The Poisson-Rama distribution with properties and applications to model over-dispersed count data
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Abstract
The discrete data available in any fields of knowledge is influenced by several known and unknown factors and the factors which affect the discrete data are stochastic in nature. The stochastic nature of discrete data is really a challenge for statistician to model and analyse with the existing discrete distributions. In the present paper, Poisson-Rama distribution, a Poisson mixture of Rama distribution, has been proposed to model over-dispersed data. Distributional properties, estimation of parameter using maximum likelihood method, and applications of the proposed distributions have been discussed. The simulation study has been carried out to know the consistency of maximum likelihood estimates of parameter. It is observed that the proposed distribution gives much closure fit than several over-dispersed one parameter discrete distributions including Poisson-Lindley distribution, Poisson-Akash distribution and Poisson-Ishita distribution.
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References
Beall, G. The fit and significance of contagious distributions when applied to observations on larval insects, Ecology, 21, 460 – 474, (1940). https://doi.org/10.2307/1930285
Grandell, J. Mixed Poisson Processes, Chapman &Hall, London, (1997)
Janardan, K.G. and Schaeffer, D.J. Models for the analysis of chromosomal aberrations in human leukocytes, Biometrical Journal, 19(8), 599 – 612, (1977). https://doi.org/10.1002/bimj.4710190804
Kemp, C.D. and Kemp, A.W. Some properties of the Hermite distribution, Biometrika, 52, 381-394, (1965). https://doi.org/10.1093/biomet/52.3-4.381
Lindley, D.V. Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society, 20 (1), 102- 107, (1958) https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Loeschke, V. and Kohler, W. Deterministic and Stochastic models of the negative binomial distribution and the analysis of chromosomal aberrations in human leukocytes, Biometrische Zeitschrift, 18, 427 -451, (1976). https://doi.org/10.1002/bimj.19760180602
Sankaran, M. The discrete Poisson-Lindley distribution, Biometrics, 26, 145- 149, (1970) https://doi.org/10.2307/2529053
Shanker, R. and Hagos, F. On Poisson-Lindley distribution and its Applications to Biological Sciences, Biometrics & Biostatistics International Journal, 2(4), 103 – 107, (2015). http://dx.doi.org/10.15406/bbij.2015.02.00036
Shanker, R. Rama Distribution and Its Application, International Journal of Statistics and Applications, 7(1), 26 – 35, (2017). doi:10.5923/j.statistics.20170701.04
Shanker, R. Akash Distribution and Its Applications, International Journal of Probability and Statistics, 4 (3), 65 – 75, (2015). doi:10.5923/j.ijps.20150403.01
Shanker, R. The Discrete Poisson-Akash Distribution, International Journal of Probability and Statistics, 6(1), 1 -10, (2017) doi:10.5923/j.ijps.20170601.01
Shanker, R. and Shukla, K.K. Ishita distribution and its Applications, Biometrics & Biostatistics International Journal, 5(2), 1 – 9, (2017) https://doi.org/10.15406/bbij.2017.05.00126
Shukla, K.K. and Shanker, R. The Discrete Poisson-Ishita Distribution, International Journal of Statistics and Economics, 20(2), 109 – 122, (2019).
Tajuddin, R.R.M., Ismail, N. and Ibrahim, K. Several two-component mixture distributions for count data, Communication in Statistics-Simulation and Computation, 51, 3760 – 3771, (2022) http://dx.doi.org/10.1080/03610918.2020.1722834