Statistical Analysis of Covid-19 Data using the Odd Log Logistic Kumaraswamy Distribution
Keywords:
Odd Log Logistic-G Distribution; Kumaraswamy Distribution; Moments; Quantiles
Abstract
This paper presents a statistical analysis of Covid-19 data using the Odd log logistic kumaraswamy Kumaraswamy (OLLK) distribution. Some mathematical properties of the proposed OLLK distribution such as the survival and hazard functions, quantile function, ordinary and incomplete moments, moment generating function, probability weighted moment, distribution of order statistic and Renyi entropy were derived. Five estimators are examined for unknown model parameters. The performance of the estimators is compared using an extensive simulation study based on the bias and mean square error criteria. Two Covid-19 data sets representing the percentage of daily recoveries of Covid-19 patients are used to illustrate the applicability of the proposed OLLK distribution. Results revealed that the OLLK distribution is a better alternative to some existing models with bounded support.References
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2. Alzaatreh, A., Lee, C., and Famoye, F. (2014). T-Normal family of distributions: A new approach to generalize the normal distribution. Journal of Statistical Distributions and Applications, 1(16): 1-18.
3. Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. M. M., and
Pescim, R. R. (2015). A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepe Journal of Mathematics and Statistics, 44: 1491-1512.
4. Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2014). The Weibull-G family of
probability distributions. Journal of Data Science, 12: 53-68.
5. Cordeiro, G. M., Alizadeh, M., Tahir, M. H., Mansoor, M., Bourguignon, M., and
Hamedani, G. G. (2016). The beta odd log-logistic generalized family of distributions. Hacettepe Journal of Mathematics and Statistics, 45: 1175-1202
6. Cordeiro, G. M., and de Castro, M. (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81(7): 883-898.
7. Eugene, N., Lee, C., and Famoye, F. (2002). The beta-normal distribution and its
applications. Communications in Statistics - Theory and Methods, 31(4): 497-512.
8. Galton, F. (1883). Enquiries into Human Faculty and its Development. Macmillan & Company, London.
9. George, R., and Thobias, S. (2017). Marshall-Olkin Kumaraswamy Distribution.
International Mathematical Forum, 12(2): 47-69.
10. Gleaton, J. U., and Lynch, J. D. (2006). Properties of generalized log-logistic families of lifetime distributions. Journal of Probability and Statistical Science, 4(1): 51-64.
11. Gradshteyn, I. and Ryzhik, I. (2007). Table of Integrals, Series and Products,
Elsevier/Academic Press.
12. Greenwood, J. A., Landwehr, J. M., and Matalas, N. C. (1979). Probability weighted moments: Definitions and relations of parameters of several distributions expressible in inverse form. Water Resources Research, 15: 1049-1054.
13. Gunduz, S., and Korkmaz, M. C. (2020). A New Unit Distribution based on the
Unbounded Johnson Distribution Rule: The Unit Johnson SU Distribution. Pakistan
Journal Statistics and Operation Research, 16(3): 471-490.
14. Ibrahim, S., Doguwa, S. I., Isah, A., and Haruna, J. (2020). The Topp-Leone
Kumaraswamy-G family of distributions with applications to cancer disease data. Journal of Biostatistics and Epidemiology, 6(1): 40-51.
15. Jones, M. C. (2009). Kumaraswamy’s Distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6: 70-81.
16. Kumaraswamy, P. (1980). A generalized probability density function for doubly bounded random process. Journal of Hydrology, 46: 79-88.
17. Marshall, A. W., and Olkin, I. (1997). A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families. Biometrika, 84: 641-652.
18. Mazucheli, J., Menezes, F. A., and Dey, S. (2019). Unit-Gompertz Distribution with Applications. Statistica, 79(1): 25-43.
19. Moors, J. J. (1988). A quantile alternative for kurtosis. Statistician, 37: 25-32.
20. Mudholkar, G. S., and Srivastava, D. K. (1993). Exponentiated Weibull family for
analyzing bathtub failure rate data. IEEE Transactions on Reliability, 42: 299-302.
21. Opone, F. C., and Iwerumor, B. N. (2021). A New Marshall-Olkin Extended Family of Distributions with Bounded Support. Gazi University Journal of Science, 34(3): 899-914.
22. Rényi, A. (1961). On measure of entropy and information. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1, University of
California Press, Berkeley, 547-561.
23. Shaw, W., Buckley, I. (2007). The alchemy of probability distributions: beyond Gram Charlier expansions and a skew-kurtoticnormal distribution from a rank transmutation map. arXivprereprint, arXiv, 0901.0434.
Published
2023-11-13
How to Cite
Opone, F., Karakaya, K., & Ubaka, N. (2023). Statistical Analysis of Covid-19 Data using the Odd Log Logistic Kumaraswamy Distribution. Statistics, Optimization & Information Computing, 12(1), 210-230. https://doi.org/10.19139/soic-2310-5070-1572
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Section
Research Articles
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