In the work of Valdez and Shi (2011) and Safari-atesari and Fathi-Vajargah (2015), copula model was fitted on empirical evidence and a predictive model was developed. In this article, we anticipate accident probability after viewing the accidents for the year. This type of actuarial application is predictive modeling for considering the effect of a policyholder’s choice of coverage on frequency of accidents which can be used by using Bayes’ rule. We can compute the probability by the Frank copula expression and based on the marginal distribution of policyholder’s choice of coverage. According to the results, the largest conditional accident probability is observed for the “first level” and the lowest is observed for the "third level”. Additionally, we derive the conditional expected frequency of claims for each policyholder and to examine the effect of policy selection on frequency of accidents, we carry out a pairwise comparison for the three types of coverage. Also, we investigate the effects of covariates on the accident probability without and with the information on the coverage choice for each single policyholder.
Predictive Modeling; Collision Insurance; Conditional Probability; Bayes’ Rule.