Comparing Two-parameter Burr Type (X) and Gamma-Weibull Distributions Using Information Criteria for the Heights of Akwa Ibom State University Students

Overtime, many researchers have introduced different probability distribution functions and fitted them to a given datasets using Information Criteria. Among the distribution introduced are the four-parameter Gamma-Weibull, the beta-Weibull distribution, four-parameter beta-normal distribution provides flexibility in modelling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions, gamma-Lagrange distribution, the Kumaraswamy-Weibull Geometric distribution, beta-Laplace distribution, Kumaraswamy-generalized Exponential Pareto distribution. The AIC and BIC for the Kumaraswamy-generalized Exponential Pareto distribution are smaller than the Pareto and Exponential Pareto distribution. Thus, making Kumaraswamy-generalized Exponential Pareto distribution very competitive for the fitting an uncensored data set corresponding to 100 observations on breaking stress of carbon fibers (in Gba) using the model selection criteria. This paper compares two-parameter Burr type (X), a special case of the Beta-Weibull distribution and four-parameter Gamma-Weibull distribution using log-likelihood function, Bayesian and Akaike’s Information Criteria for fitting 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. It was observed that the log-likelihood function, Akaike information criterion (AIC) and the Bayesian information criterion (BIC) values of the Gamma-Weibull distribution are less than that of the two-parameter Burr type (X). The Gamma-Weibull distribution has a smaller AIC and BIC than that of the two-parameter Burr Type (X) distribution. Hence, the Gamma-Weibull distribution fits the data better than the two-parameter Burr Type (X) distribution. The graphs of the Gamma-Weibull distribution and the two-parameter distributions are also presented.