The generalized negative binomial distribution (GNBD) was defined and studied by Jain and Consul (1971). The GNBD model has been found useful in many fields such as random walk, queuing theory, branching processes and polymerization reaction in chemistry. In this paper, four methods by which the GNBD model gets generated are discussed. The different methods of estimating the model parameters are provided. By using the bias property, we found that the truncated version of GNBD model provides a better parameter estimates than the GNBD model when fitted to data sets from the GNBD model.