Comparing Gamma, Weibull and Cauchy Distributions Using Information Criteria and Its Application to Heights of Akwa Ibom State University Students
DOI:
https://doi.org/10.33003/fjs-2026-1009-5514Keywords:
Gamma Distribution, Weibull Distribution, Cauchy Distribution, Bayesian Information Criterion, Akaike’s Information Criterion, Log-Likelihood Function, Heights of StudentsAbstract
In this paper, we compare the gamma, Weibull and Cauchy distributions using the log-likelihood function, Akaike’s and Bayesian information Criteria for the heights of Akwa Ibom State University Students. The heights of 617 students were obtained from the medical centre of the Akwa Ibom State University, Main Campus, Ikot Akpaden. The parameters of the gamma, Weibull and Cauchy are estimated using maximum likelihood method and applied to the dataset. We observed that the gamma distribution had the lowest Akaike’s and Bayesian information criteria of -1347.098 and -1338.248 and the highest log-likelihood values of 675.5489 for the heights of students. The Weibull distribution has AIC of -1297.28 and BIC of -1288.43 and lastly the Cauchy distribution with AIC of -1156.167 and -1147.317, the model with the lowest information criteria is the best. From the result, the gamma distribution is a better fit for the heights of students than the Weibull and Cauchy distributions. The density plots for the gamma, Weibull and Cauchy showed a slight disparity and look like that of a bell-shape curve. The R codes are given for implementation.
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Copyright (c) 2026 Michael T. Itoro, Bassey B. Joseph, Ekong O. Akaninyene
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