A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic

Muhammed Rasheed Irshad, Christophe Chesneau (), Damodaran Santhamani Shibu, Mohanan Monisha and Radhakumari Maya
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Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, India
Christophe Chesneau: Department of Mathematics, Université de Caen Basse-Normandie, F-14032 Caen, France
Damodaran Santhamani Shibu: Department of Statistics, University College, Thiruvananthapuram 695 034, India
Mohanan Monisha: Department of Statistics, University College, Thiruvananthapuram 695 034, India
Radhakumari Maya: Department of Statistics, University College, Thiruvananthapuram 695 034, India

Stats, 2022, vol. 5, issue 4, 1-25

Abstract: The importance of Lagrangian distributions and their applicability in real-world events have been highlighted in several studies. In light of this, we create a new zero-truncated Lagrangian distribution. It is presented as a generalization of the zero-truncated binomial distribution (ZTBD) and hence named the Lagrangian zero-truncated binomial distribution (LZTBD). The moments, probability generating function, factorial moments, as well as skewness and kurtosis measures of the LZTBD are discussed. We also show that the new model’s finite mixture is identifiable. The unknown parameters of the LZTBD are estimated using the maximum likelihood method. A broad simulation study is executed as an evaluation of the well-established performance of the maximum likelihood estimates. The likelihood ratio test is used to assess the effectiveness of the third parameter in the new model. Six COVID-19 datasets are used to demonstrate the LZTBD’s applicability, and we conclude that the LZTBD is very competitive on the fitting objective.

Keywords: Lagrangian zero-truncated binomial distribution; index of dispersion; maximum likelihood method; generalized likelihood ratio test; COVID-19; simulation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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