• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1169-1181
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• 2006

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

• Journal of Korea Water Resources Association
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• v.37 no.1
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• pp.13-19
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• 2004

This study shows the possible use of the Poisson process for the characterization of dry year return period and duration. For the analysis we used an annual precipitation data, which has been collected since 1911 in Seoul. The highest threshold for the application of the Poisson process was determined to be the mean-0.5standard deviation, and then the results from the Poisson process are compared with the observed. Especially, the Poisson process was found to reproduce the mean duration and return interval quite well and show the possibility of using the Poisson process for the drought analysis.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.137-144
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• 1995

Hierarchical Bayes estimations of exchangeable mean vector of a multivariate Poisson distribution are obtained. Since sophiscated analytic integration procedures are needed, the Laplace method is employed in order tocompute these estimations approximately. An example is presented.

• Journal of Korean Institute of Industrial Engineers
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• v.1 no.1
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• pp.87-92
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• 1975

Three approximation methods for generating outcomes on Poisson random variables are discussed. A comparison is made to determine which method requires the least computer execution time and to determine which is the most robust approximation. Results of the comparison study suggest the method to choose for the generating procedure depends on the mean value of Poisson random variable which is being generated.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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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.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.269-284
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• 2000

We show asymptotic normality of the sample mean and sample autocovariances function generated from first-order integer valued autoregressive process(INAR(1)) with a negative binomial or a Poisson marginal. It is shown that a Poisson INAR(1) process is a special case of a negative binomial INAR(1) process.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1231-1239
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• 2012

An estimating procedure is introduced for kernel Poisson regression when the input variables consist of numerical and categorical variables, which is based on the penalized negative log-likelihood and the component-wise product of two different types of kernel functions. The proposed procedure provides the estimates of the mean function of the response variables, where the canonical parameter is linearly and/or nonlinearly related to the input variables. Experimental results are then presented which indicate the performance of the proposed kernel Poisson regression.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.355-363
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• 1997

In queueing theory, polling systems have been widely studied as a way of serving several stations in cyclic order. In this paper we consider Markov-modulated Poisson process which is useful for approximating a superposition of heterogeneous arrivals. We derive the mean waiting time of each station in a polling system where the arrival process is modeled by a Markov-modulated Poisson process.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.767-772
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• 2000

Zellner(1994) introduced the notion of a balanced loss function in the context of a general liner model to reflect both goodness of fit and precision of estimation. We study the perspective of unifying a variety of results both frequentist and Bayesian from Poisson distributions. We show that frequentist and Bayesian results for balanced loss follow from and also imply related results for quadratic loss functions reflecting only precision of estimation. Several examples are given for Poisson distribution.

• Journal of the Korea Institute of Military Science and Technology
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• v.9 no.2 s.25
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• pp.51-59
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• 2006

The purpose of this paper is to present reliability analysis procedures for repairable systems and apply the procedures for assessing the reliabilities of two subsystems of a specific group of military equipment based on field failure data. The mean cumulative function, M(t), the average repair rate, ARR(t), and analytic test methods are used to determine whether a failure process follows a renewal or non-renewal process. For subsystem A, the failure process turns out to follow a homogeneous Poisson process, and subsequently, its mean time between failures, availability, and the necessary number of spares are estimated. For subsystem B, the corresponding M(t) plot shows an increasing trend, indicating that its failure process follows a non-renewal process. Therefore, its M(t) is modeled as a power function of t, and a preventive maintenance policy is proposed based on the annual mean repair cost.