The Poisson Generalized Linear Failure Rate Model

Abstract

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 has the generalized linear failure rate distribution. A new distribution to analyze lifetime data is defined from the proposed cure rate model, and its quantile function as well as a general expansion for the moments is derived. We estimate the parameters of the model with cure rate in the presence of covariates for censored observations using maximum likelihood and derive the observed information matrix. We obtain the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. The usefulness of the proposed cure rate survival model is illustrated in an application to real data.

Keywords:

• Cure fraction model
• Generalized linear failure rate distribution
• Lifetime data
• Poisson distribution
• Sensitivity analysis

Mathematics Subject Classification:

• 60E05
• 62J05
• 62J20