• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.447-463
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• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.845-852
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• 2010

A nonlinear algebraic equation f(x) = 0 is considered to find a root with integer multiplicity $m{\geq}1$. A variant of Newton-secant method for a multiple root is proposed below: for n = 0, 1, $2{\cdots}$ $$x_{n+1}=x_n-\frac{f(x_n)^2}{f^{\prime}(x_n)\{f(x_n)-{\lambda}f(x_n-\frac{f(x_n)}{f^{\prime}(x_n)})\}$$, $$\lambda=\{_{1,\;if\;m=1.}^{(\frac{m}{m-1})^{m-1},\;if\;m{\geq}2$$ It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numerical examples successfully verified the proposed scheme with high-precision Mathematica programming.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1081-1096
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• 2011

In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).

• Journal of Applied Reliability
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• v.18 no.1
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• pp.80-86
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• 2018

Purpose: This article provides a mathematical model for the accelerated degradation test when the performance degradation characteristic follows the lognormal distribution. Method: For developing test plans, the total number of test units and the test time are determined based on the minimization of the asymptotic variance of the q-th quantile of the lifetime distribution at the use condition. Results: The mathematical model for the accelerated degradation test is provided. Conclusion: Accelerated degradation test method is widely used to evaluate the product lifetime within a resonable amount of cost and time. In this article. a mathematical model for the accelerated degradation test method is newly developed for this purposes.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.2
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• pp.1-7
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• 1992

The computational methods of extreme sea level are developed in this study. Based on type III asymptotic distribution, non-linear multiple regression method, skewness method and maximum likelihood method are used to evaluate the parameters of the distribution. The difference between real data and evaluated distribution function is fitted to get more desirable accuracy by employing polynominals. The numerical examples are given in the last section in order to illustrate the application of the present scheme.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.89-99
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• 2006

A new classes of life distribution, namely harmonic used better than aged in expectation in upper tail (HUBAEUT) is introduced. Testing exponentiality against this class is investigated using kernel method. The limiting null and nonnull distribution of the test statistics is normal and the null variance is calculated exactly. Selected critical values are tabulated for sample sizes of 5(1)40. Power of the test are estimated by simulation. the efficacies of the test statistics used for testing against HUBAEUT are calculated for som common alternatives and are compared to some other procedures. It is shown that proposed test is simple, has high relative efficiency and power for some commonly used alternatives. The set of real data are used as an examples to elucidate the use of the proposed test statistics for practical reliability.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.419-428
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• 2006

The method of Reverse Ranked Ordering-Set Sampling(RROSS) as an opposed Ranked Ordering-Set Sampling(ROSS) and Ranked-Set Sampling(RSS) is discussed. We propose the test statistic using sign test on RROSS. This method is effective when observations are expensive and measurement is perhaps destructive or invasive. This method obtains more informations than ROSS and RSS. The asymptotic relative efficiencies of RROSS with respect to ROSS and RSS are always greater than 1 for all sample sizes. We consider a simple model to describe the effect of imperfect judgment errors.

• Journal of applied mathematics & informatics
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• v.41 no.6
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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.