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Volume 38, Issue 1
The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression

Christophe Chesneau, Hassan S. Bakouch, Yunus Akdoğan & Kadir Karakaya

DOI: 10.4208/cmr.2021-0045

Commun. Math. Res., 38 (2022), pp. 28-51.

Published online: 2021-11

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  • Abstract

On the basis of a well-established binomial structure and the so-called Poisson-Lindley distribution, a new two-parameter discrete distribution is introduced. Its properties are studied from both the theoretical and practical sides. For the theory, we discuss the moments, survival and hazard rate functions, mode and quantile function. The statistical inference on the model parameters is investigated by the maximum likelihood, moments, proportions, least square, and weighted least square estimations. A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates. Then, applications to two practical data sets are given. Finally, we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.

  • Keywords

Binomial-discrete family, Poisson-Lindley distribution, estimation, data analysis, count regression.

  • AMS Subject Headings

60E05, 62E10, 62E15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-38-28, author = {Chesneau , ChristopheBakouch , Hassan S.Akdoğan , Yunus and Karakaya , Kadir}, title = {The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {38}, number = {1}, pages = {28--51}, abstract = {

On the basis of a well-established binomial structure and the so-called Poisson-Lindley distribution, a new two-parameter discrete distribution is introduced. Its properties are studied from both the theoretical and practical sides. For the theory, we discuss the moments, survival and hazard rate functions, mode and quantile function. The statistical inference on the model parameters is investigated by the maximum likelihood, moments, proportions, least square, and weighted least square estimations. A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates. Then, applications to two practical data sets are given. Finally, we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0045}, url = {http://global-sci.org/intro/article_detail/cmr/19955.html} }
TY - JOUR T1 - The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression AU - Chesneau , Christophe AU - Bakouch , Hassan S. AU - Akdoğan , Yunus AU - Karakaya , Kadir JO - Communications in Mathematical Research VL - 1 SP - 28 EP - 51 PY - 2021 DA - 2021/11 SN - 38 DO - http://doi.org/10.4208/cmr.2021-0045 UR - https://global-sci.org/intro/article_detail/cmr/19955.html KW - Binomial-discrete family, Poisson-Lindley distribution, estimation, data analysis, count regression. AB -

On the basis of a well-established binomial structure and the so-called Poisson-Lindley distribution, a new two-parameter discrete distribution is introduced. Its properties are studied from both the theoretical and practical sides. For the theory, we discuss the moments, survival and hazard rate functions, mode and quantile function. The statistical inference on the model parameters is investigated by the maximum likelihood, moments, proportions, least square, and weighted least square estimations. A simulation study is conducted to observe the performance of the bias and mean square error of the obtained estimates. Then, applications to two practical data sets are given. Finally, we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.

Chesneau , ChristopheBakouch , Hassan S.Akdoğan , Yunus and Karakaya , Kadir. (2021). The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression. Communications in Mathematical Research . 38 (1). 28-51. doi:10.4208/cmr.2021-0045
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