On left-truncating and mixing Poisson distributions
Jordi Valero, Marta Pérez‐Casany, Josep Ginebra · Communication in Statistics- Theory and Methods · 2014
The distributions obtained by left-truncating at k a mixed Poisson distribution, denoted kT-MP, and those obtained by mixing previously left-truncated Poisson distributions, denoted M-kTP, are characterized by means of their probability generating function. The main consequence is that every kT-MP distribution is a M-kTP distribution, but not the other way around.