• Journal of Korean Society for Quality Management
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• v.13 no.1
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• pp.31-40
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• 1985

In this paper, statistical estimation of the parameters of the bivariate exponential distribution are studied. Bayes estimators of the parameters are obtained and compared with the maximum likelihood estimators which are introduced by Freund. We know that the method of moments estimators coincide with the maximum likelihood estimators and Bayes estimators are more efficient than the maximum likelihood estimators in moderate samples. The asymptotic distributions of the maximum likelihood estimators and the estimator of mean time to system failure are obtained.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.239-250
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• 2004

We shall propose maximum likelihood, Bayesian and generalized maximum likelihood estimation for the reliability of the two-unit hot standby system with Rayleigh lifetime distribution that switch is perfect. Each estimation will be compared numerically in terms of various mission times, parameter values and asymptotic relative efficiency through Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.261-269
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• 2015

Nowadays the application of change point analysis has been indispensable in a wide range of areas such as quality control, finance, environmetrics, medicine, geographics, and engineering. Identification of times where process changes would help minimize the consequences that might happen afterwards. The main objective of this paper is to compare the change-point detection capabilities of Bayesian estimate and maximum likelihood estimate. We applied Bayesian and maximum likelihood techniques to formulate change points having a step change and multiple number of change points in a Poisson rate. After a signal from c-chart and Poisson cumulative sum control charts have been detected, Monte Carlo simulation has been applied to investigate the performance of Bayesian and maximum likelihood estimation. Change point detection capacities of Bayesian and maximum likelihood estimation techniques have been investigated through simulation. It has been found that the Bayesian estimates outperforms standard control charts well specially when there exists a small to medium size of step change. Moreover, it performs convincingly well in comparison with the maximum like-lihood estimator and remains good choice specially in confidence interval statistical inference.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.647-658
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• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• 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.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.269-276
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• 2000

there are several methods available for estimating parameters in overdispersed binary response data with the litter effect. Simulations are performed to compare methods for estimating an overall mean and an overdispersion parameter using moments a maximum likelihood under a beta-binomial distribution a maximum quasi-likelihood and a maximum extended quasi-likelihood.

• 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.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.97-108
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• 2020

This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

• The Journal of the Acoustical Society of Korea
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• v.19 no.8
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• pp.47-53
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• 2000

In order to classify the underwater vehicles due to propeller propulsion, maximum likelihood classifier was developed. Propeller produces the cavitation and noise during its work. Cavitation-bubble makes the nonlinear medium in the water. The nonlinearity of cavitation leads to the generation of a complete spectrum of combination harmonics of the tonals of noise, and modulation of cavitation noise with propeller shaft-rates and blade-rates. The optimal estimator was derived mathematically and its capabilities were proven by simulation and real test.