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

The modeling of lifetime data has become popular in the area of reliability and survival analysis. In recent years, many distributions have been introduced to model these types of data. Since 1958, many modifications of the Weibull distribution have been proposed to achieve a better fit for several lifetime data. On the other hand, the number of parameters has increased, the forms of the cumulative distribution, survival and hazard functions have become more complicated and the estimation problems have been risen. In this thesis a new four-parameter lifetime distribution that is a modification of the Weibull distribution is proposed. This new distribution can serve as an important reference for lifetime data analysis and encourage further modifications of the Weibull distribution. This modification is the exponentiated version of the power generalized Weibull distribution. Estimation of the four-parameters is made using maximum likelihood estimation method based on simple random samples and ranked set samples

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