• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1811-1822
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• 2018

In this paper, we exhibit the explicit forms of continued fraction expansions of a family of algebraic power series over a finite field and we study their asymptotic distribution of approximation exponents.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.103-115
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• 2007

In this paper we studied the small sample asymptotic inference for the autoregressive coefficient in AR(1) model. Based on saddlepoint approximations to the distribution of quadratic forms, we suggest a new approximation to the distribution of the estimators of the noncircular autoregressive coefficients. Simulation results show that the suggested methods are very accurate even in the small sample sizes and extreme tail area.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.15-28
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• 2018

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.22-32
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• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.29-36
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• 1999

We propose a new method of asymptotic inference on the odds ratio (or cross-product ratio) in $2{\times}2$ contingency table. Saddlepoint approximations to the conditional tail probability we used in this procedure. We assess the accuracy of the suggested method by comparing with the exact one. To obtain the exact values, we need very complicated calculations containing the cumulative probabilities of non-central hypergeometric distribution. The suggested method in this paper is very accurate even for small or moderate sample sizes as well as simple and easy to use. Example with a real data is also considered.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.27-43
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• 2004

Let he(x) and $h_{o}(x)$ denote the limits of the sequences $\{^{2n}x\}\;and\;\{^{2n+1}x\}$, respectively. Asymptotic formulas for the functions E\$h_e\;and\;h_o$ at the points $e^{-e}$ and 0 are established.