• 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.19 no.4
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• pp.1335-1344
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• 2008

The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.