English abstract
n this project, the maximum likelihood estimators (MLES) of the three parameters a, i and y of the Exponentiated Weibull distribution (EWD) will be considered using Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). Also, the method of moments and method of percentiles of these parameters will be considered under SRS. The above estimators will be compared via their bias and mean square error (MSE). Also, the asymptotic distribution of the MLEs ofa, 2 and y will be derived and then used to construct asymptotic confidence intervals (Cls) of the respective parameters. Then these Cls will be compared via their expected lengths and their coverage probabilities. In addition, the Bayes estimators of the three parameters will be considered using independent non-informative type of priors and the linex loss function (LEF) and square error loss (SEL) functions. Since these estimators can not be found in simple closed forms, numerical methods will be used to compare them. ords: Bayes estimation, Exponentiated Weibull distribution, Linex loss function, Maximum likelihood estimation, Method of moments estimation, Method of percentile estimation, Ranked set sample, Simple random sample, Square error loss.
