Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

Estimation of the unknown parameters of a specific population or distribution is an important issue in statistics. These parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. Different methods of estimation have been used to estimate these parameters and each method has some advantages and disadvantages. In this thesis we compare several estimation methods for the estimation of the parameters of Marshall and Olkin Extended Burr XII distribution. Namely, we have used five different estimation techniques.The methods are the maximum likelihood method, the least square method, the weighted least square method, the maximum product of spacing method and the percentiles method. Numerical study is carried out to compare the different methods and to assess the performance of the estimators through their coefficient mean, biases and root mean square errors (RMSE).The study indicated that the maximum likelihood method followed by the maximum product of spacing method dominate all other methods of estimation used in this study. Likewise it has been noticed that, least square and weighted least square techniques are both a long with percentile technique give vast root mean square errors (RMSE) regardless of the initial values of the distribution parameter

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