Abstract
In this article, we propose a new three-parameter model called compound zero-truncated Poisson gamma model. The corresponding variate of this model represents the zero-truncated Poisson sum of independent and identically distributed gamma random variables. Several mathematical properties of the proposed model are discussed. The proposed model can be unimodal as well as multimodal, moreover, gamma distribution can be obtained as a special case. The model parameters are estimated using expectation–maximization (EM)-type algorithm, and it is observed that it is quite convenient to be implemented in practice. Furthermore, an extension of the model is made to consider four-parameter bivariate model, and derived estimation of unknown parameters and confidence intervals based on EM-type algorithm. For validation purposes, some numerical simulation experiments are conducted to check how the proposed EM-type algorithm performs. Finally, the analysis of real data set has been presented to show the flexibility of the proposed models.