New flexible models generated by gamma random variables for lifetime modeling

In this paper we introduce a new three-parameter exponential-type distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have constant, decreasing, increasing, upside-down bathtub and bathtub-shaped hazard rate functions. It also generalizes some well-known distributions. We discuss maximum likelihood estimation of the model parameters for complete sample and for censored sample. Additionally, we formulate a new cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time to this event follows the proposed distribution. Maximum likelihood estimation of the model parameters of the new cure rate survival model is discussed for complete sample and censored sample. Two applications to real data are provided to illustrate the flexibility of the new model in practice.