• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.147-161
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• 2016

This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

• International Journal of Reliability and Applications
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• v.14 no.1
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• pp.27-39
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• 2013

In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.247-260
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• 1997

The quasi-likelihood models which greatly widened the scope of generalized linear models are widely used in data analysis where a likelihood is not available. Since a quasi-likelihood may not appear to be an ordinary likelihood for any known distribution in the natural exponential family, to fit the quasi-likelihood models the standard statistical packages such as GLIM, GENSTAT, S-PLUS and so on may not directly applied. SAS/IML is very useful for fitting of such models. In this paper, we present simple SAS/IML(version 6.11) program which helps to fit and analyze the quasi-likelihood models applied to the leaf-blotch data introduced by Wedderburn(1974), and the problem with deviance useful generally to model checking is pointed out, and then its solution method is mention through the data analysis based on this quasi-likelihood models checking.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.9-16
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• 2000

This article addresses the problem of maximum likelihood estimation in ARCH regression with lagged dependent variables. Some topics in asymptotics of the model such as uniform expansion of likelihood function and construction of a class of MLE are discussed, and the regularity property of MLE is obtained. The error process here is possibly non-Gaussian.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.559-570
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• 1998

This paper introduces doubly Winsorized Poisson auto-model by truncating the support of a Poisson random variable both from above and below, and shows that this model has a same form of negpotential function as regular Poisson auto-model and one-way Winsorized Poisson auto-model. Strategies for maximum likelihood estimation of parameters are discussed. In addition to exact maximum likelihood estimation, Monte Carlo maximum likelihood estimation may be applied to this model.

• Journal of the Korean Statistical Society
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• v.9 no.1
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• pp.13-29
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• 1980

The statistical theory of factor analysis is briefly reviewed with emphasis on the maximum-likelihood method. A modified version of Joreskog(1975) is used for the implementation of the maximum-likelihood method. For the minimization of the conditional minimum function, an adaptive Newton-Raphson method is applied.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.393-399
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• 1993

When we compute the maximum likelihood estimators of the parameters for the logistic regression models, which are useful in studying the relationship between the binary response variable and the explanatory variable, the standard error calculations are usually based on the second derivative of log-likelihood function. On the other hand, an estimator of the Fisher information motivated from the fact that the expectation of the cross-product of the first derivative of the log-likelihood function gives the Fisher information is expected to have similar asymptotic properties. These estimators of Fisher information are closely related with the iterative algorithm to get the maximum likelihood estimator. The average numbers of iterations to achieve the maximum likelihood estimator are compared to find out which method is more efficient, and the estimators of the variance from each method are compared as estimators of the asymptotic variance.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.613-618
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• 2011

The proposed method is based on a penalized log partial likelihood of Cox proportional hazard model with L1-penalty. We use the iteratively reweighted least squares procedure to solve L1 penalized log partial likelihood function of Cox proportional hazard model. It provide the ecient computation including variable selection and leads to the generalized cross validation function for the model selection. Experimental results are then presented to indicate the performance of the proposed procedure.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.767-772
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• 2007

A kernel machine is proposed as an estimating procedure for the linear and nonlinear Poisson regression, which is based on the penalized negative log-likelihood. The proposed kernel machine provides the estimate of the mean function of the response variable, where the canonical parameter is related to the input vector in a nonlinear form. The generalized cross validation(GCV) function of MSE-type is introduced to determine hyperparameters which affect the performance of the machine. Experimental results are then presented which indicate the performance of the proposed machine.