POISSON PRATIBHA DISTRIBUTION AND ITS APPLICATIONS
Keywords:
moments, Poisson mixture, Pratibha distribution, estimation, goodness of fitDOI:
https://doi.org/10.17654/0973514325019Abstract
Poisson Pratibha distribution (PPD) is a Poisson mixture of Pratibha distribution [12] proposed in this paper. The shape of the probability mass function (pmf) has been provided to get the expression for the rth factorial moment concerning origin. The generating functions, mean, variance, skewness, kurtosis, index of dispersion, and others have been provided and visually represented for a range of parameter values. To estimate the parameter, the maximum likelihood and method of moment estimators were employed. The suggested distribution’s goodness of fit has been tested on four actual data sets.
Received: May 1, 2025
Revised: May 25, 2025
Accepted: June 12, 2025
References
M. Sankaran, The discrete Poisson-Lindley distribution, Biometrics 26(1) (1970), 145-149. https://doi.org/10.2307/2529053.
R. Shanker, The discrete Poisson-Sujatha distribution, International Journal of Probability and Statistics 5(1) (2016), 1-9. doi:10.5923/j.ijps.20160501.01.
R. Shanker, The discrete Poisson-Shanker distribution, Jacobs Journal of Biostatistics 1(1) (2016), 1-7. https://doi.org/10.15406/bbij.2017.05.00121.
R. Shanker and F. Hagos, On Poisson-Lindley distribution and its applications to biological sciences, Biom. Biostat. Int. J. 2(4) (2015), 1-5.
https://doi.org/10.15406/bbij.2015.02.00036.
R. Shanker, F. Hagos and S. Sujatha, On modeling of lifetime data using exponential and Lindley distributions, Biom. Biostat. Int. J. 2(5) (2015), 1-9. https://doi.org/10.15406/bbij.2015.02.00042.
D. Karlis and E. Xekalaki, Mixed Poisson distributions, International Statistical Review 73(1) (2005), 35-58. https://doi.org/10.1111/j.1751-5823.2005.tb00251.x.
C. R. Rao, Statistics and Truth: Putting Chance to Work, 2nd ed., World Scientific, 1997.
Bilal Ahmad, Tariq Rashid Jan and Hassan S. Bakouch, Poisson Xgamma distribution: a discrete model for count data analysis, Model Assisted Statistics and Applications 15 (2020), 139-151. https://doi.org/10.3233/MAS-200484.
D. Lambert, Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics 34(1) (1992), 1-14.
https://doi.org/10.2307/1269547.
A. H. El-Shaarawi and R. Zhu, Modelling skewed data with mixtures of distributions, Canad. J. Statist. 30(4) (2002), 563-581.
https://doi.org/10.2307/3316156.
J. Aitchison and C. H. Ho, The multivariate Poisson-log normal distribution, Biometrika 76(4) (1989), 643-653. https://doi.org/10.1093/biomet/76.4.643.
Rama Shanker, Pratibha distribution with properties and application, Biom. Biostat. Int. J. 12(5) (2023), 136-142.
https://doi.org/10.15406/bbij.2023.12.00397.
J. Grandell, Mixed Poisson Processes, Chapman & Hall, London, 1997.
C. D. Kemp and A. W. Kemp, Some properties of the Hermite distribution, Biometrika 52(3-4) (1965), 381-394. https://doi.org/10.1093/biomet/52.3-4.381.
D. G. Catcheside, D. E. Lea and J. M. Thoday, The production of chromosome structural changes in Tradescantia microspores in relation to dosage, intensity and temperature, Journal of Genetics 47 (1946), 137-149. DOI: 10.1007/BF02986783.
R. Shanker, H. Fesshaye, R. Shanker, T. A. Leonida and S. Sium, On discrete Poisson-Shanker distribution and its applications, Biom. Biostat. Int. J. 5 (2017), 1-9. DOI:10.15406/bbij.2017.05.00121.
Han Wang and Wangxue Chen, Large sample properties of modified maximum likelihood estimator of the location parameter using moving extremes ranked set sampling, Statist. Probab. Lett. 223 (2025), 110430.
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