# Estimation of the exponential distribution based on multiply Type I hybrid censored sample

• Lee, Kyeongjun (Department of Statistics, Pusan National University) ;
• Sun, Hokeun (Department of Statistics, Pusan National University) ;
• Cho, Youngseuk (Department of Statistics, Pusan National University)
• Accepted : 2014.04.12
• Published : 2014.05.31
• 71 14

#### Abstract

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.

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