• 대한수학회보
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• 제59권4호
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• pp.979-991
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• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• 대한산업공학회지
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• 제33권4호
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• pp.410-418
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• 2007

This article suggests the methods to investigate adverse movement across global stock markets arising from insolvency of subprime mortgage in U.S. Our application deals with asymptotic tail dependence of daily stock index returns (KOSPI, DJIA, Shanghai Composite) of three countries; Korea, U.S., and China, over specific period via extreme value theory and copula functions. Daily stock index returns among three countries show higher extremal dependence during the period exposed to systematic shock. We confirm that extreme value theory and copula functions have potential to well describe the extreme dependence between three countries' daily stock index returns.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• 대한교통학회지
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• 제17권2호
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• pp.193-198
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• 1999

통행시간가치는 교통계획 및 교통투자정책 평가에 있어서 매우 중요한 의미를 갖는다. 특히 교통시설투자와 관련된 타당성분석에서 통행시간가치는 해당사업의 경제적 타당성을 판단함에 있어 결정적인 영향을 미치게 된다. 지금까지 교통시설투자와 관련된 많은 타당성조사사업에서 시간절약 편익산정 결과에 대한 신뢰성문제가 빈번하게 제기되어 왔고, 심지어는 시간절약편익을 편익항목에서 제외하여야 할 것이라는 극단적인 주장도 있었다. 'IMF시대'로 이야기되는 최근의 경제상황을 고려할 때 투자사업평가에 대한 분석결과의 정확성에 대한 사회적 및 행정적 요구는 더욱 커질 것이며, 따라서 시간절약편익에 대한 신뢰성의 문제는 앞으로 더욱 강조될 것으로 예상된다. 본고에서는 통행시간과 통행비용의 비율에 대한 점근분포함수를 추정하고 이를 통하여 통행시간가치의 신뢰구간을 추정하는 방법을 제시하였다. 점근분포함수를 이용한 AD법은 파라메타의 신뢰구역을 이용한 기존의 CR법에 비하여 통계이론적 기초가 탄탄하며, 또한 사례연구의 결과를 통해서 볼 때 CR법에 비하여 그 분석결과가 더 정교한 것으로 분석되었다. 그러나 AD법은 선택모형을 정산하기 위하여 사용되는 표본자료의 수가 많아야 한다 한계를 갖으며, 따라서, 모형정산을 위한 표본자료의 수가 충분하지 못한 경우에 있어서는 CR법이 사용되어야 할 것이다. AD법을 이용하여 분석된 서울시 출근통행자 시간가치의 95%신뢰구간은 7341.25${\pm}$1945.05(원/시간)로 추정되었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• 태양에너지
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• 제8권1호
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• pp.82-94
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• 1988

The hydrodynamic stability equations for natural convection flows adjacent to a vertical isothermal surface in cold or warm water (Boussinesq or non-Boussinesq situation for density relation), constitute a two-point-boundary-value (eigenvalue) problem, which was solved numerically using the simple shooting and the orthogonal collocation method. This is the first instance in which these stability equations have been solved using a computer code COLSYS, that is based on the orthogonal collocation method, designed to solve accurately two-point-boundary-value problem. Use of the orthogonal collocation method significantly reduces the error propagation which occurs in solving the initial value problem and avoids the inaccuracy of superposition of asymptotic solutions using the conventional technique of simple shooting.

• 대한수학회지
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• 제39권2호
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• 품질경영학회지
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• 제23권1호
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• pp.29-40
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• 1995

This paper considers the problem of optimally designing accelerated degradation tests in which the performance value of a specimen is measured only at one of three test conditions for a given exposure time. For the product having lognormally distributed performance, the optimum plan-low stress level and sample proportion allocated to each test condition - is obtained, which minimize the asymptotic variance of maximum likelihood estimator of a stated quantile at design stress. An illustrative example for the optimum plan is given.