Research Article
Transmuted Power Gumbel Distribution: Estimation and Applications
Ahmed Ali Hurairah*,
Nasr Tawfiq Almazaqi
Issue:
Volume 10, Issue 3, September 2024
Pages:
48-59
Received:
6 August 2024
Accepted:
5 September 2024
Published:
23 September 2024
Abstract: In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.
Abstract: In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRT...
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Research Article
Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application
Jones Asante Manu*
,
Samuel Darkwah
Issue:
Volume 10, Issue 3, September 2024
Pages:
60-77
Received:
8 July 2024
Accepted:
20 September 2024
Published:
31 October 2024
Abstract: This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.
Abstract: This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. Th...
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