How to fit a response time distribution

Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data--response time distributions, in particular. However, techniques for fitting distributions very widely, and little is known about the efficacy of different techniques. In this article, we assess several fitting techniques by simulating six widely cited models of response time and using the fitting procedures to recover model parameters. The techniques include the maximization of likelihood and least squares fits of the theoretical distributions to different empirical estimates of the simulated distributions. A running example is used to illustrate the different estimation and fitting procedures. The simulation studies reveal that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yield more accurate and less variable parameter estimates than do others. Methods that involve least squares fits to density estimates generally yield very poor parameter estimates.