On Maximum Likelihood Estimators of the Parameters of Three-Parameters Weibull Distribution Using Different Ranked Set Sampling Schemes

Abstract

Al-Saleh and Al-Kadiri first proposed double rank set sampling (DRSS). It seems that this ranked set sampling (RSS) modification can reduce the loss of RSS efficiency caused by ranking errors, and it is more effective than RSS and simple random sampling (SRS) to estimate the population mean. The proposed likelihood function is used to estimate the parameters of the three-Parameters Weibull distribution. Based on double ranked set sampling, extreme ranked set sampling, ranked set sampling (RSS) and simple random sampling (SRS) designs, the maximum likelihood estimator (MLE) is compared with the corresponding likelihood estimator. A simulation was carried out and the absolute relative biases, mean square error (MSE) and relative efficiency of different schemes were compared. It is found that, MSEs based SRS data has the largest MSEs comparing to RSS and its modifications schemes. This study revealed that DRSS technique has the superior over the rest of other sampling schemes. In almost all cases, DRSS has the smallest MSEs and largest efficiencies.