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Parametric and semi -parametric survival models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This book uses for comparing the efficiency of the two survival regression models: Semi parametric (Cox PH) and different parametric survival models (AFT) with the application to time - to- menarche data. Different statistical methods have been utilized so as to compare the Cox Proportional Hazard versus Accelerated Failure Time Models as well as comparing efficiency of models with in parametric survival models. The book devotes several pages to deal with general and mathematical theories about the two modeling techniques- semi- parametric and parametric models If you do start to read this book, you will get sophisticated methods for comparing the goodness of fit of the two different modeling techniques.