Generalized Weibull Distributions and parameter estimation

Although Weibull distribution is one of the most widely used distributions in reliability and survival analysis applications, it is not useful for modelling data that has non-monotonic hazard rates. For this reason, many modified and generalized forms of the Weibull distribution have been proposed in the literature in recent years. In this study, some statistical properties of Weibull distribution and Inverse Weibull, Log Weibull, Exponentiated Weibull, Weibull Geometric, Flexible Weibull, Odd Weibull,Marshall Olkin Extended Weibull and Gamma Weibull which are obtained by generalizing or modifying Weibull distribution has been mentioned and estimation of parameters has been obtained. For estimating unknown parameters of the considered distributions, maximum likelihood, least squares, weighted least squares and if it exists, moment estimators were used. In addition, performance of parameter estimators used for each distribution was evaluated by simulation studies for different sample sizes and parameter values and two different applications based on real data were performed.