• 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).

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.633-641
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• 2014

The exponential distibution is one of the most popular distributions in analyzing the lifetime data. In this paper, we propose multiply Type I hybrid censoring. And this paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply Type I hybrid censoring. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator (MLE) of the scale parameter ${\sigma}$ under the proposed multiply Type I hybrid censored samples. We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The $AMLE_{II}$ is better than $AMLE_I$ in the sense of the RMSE.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1581-1589
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• 2014

In this paper, we consider maximum likelihood estimators of the location and scale parameters for the half-logistic distribution when samples are multiply Type I hybrid censored. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($\hat{\sigma}_I$, $\hat{\sigma}_{II}$). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The approximate MLE of the second type is better than that of the first type in the sense of the RMSE. Further an illustrative example with the real data is presented.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.697-704
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• 2012

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The $AMLE_{II}$ is better than MLE and $AMLE_I$ in the sense of the MSE.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.57-64
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• 2000

By assuming a Type-I censored sample, we propose the approximate maximum likelihood estimators(AMLE) of the scale and location parameters of the gamma distribution. We compare the proposed estimators with the maximum likelihood estimators(MLE) in the sense of the mean squared errors(MSE) through Monte Carlo method.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.961-969
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• 2009

A hybrid censoring is a mixture of Type-I and Type-II censoring schemes. This paper deals with estimation based on Type-I hybrid censored samples from the half triangle distribution. We derive some estimators of the scale parameter of the half triangle distribution based on Type-I hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.289-302
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• 1993

A goodness-of-fit test for the two-parameter exponential distribution, for use with the singly Type I and Type II right censored samples, is proposed. The test statistic is based on the $L_1$-norm of discrepancy between the cumulative distribution function and the empirical distribution function. To deal with the unknown parameters problem, the K- transformation is considered and modified to be applied to the censored samples. Rosenblatt's transformation is extended to the cases of Type I and Type II censored samples, in order to transform the censored samples into the complete ones. The critial values of the test statistic are obtained by Monte Carlo simulations for some finite sample sizes. The power studies are conducted to compare the proposed test with the Pettitt(1977) test for exponentiality with censored samples. It appears that the proposed test has relatively good power properties for moderate and large sample sizes.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.927-934
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• 2010

In this paper, we introduce a method of parameter estimation of progressive Type I interval censored sample and progressive type II censored sample. We propose a new parameter estimation method, that is converting the data which obtained by progressive type I interval censored, those data be used to estimate of the parameter in progressive type II censored sample. We used exponential distribution with unknown scale parameter, the maximum likelihood estimator of the parameter calculates from the two methods. A simulation is conducted to compare two kinds of methods, it is found that the proposed method obtains a better estimate than progressive Type I interval censoring method in terms of mean square error.

• 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.

• 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.