• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.69-81
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• 1990

In this paper we investigate the problem of exponential asymptotic stability (EAS) in perturbed nonlinear systems of the differential system x' = f(t, x). Also, a simple method for constructing Liapunov functions is used to prove a kind of Massera type converse theorem.

• Journal of the Korea Safety Management & Science
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• v.3 no.4
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• pp.91-101
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• 2001

This paper is to develop replacement models under minimal repair with exponential polynomial wavelet failure rate function. Wavelets have good time-frequency localization, fast algorithms and parsimonious representation. Also this study is presented along with numerical examples using sensitivity analysis for exponential polynomial trigonometric failure rate function.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.77-84
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• 1995

Many authors have utilized an exponential distribution because of its wide applicability in reliability engineering and statistical inferences (see Bain & Engelhart(1987) and Saunders & Mann(1985)). Here we are considering the parametric estimation in an exponential distribution when its scale and location parametes are linear functions of a known exposure level t, which often occurs in the engineering and physical phenomena.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.603-613
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• 2005

We propose some estimators of the location parameter and derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter in the exponential distribution based on multiply Type-II censored samples. We calculate the moments for the proposed estimators of the location parameter, and the AMLEs which are the linear functions of the order statistics. We compare the proposed estimators in the sense of the mean squared error (MSE) for various censored samples.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.661-668
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• 1999

Reliability estimation using Gibbs sampler considered for modeling mixture exponential reliability problems. Gibbs sampler is developed to compute the features of the posterior distribution. Bayesian estimation of complicated functions requires simpler esti-mation techniques due to the mathematical difficulties involved in the Bayes approach. The Maximum likelihood estimator and the Gibbs estimator of reliability of the system are derived. By simula-tion risk behaviors of derived estimators are compared. model de-termination based on relative error is considered. A numerical study with a simulated data set is provided.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.507-514
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• 2007

We shall propose several estimators for the scale parameter in the Pareto distribution with an unidentified exponential outlier when the scale parameter is functions of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically efficiencies for proposed estimators of the scale and shape parameters in the small sample sizes.

• 한국데이터정보과학회:학술대회논문집
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• 2004.04a
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• pp.203-210
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• 2004

When the available sample is multiply Type-II censored, the maximum likelihood estimators of the location and the scale parameters of two- parameter exponential distribution do not admit explicitly. In this case, we propose some estimators which are linear functions of the order statistics and also propose some estimators by approximating the likelihood equations appropriately. We compare the proposed estimators by the mean squared errors.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.295-305
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• 2008

This paper demonstrates how composite-exponential-fitting interpolation rules can be constructed to fit an oscillatory function using not only pointwise values of that function but also of that functions's derivative on a closed and bounded interval of interest. This is done in the framework of exponential-fitting techniques. These rules extend the classical composite cubic Hermite interpolating polynomials in the sense that they become the classical composite polynomials as a parameter tends to zero. Some examples are provided to compare the newly constructed rules with the classical composite cubic Hermite interpolating polynomials (or recently developed interpolation rules).

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.141-145
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• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.873-887
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• 2007

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.