Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

The Weibull distribution is used widely to analyze the life testing data, but it cannot be used at all if the data indicate a non-monotone and uni-modal hazard function. Keller and Kamath (1982) introduced the inverse Weibull (IW) distribution with to parameters n and Ý to solve the Weibull distribution problem. The IW distribution is one of the famous distributions in analyzing the data from the reliability engineering and life testing experiment, it has been used to model, many real life applications for example degradation of mechanical components such as pistons and crankshafts of diesel engines.Recently, Mahdavi and Kundu (2017) introduced a new class of distributions by adding a new parameter to obtain a family of distributions this family is called the alpha power transformation (APT). Basheer (2019) had been used the method of the APT that proposed by Mahdavi and Kundu (2017) to introduce a new generalized alpha power inverse Weibull distribution. The alpha power inverse Weibull (APIW)distribution is more flexible over the IW distribution and it can be used to describe the data from the lifetime experiments, clinical trial and reliability engineering. In this thesis, we have studied the properties of the IW and APIW distributions, and then we have studied the problem of estimation for the unknown parameters for both distributions under random censoring data by using Bayesian and non Bayesian estimation methods. We computed the maximum likelihood estimates and Bayes estimates, for Bayes estimates we used the Markov Chain Monte Carlo (MCMC) techniques and we used the metropolis hasting algorithm, where it used when we can not directly sample from the conditional posterior distribution which we can not write an analytical expression for the posterior distribution

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