On New Bivariate Poisson - Lindley distribution with Application of Correlated Bivariate Count Data Analysis
Keywords:
Bivariate discrete distribution, bivariate Poisson Lindley, correlated bivariate count data, maximum likelihood estimationAbstract
This paper proposes a bivariate generalized Poisson-Lindley (BGPL) distribution, which is an alternative to analyse correlated bivariate count data. The joint probability mass function, covariance, and correlation coefficient of the proposed distribution, are discussed. It has two sub-models, such as the bivariate Poisson-Lindley (BPL) and bivariate geometric (BGeo) distributions. The unknown parameters of the proposed distribution are estimated with the maximum likelihood method. In addition, some examples of correlated bivariate count data are fitted with the proposed distribution and it compares with the BPL, BGeo, and bivariate Poisson distributions. The results show that the BGPL distribution provides the lowest value of the Akaike information criterion and Bayesian information criterion than other distributions. It is indicated that the BGPL distribution can be used as an alternative flexible distribution for modeling correlated bivariate count data which are either positive or negative correlations.
References
Bhati D, Sastry DVS, Qadri PM. A new generalized Poisson-Lindley distribution: Applications and properties. Austrian J Stat. 2015; 44(4): 35-51.
Deepesh B, Kumawat P, Gomez-D ´ eniz E. Mixed Poisson distributions. Commun Stat Theory. 2017; 46(22): 11060-11076.
Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math Comput Simul. 2008; 78(4): 493-506
Gomez-D ´ eniz E, Sarabia JM, Calder ´ ´ın-Ojeda E. Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications. Insur.: Math Econ. 2012; 42(1): 39-49.
Holla MS. On a Poisson-inverse Gaussian distribution, Metrika. 1967; 11(1): 115-121.
Karlis D, Xekalaki E. Mixed Poisson distributions. Internat Statist Rev. 2005; 73(1): 35-58.
Lakshminarayana J, Pandit SNN, Rao KS. On a bivariate Poisson distribution. Commun Stat Theory. 1999; 28(2): 267-276.
Mahmoudi E, Zakerzadeh H. Generalized Poisson-Lindley Distribution. Commun Stat Theory. 2010; 39(10): 1785-17.
Marshall A, Olkin I. Multivariate distributions generated from mixtures of convolution and product families, Lect. Notes Monograph Ser. 1990; 16: 371-393.
Mitchell CR, Paulson AS. A new bivariate negative binomial distribution. Nav Res Logist Q. 1981; 28(3): 359-374.
R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available from: https://www.R-project.org/(2021).
Sankaran M. The discrete Poisson-Lindley distribution. Biometrics. 1970; 26(1): 145-149.
Shanker R, Sharma S, Shanker R. A discrete two-parameter Poisson Lindley distribution. J Ethiop Stat Assoc. 2012; 21: 15-22.
Shanker R, Mishra A. A two-parameter Poisson-Lindley distribution, Int J Stat Syst. 2014; 9(1):79-85.
Shanker R, Sharma S, Shanker R. A two-parameter Lindley distribution for modeling waiting and survival times data. Appl Math. 2013; 4(2): 363-368.
Soetaert K. plot3D: Plotting Multi-Dimensional Data. R package version 1.4. Available from: https://CRAN.R-project.org/package=plot3D(2021).
Wongrin W, Bodhisuwan W. The Poisson-generalised Lindley distribution and its applications. Songklanakarin J Sci Technol. 2016; 38(6): 645-656.
Zamani H, Ismail N, Faroughi P. Poisson-weighted exponential univariate version and regression model with applications, J Math Stat. 2014; 10(2): 148-154.
Zamani H, Ismail N, Faroughi P. Bivariate Poisson-weighted exponential distribution with applications. AIP Conf Proc. 2014; 1602(1): 964-968.
Zamani H, Faroughi P, Ismail N. Bivariate Poisson-Lindley distribution with application. J Math Stat. 2015; 11(1): 1-6
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