Prediction of settlement delay in critical illness insurance claims by using the generalized beta of the second kind distribution

We analyse the delay between diagnosis of illness and claim settlement in critical illness insurance by using generalized linear-type models under a generalized beta of the second kind family of distributions. A Bayesian approach is employed which allows us to incorporate parameter and model uncertainty and also to impute missing data in a natural manner. We propose methodology involving a latent likelihood ratio test to compare missing data models and a version of posterior predictive p-values to assess different models. Bayesian variable selection is also performed, supporting a small number of models with small Bayes factors, and therefore we base our predictions on model averaging instead of on a best-fitting model.