Handling missing data and parameters initialization method for the ex-gaussian distribution

This paper focuses on parameter estimation for the ex-gaussian distribution, a widely used model for analyzing Reaction Time (RT) data in psychology. We introduce a Bayesian estimation method designed to achieve unbiased predictions for small sample sizes. The study has two main objectives. The first is to extend the arbitrary Bayesian proposed method in 2021 by incorporating a bootstrap-based initialization procedure, which we compare with arbitrary initialization and Maximum Likelihood Estimation (MLE). The second is to address the problem of missing data (NA) of type Missing At Random (MAR). We therefore conduct a comparative analysis between our proposed method and three alternative imputation strategies. The effectiveness of our approach is validated through both simulation studies and an application to real psychological data, which further demonstrate the feasibility of the proposed method.