Abstract: In the area of survival analysis the most popular regression model is the Cox proportional hazards (PH) model. Unfortunately, in practice not all data sets satisfy the PH condition and thus the PH model cannot be used. To overcome the problem, the proportional odds (PO) model ( Pettitt 1982 and Bennett 1983a) and the generalized proportional odds (GPO) model ( Dabrowska and Doksum, 1988) were proposed, which can be considered in some sense generalizations of the PH model. However, there are examples indicating that the use of the PO or GPO model is not appropriate. As a consequence, a more general model must be considered. In this paper, a new model, called the proportional generalized odds (PGO) model, is introduced, which covers PO and GPO models as special cases. Estimation of the regression parameters as well as the underlying survival function of the GPO model is discussed. An application of the model to a data set is presented.
Compound distributions gained their importance from the fact that natural factors have compound effects, as in the medical, social and logical experiments. Dubey (1968) introduced the compound Weibull by compounding Weibull distribution with gamma distribution. The main aim of this paper is to define a bivariate generalized Burr (compound Weibull) distribution so that the marginals have univariate generalized Burr distributions. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance- covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.