A Quasi Poisson-Suja Distribution with Properties and Applications
Rama Shanker, Riki Tabassum, Mousumi Ray, Hosenur Rahman Prodhani, Puja Nath
Abstract
Here, the Poisson compound of quasi Suja distribution called quasi Poisson-Suja distribution is proposed. A general expression for the rth factorial moment of this distribution has been obtained to derive its first four moments about origin and the central moments. The descriptive properties based on moments have been discussed. The proposed distribution is unimodal having increasing hazard rate and over-dispersed. Some interesting and useful statistical properties including unimodality and increasing hazard rate have been discussed. A simulation study has been done to test the performance of maximum likelihood estimates of parameters. Finally, the goodness of fit of the distribution discussed with two discrete datasets, the first from biological sciences and the second from thunderstorms and compared with the goodness of fit of Poisson- Lindley distribution, Poisson-Akash distribution, Poisson-Suja distribution, quasi Poisson-Lindley distribution and quasi Poisson-Akash distribution. The result shows that the proposed distribution provides greater flexibility in modeling real over-dispersed count data over the considered distributions.
References
1. D.V. Lindley; Fiducial Distributions and Bayes’ Theorem. Journal of the Royal Statistical Society, Series B, 20(1), 102-107 (1958).
2. J. Grandell; Mixed Poisson Processes. Chapman & Hall, London (1997).
3. J.U.M. Guire; T.A. Brindley; T.A Bancroft; The Distribution of European Corn-Borer Larvae Pyrausta in
Field Corn. Biometrics, 13, 65-78 (1957).
4. L.W. Falls; W.O. Williford; M.C. Carter; Probability Distributions for Thunderstorm Activity at Cape
Kennedy, Florida. Journal of Applied Meteorology, 10, 97-104 (1970).
5. M. Sankaran; The Discrete Poisson-Lindley Distribution; Biometrics, 26(1), 145-149 (1970).
6. R. Shanker; Akash Distribution and Its Applications. International Journal of Probability and Statistics, 4(3), 65 -75 (2015).
7. R. Shanker; The Discrete Poisson-Akash Distribution. International Journal of Probability and Statistics, 6(1), 1 -10 (2017a).
8. R. Shanker; Suja Distribution and Its Application. International Journal of Probability and Statistics, 6(2), 11-19 (2017b).
9. R. Shanker and F. Hagos; On Poisson-Lindley Distribution and Its Applications to Biological Sciences. Biometrics & Biostatistics International Journal, 2(4), 103-107 (2015).
10. R. Shanker and A. Mishra; A Quasi Poisson-Lindley Distribution. Journal of Indian Statistical Association, 54 (1&2), 113 – 125 (2016).
11.R. Shanker; K.K. Shukla and R. Shanker; A Quasi Poisson-Akash Distribution and Its Applications to Ecology. International Journal of Statistics and Applied Mathematics, 3(3), 111- 119 (2018).
12.R. Shanker; R. Upadhaya and K.K. Shukla; A Quasi Suja Distribution. Reliability: Theory and Applications, 17(3), 162-178 (2022).
13. R. Shanker; J. Saharia and K.K. Shukla; The Poisson-Suja Distribution with Properties and Applications. Reliability: Theory & Application, 20(1), 1009-1019 (2025).
14.R.R.M. Tajuddin; N. Ismail and K. Ibrahim; Several Two-Component Mixture Distributions for Count Data. Communication in Statistics-Simulation and Computation, 51, 3760-3771 (2022).
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