• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.527-538
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• 2019

This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.

• 대한간호학회지
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• 제29권5호
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• pp.1030-1041
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• 1999

This study examined those problems noticed under the Asymptotically Generalized Least Squares estimator in evaluating a structural model of physical health. The problems were highly correlated parameter estimates and high standard errors of some parameter estimates. Separate analyses of the endogenous part of the model and of the metric of a latent factor revealed a highly skewed and kurtotic measurement indicator as the focal point of the manifested problems. Since the sample sizes are far below that needed to produce adequate AGLS estimates in the given modeling conditions, the adequacy of the Maximum Likelihood estimator is further examined with the robust statistics and the bootstrap method. These methods demonstrated that the ML methods were unbiased and statistical decisions based upon the ML standard errors remained almost the same. Suggestions are made for future studies adopting structural equation modeling technique in terms of selecting of a reference indicator and adopting those statistics corrected for nonormality.

• Industrial Engineering and Management Systems
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• 제10권2호
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• pp.154-160
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• 2011

In this paper, a reliability sampling plan under progressively type-1 interval censoring is proposed when the lifetime of products follows the Pareto distribution of second kind. We use the maximum likelihood estimator for the median life and its asymptotic distribution. The cost model is proposed and the design parameters are determined such that the given producer's and the consumer's risks are satisfied. Tables are given and the results are explained with examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.31-39
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• 1997

we shall propose some Bayes estimators and some generalized maximum likelihood estimators for reliability of a two-unit hot standby system with perfect switch based upon a complete sample of failure times observed from the exponential model and compare the peformances of the proposed estimators in terms of mean squared error.

• 디지털산업정보학회논문지
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• 제7권4호
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• pp.7-14
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• 2011

Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rate per fault (hazard function). This infinite non-homogeneous Poisson process is model which reflects the possibility of introducing new faults when correcting or modifying the software. In this paper, polynomial hazard function have been proposed, which can efficiency application for software reliability. Algorithm for estimating the parameters used to maximum likelihood estimator and bisection method. Model selection based on mean square error and the coefficient of determination for the sake of efficient model were employed. In numerical example, log power time model of the existing model in this area and the polynomial hazard function model were compared using failure interval time. Because polynomial hazard function model is more efficient in terms of reliability, polynomial hazard function model as an alternative to the existing model also were able to confirm that can use in this area.

• Nuclear Engineering and Technology
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• 제44권4호
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• pp.355-362
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• 2012

The aim of this study was to develop a bundle position-wise linear model (BPLM) to predict Pressure Tube (PT) diametral creep employing the previously measured PT diameters and operating conditions. There are twelve bundles in a fuel channel, and for each bundle a linear model was developed by using the dependent variables, such as the fast neutron fluences and the bundle coolant temperatures. The training data set was selected using the subtractive clustering method. The data of 39 channels that consist of 80 percent of a total of 49 measured channels from Units 2, 3, and 4 of the Wolsung nuclear plant in Korea were used to develop the BPLM. The data from the remaining 10 channels were used to test the developed BPLM. The BPLM was optimized by the maximum likelihood estimation method. The developed BPLM to predict PT diametral creep was verified using the operating data gathered from Units 2, 3, and 4. Two error components for the BPLM, which are the epistemic error and the aleatory error, were generated. The diametral creep prediction and two error components will be used for the generation of the regional overpower trip setpoint at the corresponding effective full power days. The root mean square (RMS) errors were also generated and compared to those from the current prediction method. The RMS errors were found to be less than the previous errors.

• 정보학연구
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• 제10권2호
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• pp.47-64
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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. Accurate predictions of software release times, and estimation of the reliability and availability of a software product require quantification of a critical element of the software testing process : test coverage. This model called enhanced non-homogeneous poission process(ENHPP). In this paper, exponential coverage and S-coverage model was reviewed, proposes the exponentiated exponential coverage reliability model, which maked out efficiency substituted for gamma and Weibull model(2 parameter shape illustrated by Gupta and Kundu(2001). In this analysis of software failure data, algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE statistics for the sake of efficient model, was employed.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.445-461
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• 2019

It is possible that data are not always fitted with sufficient precision by the existing distributions; therefore this article presents a methodology that enables the use of families of asymmetric distributions as alternative probabilistic models for survival analysis, with censorship on the right, different from those usually studied (the Exponential, Gamma, Weibull, and Lognormal distributions). We use a more flexible parametric model in terms of density behavior, assuming that data can be fit by a distribution of stable distribution families considered unconventional in the analyses of survival data that are appropriate when extreme values occur, with small probabilities that should not be ignored. In the methodology, the determination of the analytical expression of the risk function h(t) of the $L{\acute{e}}vy$ distribution is included, as it is not usually reported in the literature. A simulation was conducted to evaluate the performance of the candidate distribution when modeling survival times, including the estimation of parameters via the maximum likelihood method, survival function ${\hat{S}}$(t) and Kaplan-Meier estimator. The obtained estimates did not exhibit significant changes for different sample sizes and censorship fractions in the sample. To illustrate the usefulness of the proposed methodology, an application with real data, regarding the survival times of patients with colon cancer, was considered.

• 품질경영학회지
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• 제24권2호
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• pp.77-86
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• 1996

In this paper, we consider the problem of testing independence in the absolutely continuous bivariate exponential distribution of Block and Basu(1974). We construct a bootstrap procedure for testing zero and non-zero values of the parameter ${\lambda}_3$ which measures the degree of dependence and compare the power of the bootstrap test with likelihood ratio test(LRT) by Gupta et al.(1984) and the test based on maximum likelihood estimator(MLE) $\hat{{\lambda}}_3$ by Hanagal and Kale(1991) for small and moderate sample sizes.