• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.

• International Journal of Reliability and Applications
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• v.15 no.2
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• pp.111-123
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• 2014

A new class of bivariate distributions is derived by specifying its conditionals as the exponential and gamma distributions. Some properties and relations with other distributions of the new class are studied. In particular, the estimation of parameters is considered by the methods of maximum likelihood and pseudolikelihood of a special case of the new class. An application using a real bivariate data is given for illustrating the flexibility of the new class in this context, and, also, for comparing the estimation results obtained by the maximum likelihood and pseudolikelihood methods.

• International Journal of Reliability and Applications
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• v.15 no.1
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• pp.65-76
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• 2014

In this article, a new model based on Lomax distribution is introduced. This new model is both useful and practical in areas such as economic, reliability and life testing. Some statistical properties of this model are presented including moments, hazard rate, reversed hazard rate, mean residual life and mean inactivity time functions, among others. It is also shown that the distributions of the new model are ordered with respect to the strongest likelihood ratio ordering. The method of moment and maximum likelihood estimation are used to estimates the unknown parameters. Simulation is utilized to calculate the unknown shape parameter and to study its properties. Finally, to illustrate the concepts, the appropriateness of the new model for real data sets are included.

• 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.16 no.3
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• pp.479-485
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• 2009

When a part of data is unobserved the marginal likelihood of parameters given the observed data often involves analytically intractable high dimensional integral and hence it is hard to find the maximum likelihood estimate of the parameters. Simulated maximum likelihood(SML) method which estimates the marginal likelihood via Monte Carlo importance sampling and optimize the estimated marginal likelihood has been used in many applications. A key issue in SML is to find a good proposal density from which Monte Carlo samples are generated. The optimal proposal density is the conditional density of the unobserved data given the parameters and the observed data, and attempts have been given to find a good approximation to the optimal proposal density. Algorithms which adaptively improve the proposal density have been widely used due to its simplicity and efficiency. In this paper, we describe a fully adaptive algorithm which has been used by some practitioners but has not been well recognized in statistical literature, and evaluate its estimation performance and robustness via a simulation study. The simulation study shows a great improvement in the order of magnitudes in the mean squared error, compared to non-adaptive or partially adaptive SML methods. Also, it is shown that the fully adaptive SML is robust in a sense that it is insensitive to the starting points in the optimization routine.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.529-544
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• 1996

This paper deals with the problem of estimating the autoregressive random coefficient of a first-order random coefficient autoregressive time series model applied to panel data of time series. The autoregressive random coefficients across individual units are assumed to be a random sample from a truncated normal distribution with the space (-1, 1) for stationarity. The estimates of random coefficients are obtained by an empirical Bayes procedure using the estimates of model parameters. Also, a Monte Carlo study is conducted to support the estimation procedure proposed in this paper. Finally, we apply our results to the economic panel data in Liu and Tiao(1980).

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.12
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• pp.971-982
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• 1989

An integrating position estimation algorithm has been developed for the navigation system of a free-ranging AGV system. The navigation system focused in this research work consists of redundant wheel encoders for the relative position measurement and a vision sensor for the absolute position measurement. A maximum likelihood method and an extended Kalman filter are implemented for enhancing the performance of the position estimator. The maximum likelihood estimator processes noisy, redundant wheel encoder measurements and yields efficient estimates for the AGV motion between each sampling interval. The extended Kalman filter fuses inharmonious positional data from the deadreckoner and the vision sensor and computes the optimal position estimate. The simulation results show that the proposed position estimator solves a generalized estimation problem for locating the vehicle accurately in space.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1271-1277
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• 2012

In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

• IE interfaces
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• v.21 no.2
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• pp.151-160
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• 2008

Defect size distribution is a probability density function for the defects that occur on wafers or glasses during semiconductor/LCD fabrication. It is one of the most important information to estimate manufacturing yield using well-known statistical estimation methods. The defects are detected by automatic optical inspection (AOI) facilities. However, the data that is provided from AOI is not accurate due to resolution of AOI and its defect detection mechanism. It causes distortion of defect size distribution and results in wrong estimation of the manufacturing yield. In this paper, I suggest a size conversion method and a maximum likelihood estimator to overcome the vague defect size information of AOI. The methods are verified by the Monte Carlo simulation that is constructed as similar as real situation.

• Journal of Applied Reliability
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• v.1 no.1
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• pp.47-54
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• 2001

This paper considers the parameter estimation problem of the failure intensity function and maintenance effect in a repairable system. We propose estimation procedures for repairable systems on which preventive maintenance is performed. The failure process is modeled by a proportional age reduction model [Brown, Mahoney and Sivazlian(1983)] which is useful to model the imperfect effect of preventive maintenance. When failure and maintenance (preventive) times are given, the maximum likelihood method is used to estimate the maintenance effect and the parameters of intensity function, simultaneously We obtain the maximum likelihood estimators using a genetic algorithm. A numerical example is also presented.