The Zero-Truncated Poisson Generalized Lindley Distribution: Regression Model and Applications

Yupapin  Atikankul; Chanakarn  Jornsatian; Chawanee  Suphirat; Pennapa  Suwanbamrung

Authors

Yupapin Atikankul Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok, Thailand
Chanakarn Jornsatian Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok, Thailand
Chawanee Suphirat Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok, Thailand
Pennapa Suwanbamrung Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok, Thailand

Keywords:

Count data analysis, regression model, maximum likelihood estimation, truncated count, mixed Poisson distribution

Abstract

This article introduces a new discrete distribution for nonzero count data. Some distributional properties, such as shape, probability generating function, moment generating function, and raw moments, are studied. The maximum likelihood method is applied to estimate the distribution parameters. A nonzero count regression model based on the proposed distribution is developed. The
performance of the proposed distribution and its regression model are shown through real nonzero count data, which shows that they outperform other competitive models. Therefore, the proposed model can be considered for count data excluding zero.

References

Abouammoh AM, Alshangiti AM, Ragab IE. A new generalized Lindley distribution. J Stat Comput Simul. 2015; 85(18): 3662-3678.

Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr. 1974; 19: 716-723.

Atikankul Y, Thongteeraparp A, Bodhisuwan W, Qin J, Boonto S. The zero-truncated Poisson-weighted exponential distribution with applications. Lobachevskii J Math. 2021; 42(13): 3088-3097.

Atikankul Y. A new Poisson generalized Lindley regression model. Austrian J Stat. 2023; 52: 39-50.

Borah M, Saikia KR. Zero-truncated discrete Shanker distribution and its applications. Biom Biostat Int J. 2017; 5: 232-237.

Choulakian V, Lockhart RA, Stephens MA. Cramer-von Mises statistics for discrete distributions. ´Can J Stat. 1994; 22: 125-137.

David FN, Johnson NL. The truncated Poisson. Biometrics. 1952; 8: 275-285.

Ghitany ME, Al-Mutairi DK, Nadarajah S. Zero-truncated Poisson-Lindley distribution and its application. Math Comput Simul. 2008; 79: 279-287.

Hilbe JM. Modeling Count Data. New York: Cambridge University Press; 2014.

Hilbe JM. Negative Binomial Regression. New York: Cambridge University Press; 2011.

Hussain T. A zero truncated discrete distribution: Theory and applications to count data. Pak J Stat Oper Res. 2020; 16(1): 167-190.

Johnson NL, Kemp AW, Kotz S. Univariate discrete distributions. New York: Wiley; 2005.

Nash JC, Varadhan R. Unifying optimization algorithms to aid software system users: optimx for R. J Stat Softw. 2011; 43: 1-14.

R Core Team. R: A language and environment for statistical computing. Vienna, Austria. 2023; Available from: https://www.R-project.org/.

Schwarz G. Estimating the dimension of a model. Ann Stat. 1978; 461-464.

Shanker R. Zero-truncated Poisson-Akash distribution and its applications. Am J Math Stat. 2016; 7: 227-236.

Shanker R, Shukla KK. Zero-truncated new quasi Poisson-Lindley distribution and its applications. Philipp Stat. 2017; 66(2): 33-46.

Shanker R, Shukla KK. A zero-truncated two-parameter Poisson-Lindley distribution with an application to biological science. Turk Klin J Biostatistics. 2017; 9(2): 85-95.

Shukla KK, Shanker R, Tiwari MK. Zero-truncated Poisson-Ishita distribution and its applications. J Sci Res. 2020; 64(2): 287-294.