.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.129-135
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• 1991

A few simple methods to find $L_1$-unbiased estimators for location and scale parameters are summarized and examples utilizing diffusivity, a natural measure of dispersion for $L_1$-unbiased estimators, are given.

• Journal of Applied Reliability
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• v.14 no.1
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• pp.53-57
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• 2014

In the fields of reliability application, the most commonly used test methods for reliability demonstration are zero-failure acceptance tests since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. For products with lognormal lifetime distribution, the value of scale parameter is usually assumed to be known in designing reliability demonstration tests. It is important to select correct values of scale parameters to guarantee the specified reliability with given confidence level exactly. The effect of using wrong values of scale parameters in designing reliability demonstration test for products with lognormal lifetime distribution is examined and selecting proper values of scale parameters for conservative reliability demonstration is discussed.

• The Korean Journal of Applied Statistics
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• v.1 no.2
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• pp.27-33
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• 1987

Let $\Pi_i, \cdots, \Pi_k$ denote k gamma distributions with a common known shape parameter (degrees of freedom) r and scale parameters $\theta_1, \cdots, \theta_k$, respectively. Kim proposed an improved lower bound LB$(\delta^*)$, which concerns a two-stage elimimation type procedure for selecting the population associated with the largest scale parameter $max_{1\leqi\leqk} \theta_i$. The design constants (nr, mr, c) are given for k=4(1)10, $p^*=.95,.90 and \delta^*=1.75,2.0$. With these design constants, a comparison study was made with the procedure of Lee and Choi. As can be seen from the table, these are moderate amount of savings in the expected total sample size. Thus, together with the result in Lee and Choi, the two-stage procedure can perform much better than a single stage procedure.

• 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.33 no.4
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• pp.467-482
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• 2020

We investigate a monitoring procedure for the early detection of parameter changes in location-scale time series models. We introduce a detector for monitoring procedure based on modified residual cumulative sum (CUSUM). The asymptotic properties of the monitoring procedure are established under the null and alternative hypotheses. Simulation results and data analysis are also provided for illustration.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.927-934
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• 2010

In this paper, we introduce a method of parameter estimation of progressive Type I interval censored sample and progressive type II censored sample. We propose a new parameter estimation method, that is converting the data which obtained by progressive type I interval censored, those data be used to estimate of the parameter in progressive type II censored sample. We used exponential distribution with unknown scale parameter, the maximum likelihood estimator of the parameter calculates from the two methods. A simulation is conducted to compare two kinds of methods, it is found that the proposed method obtains a better estimate than progressive Type I interval censoring method in terms of mean square error.

• Convergence Security Journal
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• v.7 no.1
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• pp.45-53
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• 2007

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the hyper-exponential distribution reliability model, which maked out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method. For model determination and selection, explored goodness of fit (the error sum of squares). The methodology developed in this paper is exemplified with a software reliability random data set introduced by of Weibull distribution (shape 0.1 & scale 1) of Minitab (version 14) statistical package.