Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

In this paper, we construct a new Lagrangian discrete distribution, named the zero truncated Poisson distribution (LZTPD). It can be presented as generalization of Poissson (ZTPD) and an alternative to intervened (IPD), which was elaborated for modelling both over-dispersed under-dispersed count datasets. The mathematical aspects LZTPD are thoroughly investigated, its connection other distributions is crucially observed. Further, define finite mixture LZTPDs establish identifiability condition along with some distributional aspects. Statistical work then performed. maximum likelihood method moment approaches used estimate unknown parameters LZTPD. Simulation studies also undertaken assessment long-term performance estimates. significance one additional parameter in tested using generalized ratio test. Moreover, propose regression model (LZTPRM) estimated by estimation method. Two real-world datasets considered demonstrate LZTPD’s applicability, healthcare data analyzed LZTPRM’s superiority.