• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.565-574
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• 2011

The exponenetiated distribution has been used in reliability and survival analysis especially when the data is censored. In this paper, we derive Bayesian estimation of shape parameter and reliability function in the exponenetiated half triangle distribution based on Type-I hybrid censored data. Here we consider conjugate prior and noninformative prior and obtained corresponding posterior distributions. As an illustration, the mean square errors of the estimates are computed. Comparisons are made between these estimators using Monte Carlo simulation study.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.63-75
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• 2013

In this paper, we derive maximum likelihood estimators (MLEs) and approximate maximum likelihood estimators (AMLEs) of unknown parameters in a generalized half logistic distribution under Type-II hybrid censoring. We also obtain approximate confidence intervals using asymptotic variance and covariance matrices based on the MLEs and the AMLEs. As an illustration, we examine the validity of the proposed estimation using real data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE), bias, and length of the approximate confidence interval through a Monte Carlo simulation for various censoring schemes.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.12
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• pp.116-123
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• 1994

A modified Hybrid learning rule(MHLR) is proposed, which is derived from combining the Back Propagation algorithm that is known as an excellent classifier with modified Hebbian by changing the orginal Hebbian which is a good feature extractor. The network architecture of MHLR is multi-layered neural network. The weights of MHLR are calculated from sum of the weight of BP and the weight of modified Hebbian between input layer and higgen layer and from the weight of BP between gidden layer and output layer. To evaluate the performance, BP, MHLR and the proposed Hybrid learning rule (HLR) are simulated by Monte Carlo method. As the result, MHLR is the best in recognition rate and HLR is the second. In learning speed, HLR and MHLR are much the same, while BP is relatively slow.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.665-677
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• 2022

This paper proposes a new estimation method based on the maximum product of spacings for estimating unknown parameters of the three-parameter Weibull distribution under a generalized Type-II progressive hybrid censoring scheme which guarantees a constant number of observations and an appropriate experiment duration. The proposed approach is appropriate for a situation where the maximum likelihood estimation is invalid, especially, when the shape parameter is less than unity. Furthermore, it presents the enhanced performance in terms of the bias through the Monte Carlo simulation. In particular, the superiority of this approach is revealed even under the condition where the maximum likelihood estimation satisfies the classical asymptotic properties. Finally, to illustrate the practical application of the proposed approach, the real data analysis is conducted, and the superiority of the proposed method is demonstrated through a simple goodness-of-fit test.

• Wind and Structures
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• v.18 no.5
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• pp.549-566
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• 2014

In spite of progress in the numerical simulation of typhoon wind field in atmospheric boundary layer (ABL), using typhoon wind field model in conjunction with Monte Carlo simulation method can only accurately evaluate typhoon wind field over a general terrain. This method is not enough for a reliable evaluation of typhoon wind field over the actual complex terrain with surface roughness and topography variations. To predict typhoon wind field over the actual complex terrain in ABL, a hybrid numerical simulation method combined typhoon simulation used the typhoon wind field model proposed by Meng et al. (1995) and CFD simulation in which the Reynolds averaged Navier-Stokes (RANS) equations and k-${\varepsilon}$ turbulence model are used. Typhoon wind filed during typhoon Dujuan and Imbudo are simulated using the hybrid numerical simulation method, and compared with the results predicted by the typhoon wind field model and the wind field measurement data collected by Fugro Geotechnical Services (FGS) in Hong Kong at the bridge site from the field monitoring system of wind turbulence parameters (FMS-WTP) to validate the feasibility and accuracy of the hybrid numerical simulation method. The comparison demonstrates that the hybrid numerical simulation method gives more accurate prediction to typhoon wind speed and direction, because the effect of topography is taken into account in the hybrid numerical simulation method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.6
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• pp.144-150
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• 1996

The purpose of this paper is to develop a simulation program to predict resist prifile in electron-beam lithography, where the main issue is proximity effect. The simualtion program composes of monte-carlo simulation, exposure simulation and development simulation. In nonte-carlo simulation, the absorbed energy in the resist is calculated when one electron is incident into resist, using hybrid model on the basis of the rutherford differential scattering cross section and moller theory. In exposure simulation, the absorbed energy in the resist is calculated when electrons are incident in exposure pattern. In the program, the developed profile depending on time is obtained by string model. The 0.2$\mu$m and the 0.3$\mu$m line and space patterns are experimentally delineated and compared to the simulation results to check the relevance of the program.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.2
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• pp.131-137
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• 2016

In reliability analysis, it is quite common for the failure of any individual or item to be attributable to more than one cause. Moreover, observed data are often censored. Recently, progressive hybrid censoring schemes have become quite popular in life-testing problems and reliability analysis. However, a limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time T. Therefore, generalized progressive hybrid censoring schemes have been introduced. In this article, we derive the likelihood inference of the unknown parameters under the assumptions that the lifetime distributions of different causes are independent and exponentially distributed. We obtain the maximum likelihood estimators of the unknown parameters in exact forms. Asymptotic confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods are compared using Monte Carlo simulations. One real data set is analyzed for illustrative purposes.