Validation of the Best Functions

Statistical Parameters for Regression Analysis for Data Set Validation 

FIGURE 12.16 Residual plot for validation data set. (+) Weibull extreme (o) normalized alpha. 

5 versus 4.1). The correlation coefficients and slopes of the parity plots are closer to unity and intercepts closer to zero for the best four functions as compared to the worst function. Additionally, the absolute difference between the number of positive and negative residuals of the Normalized Alpha function is more than twice compared with the other functions, which means that the former is overestimating the experimental values. Inspection of the AlC and BIC values, A and evidence ratios yielded the same order in the ranking from the validation set as from the testing data set. These validation results corroborate that Weibull Extreme, Kumaraswamy, and Weibull are the best distribution functions to fit distillation data. 

Modeling of Processes and Reactors for Upgrading of Heavy Petroleum 

FIGURE 12.17 Comparison of Weibull extreme distribution function (—) and Hermite interpolation method (-) for representing experimental distillation data of products from hydrocracking at different temperatures ( ) 410°C, ( ) 430°C, and (A) 450°C. (Data from El-Kady, F.Y., Indian J. TechnoL, 17, 176, 1979.) 

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