A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications

Emrah Altun; Hana Alqifari; Mohamed S. Eliwa; Emrah Altun; Hana Alqifari; Mohamed S. Eliwa

doi:10.3934/math.20231183

AIMS Mathematics

2023, Volume 8, Issue 10: 23272-23290. doi: 10.3934/math.20231183

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A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications

1.
Department of Mathematics, Bartin University, Bartin, Turkey
2.
Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 26 April 2023 Revised: 09 June 2023 Accepted: 25 June 2023 Published: 21 July 2023
MSC : 62E15

Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.
- negative-binomial regression,
- over-dispersion,
- Poisson regression,
- Poisson generalized-Lindley,
- zero-inflation distribution,
- statistical model,
- simulation
Citation: Emrah Altun, Hana Alqifari, Mohamed S. Eliwa. A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications[J]. AIMS Mathematics, 2023, 8(10): 23272-23290. doi: 10.3934/math.20231183

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Abstract

Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.

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