• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.645-655
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• 2011

Chandrasekar et al. (2004) introduced a generalized Type-II hybrid censoring. In this paper, we propose generalized doubly Type-II hybrid censoring. In addition, this paper presents the statistical inference on the scale parameter for the half logistic distribution when samples are generalized doubly Type-II hybrid censoring. The approximate maximum likelihood(AMLE) method is developed to estimate the unknown parameter. The scale parameter is estimated by the AMLE method using two di erent Taylor series expansion types. We compar the AMLEs in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20; 30; 40 and various censored samples. The $AMLE_I$ is better than $AMLE_{II}$ in the sense of the MSE.

• Journal of Korean Society for Quality Management
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• v.38 no.4
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• pp.480-490
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• 2010

In this paper, two estimation methods(least square estimation and maximum likelihood estimation) were compared for Weibull distribution and Type I censoring. Data obtained by Monte Carlo simulation were analyzed using two estimation methods and analysis results were compared by MSE(Mean Squared Error). Comparison results show that maximum likelihood estimator is better for censored data and complete data with more than 30 samples and least square estimator is better for small size complete data(less than and equal to 20 samples).

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.115-123
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• 2012

In animal tumorigenicity data, tumor onsets occur at several sites and onset times cannot be exactly observed. Instead, the existence of tumors is examined only at death time or sacrifice time of the animal. Such an incomplete data structure makes it difficult to investigate the effect of treatment on tumor onset times; in addition, such dependence should be considered when censoring due to death is related with tumor onset. A bivariate frailty effect is incorporated to model bivariate tumor onsets and to connect death with tumor. For the inference of parameters, EM algorithm is applied and a real NTP(National Toxicology Program) dataset is analyzed as an illustrative example.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.529-538
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• 2014

In this paper, we consider maximum likelihood estimators of normal distribution based on type II censoring. Gupta (1952) and Cohen (1959, 1961) required a table for an auxiliary function to compute since they did not have an explicit form; however, we derive an explicit form for the estimators using a method to approximate the likelihood function. The derived estimators are a special case of Balakrishnan et al. (2003). We compare the estimators with the Gupta's linear estimators through simulation. Gupta's linear estimators are unbiased and easily calculated; subsequently, the proposed estimators have better performance for mean squared errors and variances, although they show bigger biases especially when the ratio of the complete data is small.

• Communications for Statistical Applications and Methods
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• v.16 no.6
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• pp.1055-1066
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• 2009

Many articles have considered a hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes. We introduce a double hybrid censoring scheme and derive some approximate maximum likelihood estimators(AMLEs) of the scale parameter for the half logistic distribution under the proposed double hybrid censored samples. The scale parameter is estimated by approximate maximum likelihood estimation method using two different Taylor series expansion types. We also obtain the maximum likelihood estimator(MLE) and the least square estimator(LSE) of the scale parameter under the proposed double hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error. The simulation procedure is repeated 10,000 times for the sample size n = 20(10)40 and various censored samples. The performances of the AMLEs and MLE are very similar in all aspects but the MLE and LSE have not a closed-form expression, some numerical method must be employed.

• 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.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.30 no.4
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• pp.411-421
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• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.32 no.1
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• pp.21-30
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• 2022

Objectives: The purpose of this study is to suggest an optimal method by comparing the analysis methods of work environment measurement datasets including left-censored data where one or more measurements are below the limit of detection (LOD). Methods: A computer program was used to generate left-censored datasets for various combinations of censoring rate (1% to 90%) and sample size (30 to 300). For the analysis of the censored data, the simple substitution method (LOD/2), β-substitution method, maximum likelihood estimation (MLE) method, Bayesian method, and regression on order statistics (ROS)were all compared. Each method was used to estimate four parameters of the log-normal distribution: (1) geometric mean (GM), (2) geometric standard deviation (GSD), (3) 95th percentile (X95), and (4) arithmetic mean (AM) for the censored dataset. The performance of each method was evaluated using relative bias and relative root mean squared error (rMSE). Results: In the case of the largest sample size (n=300), when the censoring rate was less than 40%, the relative bias and rMSE were small for all five methods. When the censoring rate was large (70%, 90%), the simple substitution method was inappropriate because the relative bias was the largest, regardless of the sample size. When the sample size was small and the censoring rate was large, the Bayesian method, the β-substitution method, and the MLE method showed the smallest relative bias. Conclusions: The accuracy and precision of all methods tended to increase as the sample size was larger and the censoring rate was smaller. The simple substitution method was inappropriate when the censoring rate was high, and the β-substitution method, MLE method, and Bayesian method can be widely applied.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.205-211
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• 2008

This paper deals with the estimations of kernel ridge regression when the responses are subject to randomly right censoring. The iterative reweighted least squares(IRWLS) procedure is employed to treat censored observations. The hyperparameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation(GCV) function. Experimental results are then presented which indicate the performance of the proposed procedure.