Generalization of the Mixture Model Using a Copula Function

In the mixture distribution model (for continuous and discrete cases) the density function, f̃ (t) is given by a linear combination of k density functions, fi(t), i= 1, · · · ,k, with non-negative weights pi which must sum to 1.0. We propose a generalization of the mixture model where the weights are not restricted to being constant. The specification of the weight functions is not easy because f̃ (t) must be integrated to one. This is done by defining a random variable which has a density with the desired form. The definition of the random variable includes random variables with the densities fi(t) and a copula function. The proposed model includes the traditional mixture model, the polyhazard and the fraction of cure models. Real applications are used to illustrate the model.