Estimation and Some Statistical Properties of the hybrid Weibull Inverse Burr Type X Distribution with Application to Cancer Patient Data

In this paper, the Burr type X distribution is represented as a mixture with the hybrid Weibull family, called hybrid hybrid Hybrid Weibull Inverse Burr Type X (HWIBX) distribution in order to justify its usefulness in modeling statistical regularities in extreme values recorded in non-stationary streams of media events, the basic new distribution functions are presented in addition to several statistical and mathematical properties of the hybrid distribution as well as estimating the model parameters by three methods, namely maximum likelihood, least squares, and weighted least squares with Conduct Monte Carlo simulations for the three methods. Finally, these results are illustrated through an example of matching the hybrid distribution with data representing the values Bladder cancer and survival times (given in years) of a group comprising 46 patients treated with chemotherapy alone and knowing the results of the improvement of this expansion through comparison with some other distributions using some Statistical metrics.