Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

Abstract

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

On Zero-Truncated Negative Binomial with Excess Ones

“…This leads to the development of zero-truncated models, such as zero-truncated Poisson distribution [6] and zero-truncated Negative Binomial distribution [7]. Most recently introduced are the Zero-truncated negative binomial-Erlang distribution [8], a zero-truncated distribution [9] and Lagrangian Zero-truncated Poisson Distribution [10] among others.…”

A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences

“…Furthermore, the authors in [18] also used the LD 2 to create the generalized LKD of type two. The competence of the distributions proposed based on the LD 2 profoundly attracted our team, and as a result, we suggested the Lagrangian version of the ZTPD, the zero-truncated binomial distribution, and the IPD (see [26][27][28]). Moreover, the authors in [24] demonstrated that every member of the LD 2 was also a member of the LD 1 .…”

A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

“…Furthermore, the authors in [16] discussed the methods for generating different classes of Lagrangian probability distributions. Our team was very impressed by the competency of the distributions proposed based on the Lagrangian method, and as a result, we proposed the Lagrangian version of ZTPD through the work published in [17]. Furthermore, the authors in [18] concentrated on the Lagrangian approach's construction of the zero-truncated binomial distribution (ZTBD) and explained how effective it was in comparison to other zero-truncated distributions.…”