The Generalization Inverse Weibull Distribution Related to X-Gamma Generator Family: Simulation and Application for Breast Cancer

Abstract

The aim of this paper is to propose the new three-parameter X-Gamma inverse Weibull (XGAIW) distribution which generalizes the inverse Weibull model. The density function of the XGAIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities (reliability and hazard rate properties) of the proposed XGAIW model are derived. Moreover, four estimation methods, namely, the maximum likelihood, maximum product spacing, least squares, and weighted least squares methods, are utilized to estimate the XGAIW parameters. The Monte Carlo simulation study has been performed to assess the performance of the proposed estimation methods using some criteria. The importance, flexibility, and potentiality of the XGAIW model are studied via a breast cancer data set application. The XGAIW model can produce better fits than some well-known distributions, so the proposed model can be used, as a good alternative to some existing distributions, in modeling several real data.