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Volume 5
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10.3390/stats5040060
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Article

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

by
Muhammed Rasheed Irshad
1,
Christophe Chesneau
2,*,
Damodaran Santhamani Shibu
3,
Mohanan Monisha
3 and
Radhakumari Maya
3
1
Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, India
2
Department of Mathematics, Université de Caen Basse-Normandie, F-14032 Caen, France
3
Department of Statistics, University College, Thiruvananthapuram 695 034, India
*
Author to whom correspondence should be addressed.
Academic Editor: Wei Zhu
Stats 2022, 5(4), 1004-1028; https://doi.org/10.3390/stats5040060
Received: 21 September 2022 / Revised: 26 October 2022 / Accepted: 27 October 2022 / Published: 30 October 2022
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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 Lagrangian zero-truncated binomial distribution; index of dispersion; maximum likelihood method; generalized likelihood ratio test; COVID-19; simulation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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MDPI and ACS Style

Irshad, M.R.; Chesneau, C.; Shibu, D.S.; Monisha, M.; Maya, R. A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic. Stats 2022, 5, 1004-1028. https://doi.org/10.3390/stats5040060

AMA Style

Irshad MR, Chesneau C, Shibu DS, Monisha M, Maya R. A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic. Stats. 2022; 5(4):1004-1028. https://doi.org/10.3390/stats5040060

Chicago/Turabian Style

Irshad, Muhammed Rasheed, Christophe Chesneau, Damodaran Santhamani Shibu, Mohanan Monisha, and Radhakumari Maya. 2022. "A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic" Stats 5, no. 4: 1004-1028. https://doi.org/10.3390/stats5040060

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