• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.787-793
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• 2006

Recently kriging model has been widely used in the DACE (Design and Analysis of Computer Experiment) because of prominent predictability of nonlinear response. Since DACE has no random or measurement errors contrast to physical experiment, space filling experimental design that distributes uniformly design points over whole design space should be employed as a sampling method. In this paper, we examine the maximum entropy experimental design that reveals the space filling strategy in which defines the maximum entropy based on Gaussian or exponential. The influence of these two correlation functions on space filling design and their model parameters are investigated. Based on the exploration of numerous numerical tests, enhanced maximum entropy design based on exponential correlation function is suggested.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2007.05a
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• pp.103-108
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• 2007

다항지수 신뢰도 함수(multinomial-exponential reliability function ; MERF) 는 소프트웨어의 고장/수정 공정을 세밀하게 수행하는 중에 개발되는 관계에 있다. 후에 MERF는 좀더 매우 단순화한 지수 신뢰도 함수(exponential reliability function ; EARF)로 근사화되는 공정을 거치게 된다. 이는 MERF의 특성을 대부분 가지고 있어서 두 개의 함수가 하나의 신뢰도 함수로 단일화되도록 한다. 신뢰도 모델 MERF/EARF는 소프트웨어 고장 공정을 NHPP로, 수정공정을 다항분포로 고려한다. 이 모텔은 두 개의 공정 모두가 통계적 독립인 것으로 간주한다. 본 논문에서는 모델의 이론적인 기준, 수학적 특성, 소프트웨어 신뢰도에의 응용을 검토한다. 이는 물리적 인 시스템을 검사하고 유지보수하는 선도적인 모델응용이다. 본 논문에는 소프트웨어 신뢰도 분석에 응용하는 하나의 수치 예를 포함한다.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.537-547
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• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• International Journal of Advanced Culture Technology
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• v.7 no.4
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• pp.268-273
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• 2019

The apparent soil resistivity is used for estimating multilayer soil parameters, such as, layer's depth and soil resistivity. The soil parameters are estimated by continuously revising those parameters until the error between the measured and calculated apparent soil resistivity reaches to allowable level. The equation for calculating the apparent soil resistivity is complicated and time consumed, because it is composed of an infinite integral which includes a zero order Bessel's function of the first kind. In this paper, a fast algorithm for calculating the apparent soil resistivity of horizontal multilayer earth structure is proposed using exponential sampling method.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.1
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• pp.49-66
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• 2022

The G-Euler process has been proposed to overcome the difficulties of the calculation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko's graphs are reliable.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.467-475
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• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.371-383
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• 2000

Lindsay (1994) and Basu et al (1997) show that another density-based distance called the negative exponential disparity (NED) is an excellent competitor to the Hellinger distance (HD) in generating an asymptotically fully efficient and robust estimator. Bhattacharya and Basu (1996) consider estimation of the locations of several normal populations when an order relation between them is known to be true. They empirically show that the robust HD based weighted likelihood estimators compare favorably with the M-estimators based on Huber's $\psi$ function, the Gastworth estimator, and the trimmed mean estimator. In this paper we investigate the performance of the weighted likelihood estimator based on the NED as a robust alternative relative to that based on the HD. The NED based estimator is found to be quite competitive in the settings considered by Bhattacharya and Basu.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.775-795
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• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.