A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. intervened (IPD) is substitute for the ZTPD, in which some intervention processes may change mean of rare events. These two distributions exhibit underdispersion (i.e., their variance less than mean). In this research, we offer an alternative solution dealing with problems by proposing generalization IPD Lagrangian approach called (LIPD), fact generalizes both ZTPD and IPD. As notable feature, it has ability to analyze overdispersed underdispersed datasets. addition, LIPD closed-form expression all its characteristics, as well increasing, decreasing, bathtub-shaped, upside-down bathtub-shaped hazard rate function. A consequent part devoted application. maximum likelihood estimation method considered, effectiveness estimates demonstrated through simulated study. To evaluate significance new parameter LIPD, generalized ratio test performed. Subsequently, present count regression suitable datasets using mean-parametrized form LIPD. Additionally, LIPD’s relevance application are shown real-world