Applications of duration analysis in economics and finance exclusively employ methods for events of stochastic duration. In application to credit data, previous research incorrectly treats the time to predetermined maturity events as censored stochastic event times. The medical literature has binary parametric ‘cure rate’ models that deal with populations that never experienced the modelled event. We propose and develop a multinomial parametric incidence and duration model, incorporating such populations. In the class of cure rate models, this is the first fully parametric multinomial model and is the first framework to accommodate an event with predetermined duration. The methodology is applied to unsecured personal loan credit data provided by one of Australia's largest financial services organizations. This framework is shown to be more flexible and predictive through a simulation and empirical study that reveals: simulation results of estimated parameters with a large reduction in bias; superior forecasting of duration; explanatory variables can act in different directions upon incidence and duration; and variables exist that are statistically significant in explaining only incidence or duration. Copyright © 2013 John Wiley & Sons, Ltd.