Comparison of probability distribution functions for fitting distillation curves of petroleum

The fitting capability of 25 probability distribution functions for distillation data of petroleum fractions was analyzed in this work. Rankings of all the functions based on two different approaches were established after a statistical analysis of the fit of the functions with a data set of 137 distillation curves. In general; distribution functions with four parameters showed better fitting capability than those with three parameters. Two-parameter functions were not effective in fitting distillation data. The Weibull extreme, Kumaraswamy, and Weibull functions were found to be the best distribution functions for fitting distillation data considering their ranking and the required CPU time. These distribution functions exhibited the lowest Akaike information criterion and Bayesian information criterion average values, standard deviations lower than 1%, correlation coefficients higher than 0.999, and residuals randomly distributed without any tendency. The fitting capability of the best functions was validated with an independent set of distillation data, and the ranking was the same.