• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.29-41
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• 2017

The estimation problem of expected time to failure of units is studied in a discrete set up. A simple step-stress accelerated life testing is considered with a Type-I censored sample from geometric distribution that is a commonly used distribution to model the lifetime of a device in discrete case. Maximum likelihood estimators as well as the associated distributions are derived. Exact, approximate and bootstrap approaches construct confidence intervals that are compared via a simulation study. Optimal confidence intervals are suggested in view of the expected width and coverage probability criteria. An illustrative example is also presented to explain the results of the paper. Finally, some conclusions are stated.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.253-261
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• 1996

In this paper, we derive the maximum likelihood estimator of P=P(X

• Proceedings of the Korean Association for Survey Research Conference
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• 2006.06a
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• pp.131-159
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• 2006

This paper consider multinomial group testing which is concerned with classification each of N given units into one of k disjoint categories. In this paper, we propose exact Bayesian, approximate Bayesian, bootstrap methods for estimating individual category proportions using the multinomial group testing model proposed by Bar-Lev et al (2005). By the comparison of Mcan Squre Error (MSE), it is shown that the exact Bayesian method has a bettor efficiency and consistency than maximum likelihood method. We suggest an approximate Bayesian approach using Markov Chain Monte Carlo (MCMC) for posterior computation. We derive exact credible intervals based on the exact Bayesian estimators and present confidence intervals using the bootstrap and MCMC. These intervals arc shown to often have better coverage properties and similar mean lengths to maximum likelihood method already available. Furthermore the proposed models are illustrated using data from a HIV blooding test study throughout California, 2000.

• Journal of Environmental Science International
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• v.20 no.3
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• pp.321-327
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• 2011

Bootstrap methods is the computer-based resampling method that estimates the standard errors and confidence intervals of summary statistics using the plug-in principle for assessing the accuracy or uncertainty of statistical estimates, and the BCa method among the Bootstrap methods is known much superior to other Bootstrap methods in respect of the standards of statistical validation. Therefore this study suggests the method of the representation and treatment of uncertainty in flood risk assessment and water resources planning from the construction and application of rainfall frequency analysis model considersing the uncertainty based on the nonparametric BCa method among the Bootstrap methods for the assessement of the estimation of probability rainfall and the effect of uncertainty considering the uncertainty of the parameter estimation of probability in the rainfall frequency analysis that is the most fundamental in flood risk assessement and water resources planning.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.311-315
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• 1997

In this note we consider confidence interval based on Kolmogorov-Smirnov statistic. In order to obtain confidence interval we need percentage points of the statistics. Bootstrap method is examined whether it is useful to determine the points. It is concluded that the method is useful for observations with many ties, whereas it gives less conserbative points for continuous distributions.

• The Korean Journal of Physiology and Pharmacology
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• v.13 no.5
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• pp.367-371
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• 2009

The estimation of 90% parametric confidence intervals (CIs) of mean AUC and Cmax ratios in bioequivalence (BE) tests are based upon the assumption that formulation effects in log-transformed data are normally distributed. To compare the parametric CIs with those obtained from nonparametric methods we performed repeated estimation of bootstrap-resampled datasets. The AUC and Cmax values from 3 archived datasets were used. BE tests on 1,000 resampled data sets from each archived dataset were performed using SAS (Enterprise Guide Ver.3). Bootstrap nonparametric 90% CIs of formulation effects were then compared with the parametric 90% CIs of the original datasets. The 90% CIs of formulation effects estimated from the 3 archived datasets were slightly different from nonparametric 90% CIs obtained from BE tests on resampled datasets. Histograms and density curves of formulation effects obtained from resampled datasets were similar to those of normal distribution. However, in 2 of 3 resampled log (AUC) datasets, the estimates of formulation effects did not follow the Gaussian distribution. Bias-corrected and accelerated (BCa) CIs, one of the nonparametric CIs of formulation effects, shifted outside the parametric 90% CIs of the archived datasets in these 2 non-normally distributed resampled log (AUC) datasets. Currently, the 80~125% rule based upon the parametric 90% CIs is widely accepted under the assumption of normally distributed formulation effects in log-transformed data. However, nonparametric CIs may be a better choice when data do not follow this assumption.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.235-246
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• 2004

• Journal of Multimedia Information System
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• v.2 no.3
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• pp.255-262
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• 2015

The modern manufacturing systems and technologies produce products that are more accurate day by day. This can be reached mainly by improvement the manufacturing process with at the same time restricting more and more the quality specifications and reducing the uncertainty in part. The main objective an industry becomes to lower the part's variability, since the less variability - the better is product. One of the part of this task is measuring the object's uncertainty. The main purpose of this study is to understand the application of bootstrap method for uncertainty evaluation. Bootstrap method is a collection of sample re-use techniques designed to estimate standard errors and confidence intervals. In the case study a surface of an automobile engine block - (Top view side) is measured by Coordinate Measuring Machine (CMM) and analyzed for uncertainty using Geometric Least Squares in complex with bootstrap method. The designed experiment is composed by three similar measurements (the same features in unique reference system), but with different points (5, 10, 20) concentration at each level. Then each cloud of points was independently analyzed by means of non-linear Least Squares, after estimated results have been reported. A MatLAB software tool used to generate new samples using bootstrap function. The results of the designed experiment are summarized and show that the bootstrap method provides the possibility to evaluate the uncertainty without repeating the Coordinate Measuring Machine (CMM) measurements many times, i.e. potentially can reduce the measuring time.

• Communications for Statistical Applications and Methods
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• v.23 no.4
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• pp.269-285
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• 2016

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

• Journal of the military operations research society of Korea
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• v.12 no.2
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• pp.68-81
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• 1986

This thesis studies the estimation from interarrival and service time data of the mean number of customers in service at time t for an $M/G/{\infty}$ queue. The assumption is that the parametric form of the service time distribution is unknown and the empirical distribution of twe service time is used in the estimate the mean number of customers in service. In the case in which the customer arrival rate is known the distribution of the estimate is derived and an approximate normal confidence interval procedure is suggested. The use of the nonparametric methods, which are the jackknife and the bootstrap, to estimate variability and construct confidence intervals for the estimate is also studied both analytically and by simulation.