This paper describes the specification, estimation and comparison of double generalized linear compound Poisson models based on the likelihood paradigm. The models are motivated by insurance applications, where the distribution of the response variable is composed by a degenerate distribution at the origin and a continuous distribution on the positive real line. We present maximum likelihood and restricted maximum likelihood algorithms for parameter estimation, with emphasis to the analysis of insurance data. Simulation studies are employed to evaluate the bias and consistency of the estimators in a finite sample framework. The simulation studies are also used to validate the fitting algorithms and check the computational implementation. Furthermore, we investigate the impact of an unsuitable choice for the response variable distribution on both mean and dispersion parameter estimates. We provide R implementation and illustrate the application of double generalized linear compound Poisson models using a data set about car insurances.