Extended Burr XII Regression Models: Theory and Applications

We introduce two new lifetime distributions by compounding the Burr XII (BXII) and geometric distributions. We derive their moments and moment-generating and quantile functions. We also define two new extended regression models based on the logarithms of these distributions. The regression models are very useful in the analysis of real data since they can provide better fits than other special regression models. We formulate a new cure rate survival model, where the number of competing causes of the event of interest follows a geometric distribution and the time to this event has the BXII geometric distribution. The estimation of the model parameters is performed by maximum likelihood. We illustrate the importance of the new models by means of two real datasets. The first dataset comes from a study carried out at the Department of Entomology of the Luiz de Queiroz School of Agriculture, University of São Paulo, which aims to assess the longevity of the Mediterranean fruit fly (ceratitis capitata). The second dataset comes from the area of biology.