ABSTRACT
This chapter considers the fitting of an exponential mixture model on observed data that are unclassified with respect to their component membership of the mixture. Normal mixture distributions have been applied widely in practice to model heterogeneous data, as surveyed in G. J. McLachlan and K. E. Basford. In some circumstances however, the adoption of component densities that are normal is inappropriate, such as in the modelling of failure time data. For data of this type, mixtures of exponential distributions can play a useful role. S. C. Choi used a two-component mixture model to study the toxicity of chemical agents used in chemotherapy. The assumption that the underlying distribution is a mixture of exponential distributions is widely invoked in applied science and the social sciences. It is frequently adopted to model the distribution of time to failure in those situations where the hazard function is observed empirically to decline with time.
