The article suggests an extension and refinement of the existing model for incomplete estimation of the person’s behavior characteristics using several last episodes of his risky behavior and including individual characteristics and other factors, in particular, the sex, age, etc. This extension has been made with a novel approach to formalization of the gamma Poisson model of behavior based on the random point process theory. The general form of the likelihood function for the estimates was derived. This formalization allowed to use the Cox regression model for the estimation of the process intensity parameters on the condition of only three last episodes taking into account different characteristics of the domain. The possibilities of the chosen approach were shown using the data on publication of posts in the online social media.