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A New Unit Family of Distributions with Applications to Public Health, Environmental, and Financial Data |
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PP: 1437-1461 |
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doi:10.18576/amis/190617
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Author(s) |
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Okechukwu J. Obulezi,
Emmanuel E. Oguadimma,
Chinyere P. Igbokwe,
Chinelo U. Chikwelu,
Gaber Sallam Salem Abdalla,
John T. Mendy,
Ahmed S. Abdelzaher,
Mohammed Elgarhy,
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Abstract |
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| Bounded distributions are important in statistical studies especially when investigations involve rates, proportions or experimental outcomes such as success/failure, defective/non-defectives etc. The literature on bounded or unit family of distributions is scanty. Therefore, in this study, we develop a new unit family of distributions called Dhillon-G family of distributions. The Dhillon-G family is parsimonious given that it does not introduce additional parameter. Further, the Kumaraswamy distribution was modified using the Dhillon-G family with the modified distribution offering a better flexibility in application, mathematical tractability and better goodness of fit. We studied the structural behaviour/properties of the new distribution and the studies reveal that the distribution can model both skewed, unimodal, bimodal, bath-tub shape and bounded data. We estimated its parameters using non-Bayesian and Bayesian methods and a comprehensive simulation study is implemented to determine the behaviour of the estimators using maximum likelihood, maximum product of spacing, least squares and weighted least squares at different parameter settings and sample sizes. The results reveal consistent asymptotic behaviour for the parameters in the presence of small and large sample sizes. The Dhillon- Kumaraswamy distribution and its chosen competing distributions which included (Kumaraswamy, Beta, Gumbel, Gamma, Burr XII and Weibull) were fitted to data on mortality of COVID-19 patients in Dominica, Vinyl chloride from clean upgradient ground-water monitoring wells in (g/L), weekly volume of traded Bitcoin in USD, and infant mortality rate per 1000 live-births in selected countries. All four datasets are positively skewed and the Dhillon-Kumaraswamy distribution outperformed all competing models in fitting those datasets and in parameter estimation. These demonstrate that the new distribution is useful in modeling short interval dataset namely x ∈ (0, 1) as well as asymmetric data. |
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