• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.71-76
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• 1998

By assuming a general progressive Type-II censored sample, we propose the minimum risk estimator (MRE) of the location parameter and the scale parameter of the two-parameter exponential distribution. An example is given to illustrate the methods of estimation discussed in this paper.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1249-1258
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• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1141-1151
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• 2023

Let C_a,b[0, T] denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier-Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space C_a,b[0, T]. For our purpose, we use the exponential type functions on the general Wiener space C_a,b[0, T]. The class of all exponential type functions is a fundamental set in L₂(C_a,b[0, T]).

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.69-79
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• 1996

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.697-704
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• 2012

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The $AMLE_{II}$ is better than MLE and $AMLE_I$ in the sense of the MSE.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.577-594
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• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• Journal of The Korean Astronomical Society
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• v.15 no.1
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• pp.41-48
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• 1982

PDS was used to get the structure of two barred spiral galaxies NGC 1313 and NGC 1365. The result shows that NGC 1365 has both a deep spheroidal component and an exponential disk, but NGC 1313 has only an prominent exponential component. The luminosity profiles indicate that KGC 1313 is in type I and NGC 1365 belongs to type II. The length scales $({\alpha}^{-1})$ were derived from the exponential luminosity distributions as 1.64 kpc for NGC 1313 and 2.49kpc for KGC 1365.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.677-687
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• 2004

We consider the comparison of two one-parameter exponential distributions with the complete data as well as the type II censored data. We adapt Bayesian test procedure for nested hypothesis based on the Bayesian reference criterion. Specifically we derive the expression for the Bayesian reference criterion to solve our problem. Also we provide numerical examples using simulated data sets to illustrate our results.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1573-1582
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• 2015

In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators.We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.