Testing the Mixture of Exponentials Hypothesis and Estimating the Mixing Distribution by the Method of Moments

This article presents nonparametric methods for testing the hypothesis that duration data can be represented by a mixture of exponential distributions. Both Bayesian and classical tests are developed. A variety of apparently distinct models can be written in mixture of exponentials form. This raises a fundamental identification problem. A consistent estimator for the number of points of support of a discrete mixture is developed. A consistent method-of-moments estimator for the mixing distribution is derived from the testing criteria and is evaluated in a Monte Carlo study.