On the weibull-G family of distributions / Rasha Saber Elshaarawy Elbagoury ; Supervised Mohamed A. H.Sabry , Hiba Zeyada Muhammed

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

Fitting distributions to data is the procedure of selecting a statistical distribution that best fits that data set generated by some random process. There are lots of probability distributions that can fit your data but the question is {u2018}how good can the distribution fits the data?{u2019}. To answer this question, several authors have proposed new probability distributions. Either by adding a new parameter to make the new distribution more flexible to catch as much as possible information from the data or by mixing two or more distributions together with some criteria and weights or generating new families of distributions using the concept of composite functions. In this thesis, we display the importance of generating families from numerous classical distributions in lifetime data analysis. We emphasize our work on the Weibull-G family of distributions and study its properties. As a special case, we study the three-parameter continuous model called the Weibull exponential (WE) distribution which can be seen as an extension of the Weibull distribution and discuss some of its interesting structural properties. The model parameters are estimated by the maximum likelihood estimation (MLE) method under both simple random sampling (SRS) and ranked set sampling (RSS) schemes. Simulation study is conducted to assess the performance of the model under different parameters values. One application of the new model to real data shows that it can be more reliable distribution tin modeling lifetime data than existing important lifetime models. Also, estimation of the model parameter under the RSS scheme provides more efficient estimators than those estimated under the SRS scheme

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