Risky behavior Poisson model identification: heterogeneous arguments in likelihood

We consider a problem of risky behavior intensity estimation based on data received from respondent's answers about their behavior. The method of maximum likelihood estimation is used for derivation of the estimate, and likelihood function describes the likelihood of realization of the particular system of answers. The likelihood function is derived for the situation when data about several last episodes of the behavior is available and situation when data about one last episode of the behavior and record intervals between consequent episodes of the behavior process occurred within fixed time interval is available.