• Journal of Korea Society of Industrial Information Systems
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• v.12 no.1
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• pp.80-86
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• 2007

The concept of the coverage has been played an important role in the area of reliability evaluation of a system. The widely used measures of reliability include the m time between failures, the availability and so on. In this paper, we propose an estimator of the coverage probability in a redundant system with a control unit and investigate some moments of the proposed estimator. And assuming exponential distribution of all units, we conduct a simulation study for calculating the estimates of the coverage probability and its confidence bounds. An example of evaluating the availability of an optical transportation system is illustrated.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.943-952
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• 2013

Wald, Agresti-Coull, Jeffreys, and Bayes-Laplace methods are commonly used for confidence interval of binomial proportion are applied for prediction intervals. We used coverage probability, mean coverage probability, root mean squared error, and mean expected width for numerical comparisons. From the comparisons, we found that Wald is not proper as for confidence interval and Agresti-Coull is too conservative to differ from confidence interval. However, Jeffrey and Bayes-Laplace are good for prediction interval and Jeffrey is especially desirable as for confidence interval.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.579-588
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• 2021

Wald, Agresti-Coull, Jeffreys, and Bayes-Laplace methods are commonly used for confidence interval of binomial proportion are applied for prediction intervals. We used coverage probability, mean coverage probability, root mean squared error, and mean expected width for numerical comparisons. From the comparisons, we found that Wald is not proper as for confidence interval and Agresti-Coull is too conservative to differ from confidence interval. However, Jeffrey and Bayes-Laplace are good for prediction interval and Jeffrey is especially desirable as for confidence interval.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.29-36
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• 2013

In the treatment of the sequential beta-protection procedure, we define the reasonable stopping time and investigate that for the stopping time Wijsman's requirements, coverage probability and beta-protection conditions, are satisfied in the estimation for the mean vector ${\mu}$ by the sample from the multivariate normal distributed population with unknown mean vector ${\mu}$ and a positive definite variance-covariance matrix ${\Sigma}$.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.1-9
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• 2003

In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.217-230
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• 2006

e discuss proper confidence intervals for interval estimation of a low binomial proportion. A large sample surveys are practically executed to find rates of rare diseases, specified industrial disaster, and parasitic infection. Under the conditions of 0 < p ${\leq}$ 0.1 and large n, we compared 6 confidence intervals with mean coverage probability, root mean square error and mean expected widths to search a good one for interval estimation of population proportion p. As a result of comparisons, Mid-p confidence interval is best and AC, score and Jeffreys confidence intervals are next.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.35-46
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• 2019

Multivariate Confidence Region (MCR) cannot be used to obtain the confidence region of the mean vector of multivariate data when the normality assumption is not satisfied; however, the Quantile Confidence Region (QCR) could be used with a Multivariate Quantile Vector in these cases. The coverage rate of the QCR is better than MCR; however, it has a disadvantage because the QCR has a wide shape when the probability density function follows a bimodal form. In this study, we propose a Quantile Confidence Region using the Highest density (QCRHD) method with the Highest Density Region (HDR). The coverage rate of QCRHD was superior to MCR, but is found to be similar to QCR. The QCRHD is constructed as one region similar to QCR when the distance of the mean vector is close. When the distance of the mean vector is far, the QCR has one wide region, but the QCRHD has two smaller regions. Based on these features, it is found that the QCRHD can overcome the disadvantages of the QCR, which may have a wide shape.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.171-181
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• 2006

The Wald confidence interval has been considered as a standard method for the difference of proportions. However, the erratic behavior of the coverage probability of the Wald confidence interval is recognized in various literatures. Various alternatives have been proposed. Among them, Agresti-Caffo confidence interval has gained the reputation because of its simplicity and fairly good performance in terms of coverage probability. It is known however, that the Agresti-Caffo confidence interval is conservative. In this note, a confidence interval is developed using the weighted Polya posterior which was employed to obtain a confidence interval for the binomial proportion in Lee(2005). The resulting confidence interval is simple and effective in various respects such as the closeness of the average coverage probability to the nominal confidence level, the average expected length and the mean absolute error of the coverage probability. Practically it can be used for the interval estimation of the difference of proportions for any sample sizes and parameter values.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.479-488
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• 2007

A sequential procedure is proposed in order to construct one-sided confidence intervals for a normal mean with guaranteed coverage probability and ${\beta}-protection$ when the normal mean and variance are identical. First-order asymptotic properties on the sequential sample size are found. The derived results hold with uniformity in the total parameter space or its subsets.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.47-54
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• 2001

Let {Xn, n = 1,2,${\cdots}$} be i.i.d. random variables with the only unknown parameters mean ${\mu}$ and variance a ${\sigma}^2$. We consider a sequential confidence interval C1 for the mean with coverage probability 1-${\alpha}$ and expected length of confidence interval $E_{\theta}$(Length of CI)/${\mid}{\mu}{\mid}{\leq}k$ (k : constant) and give some asymptotic properties of the stopping time in various limiting situations.