• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.113-121
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• 2009

In this paper, we consider the departure process from the open and nested tandem Queueing network with population constraint and constant service times. It is known that the Queueing network can be transformed into a simple Queueing network which can be easy to analyze. Using this simple Queueing network, upper and lower bounds on the interdeparture time are obtained. We prove that the variance of the interdeparture time is bounded within these two bounds. Validation against simulation data is shown that how it works the variance of the interdeparture time within two bounds. These bounds can be applied to obtain the better variance of the interdeparture time using a suitable method.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.147-153
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• 2007

In this note, we obtained results related to multiparameter discrete exponential families on considering lattice or semi-lattice in place of N (Natural numbers) in view of Cacoullos-type inequalities via the same arguments in Papathanasiou (1990, 1993).

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.507-518
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• 1995

The ordinary least squares based estiamte $S^2$ of the disturbance variance is considered in the linear regression model when the disturbances follow the first-order moving-average process. It is shown that $S^2$ is weakly consistent estimate for the disturbance varaince without any restriction on the regressor matrix X. Also, simple exact bounds on the relative bias of $S^2$ are given in finite sample sizes.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.449-472
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• 2001

A variety bounds are obtained for the variance and expectation of a continuous random variable whose p.d.f. is defined over a finite interval. Previous results are shown to be particular cases of the current more general development.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.49-56
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• 1998

In this paper, by the use of an Ostrowski type integral inequality for double integrals, we establish an upper bound for the estimation error variance of a continuous stream with stationary variogram.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.101-107
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• 2000

In this paper we establish an upper bound for the estimation error variance of a continuous stream with a stationary variogram V which is assumed to be of the r-Holder type (Lipschitzian) on [-d, d]. Functional properties for the mapping ${\xi}(t):=E[(X-X(t))^2]$, $t{\in}[0,d]$, are also given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.93-100
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• 2000

This paper deals with some fundamental matters pertaining to estimation of critical quantities associated with continuous processes which are frequently related to the quality rating of the product. Specifically, it examines bounds on estimation and bounds on the estimation error variance. It draws on recent results from the theory of mathematical inequalities and their applications.

• Journal of the Korean Statistical Society
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• v.19 no.1
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• pp.24-44
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• 1990

The purpose of this paper is to extend the idea of Tamhane and Bechhofer (1977, 1979) concerning the normal means problem to some general class of distributions. The key idea in Tamhane and Bechhofer is the derivation of the computable lower bounds on the probability of a correct selection. To derive such lower bounds, they used the specific covariance structure of a multivariate normal distribution. It is shown that such lower bounds can be obtained for a class of stochastically increasing distributions under certain conditions, which is sufficiently general so as to include the normal means problem as a special application. As an application of the general theory to the scale parameters problem, a two-stage elimination type procedure for selecting the population associated with the smallest variance from among several normal populations is proposed. The design constants are tabulated and the relative efficiencies are computed.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.1-10
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• 1999

When the component proportions in mixture experiments are restricted by lower and upper bounds multicollinearity appears all too frequently. The ridge regression can be used to stabilize the coefficient estimates in the fitted model. I propose a graphical method for evaluating the mixture component effects of ridge regression estimator with respect to the prediction variance and the prediction bias.