Non-Nested Test Statistic for Comparison of the Two-Parameter Burr Type X and Gamma-Weibull Distributions with Application to Heights of Students of Akwa Ibom State University, Nigeria
Itoro T. Michael *
Department of Statistics, Akwa Ibom State University, Nigeria.
Usoro Anthony
Department of Statistics, Akwa Ibom State University, Nigeria.
Iseh Matthew J
Department of Statistics, Akwa Ibom State University, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper introduces a non-nested test statistic for comparing the gamma-Weibull and the two-parameter burr type (x) distributions using the likelihood ratio test statistic and the non-nested model test statistic. The test statistic obtained is applied to the heights of 617 students collected from the Medical Centre of Akwa Ibom State University. The parameters estimate of the two-parameter Burr Type (X) and gamma-Weibull distributions were obtained using the maximum likelihood method. Some exploratory analyses were carried out using the density plots of the gamma-Weibull and the two-parameter Burr type (x) distributions. The result was compared to the critical values obtained at various levels of significance. It was observed that the four-parameter gamma-Weibull distribution is not equivalent to the two-parameter burr type (x) for heights of students at \(\alpha\) = 0.01% level of significance. R codes are provided for implementation. The four-parameter Gamma-Weibull distribution is better for the heights of 617 students of Akwa Ibom State University than the two-parameter Burr Type (X) distribution.
Keywords: Gamma-Weibull distribution, two-parameter burr type (X) distribution, non-nested model test statistic, likelihood ratio test statistic, maximum likelihood estimation