Rama Shanker,
Kamlesh Kumar Shukla,
- Associate Professor, Department of Statistics, Assam University, Silchar, Assam, India
- Assistant Professor, Department of Mathematics, Jaypee Institute of Information Technology,, Uttar pradesh, INDIA
Abstract
The discrete data available in any field of knowledge is influenced by several known and unknown factors and the factors which affect the discrete data are stochastic. The stochastic nature of discrete data is a challenge for statisticians to model and analyze with the existing discrete distributions. In the present paper, Poisson-Uma distribution, the Poisson compound of Uma distribution, has been proposed to model over-dispersed data of thunderstorm events. The descriptive statistical constants based on moments of the proposed distribution have been studied. Over-dispersion, increasing hazard rate, and unimodality of the distribution have been discussed. One of the important characteristics of the Poisson-Uma distribution is that although it is also a mixture of geometric and negative binomial distributions its nature does not exhibit multiple modes. The method of moment and maximum likelihood estimation for estimating parameters has been studied. The applications of the distribution to model thunderstorm events for June, July, August, and summer have been discussed. The proposed distribution shows a much better fit than the Poisson-Lindley distribution and the Poisson-Sujatha distribution. Therefore, Poisson-Uma distribution can be considered an important over-dispersed distribution for modeling over-dispersed data of thunderstorm events.
Keywords: Uma distribution, compounding, statistical properties, maximum likelihood estimation, goodness of fit
[This article belongs to Research & Reviews : Journal of Statistics ]
Rama Shanker, Kamlesh Kumar Shukla. The Poisson–Uma Distribution with Properties and Applications to Model Thunderstorm Events. Research & Reviews : Journal of Statistics. 2024; 13(01):20-30.
Rama Shanker, Kamlesh Kumar Shukla. The Poisson–Uma Distribution with Properties and Applications to Model Thunderstorm Events. Research & Reviews : Journal of Statistics. 2024; 13(01):20-30. Available from: https://journals.stmjournals.com/rrjost/article=2024/view=186631
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Research & Reviews : Journal of Statistics
| Volume | 13 |
| Issue | 01 |
| Received | 05/07/2024 |
| Accepted | 24/07/2024 |
| Published | 05/09/2024 |
| Publication Time | 62 Days |
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