A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

Muhammed Rasheed Irshad, Mohanan Monisha, Christophe Chesneau (), Radhakumari Maya and Damodaran Santhamani Shibu
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Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682022, India
Mohanan Monisha: Department of Statistics, University College, Thiruvananthapuram 695034, India
Christophe Chesneau: Department of Mathematics, Université de Caen Basse-Normandie, UFR de Sciences, 14032 Caen, France
Radhakumari Maya: Department of Statistics, University College, Thiruvananthapuram 695034, India
Damodaran Santhamani Shibu: Department of Statistics, University College, Thiruvananthapuram 695034, India

Stats, 2023, vol. 6, issue 1, 1-19

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

Keywords: Lagrange expansion; intervened Poisson distribution; Lagrangian intervened Poisson distribution; regression; inverse transformation method (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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